https://github.com/cran/cutpointr
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<h1 class="title toc-ignore">An introduction to cutpointr</h1>
<h4 class="author"><em>Christian Thiele</em></h4>
<h4 class="date"><em>2018-04-13</em></h4>
<div id="cutpointr" class="section level1">
<h1>cutpointr</h1>
<p><strong>cutpointr</strong> is an R package for tidy calculation of “optimal” cutpoints. It supports several methods for calculating cutpoints and includes several metrics that can be maximized or minimized by selecting a cutpoint. Some of these methods are designed to be more robust than the simple empirical optimization of a metric. Additionally, <strong>cutpointr</strong> can automatically bootstrap the variability of the optimal cutpoints and return out-of-bag estimates of various performance metrics.</p>
<p>For example, the optimal cutpoint for the included data set is 2 when maximizing the sum of sensitivity and specificity.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(cutpointr)
<span class="kw">data</span>(suicide)
<span class="kw">head</span>(suicide)</code></pre></div>
<pre><code>## age gender dsi suicide
## 1 29 female 1 no
## 2 26 male 0 no
## 3 26 female 0 no
## 4 27 female 0 no
## 5 28 female 0 no
## 6 53 male 2 no</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">cp <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide,
<span class="dt">method =</span> maximize_metric, <span class="dt">metric =</span> sum_sens_spec)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">cp</code></pre></div>
<pre><code>## # A tibble: 1 x 16
## direction optimal_cutpoint method sum_sens_spec acc
## <chr> <dbl> <chr> <dbl> <dbl>
## 1 >= 2. maximize_metric 1.75 0.865
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.889 0.863 0.924 yes no 0.0677 suicide
## predictor data roc_curve boot
## <chr> <list> <list> <lgl>
## 1 dsi <tibble [532 × 2]> <data.frame [13 × 10]> NA</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(cp)</code></pre></div>
<pre><code>## Method: maximize_metric
## Predictor: dsi
## Outcome: suicide
## Direction: >=
##
## optimal_cutpoint sum_sens_spec acc sensitivity specificity AUC
## 2 1.7518 0.8647 0.8889 0.8629 0.9238
## n_pos n_neg
## 36 496
##
## Cutpoint 2:
## observation
## prediction yes no
## yes 32 68
## no 4 428
##
##
## Predictor summary:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD
## 0 0 0 0 0.9211 1 5 11 1.8527
##
## Predictor summary per class:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max SD
## no 0 0.00 0 0 0.6331 0 4.00 10 1.4122
## yes 0 0.75 4 5 4.8889 6 9.25 11 2.5498</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(cp)</code></pre></div>
<p><img 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foCAtWFQPnsdRKye9Yo0Z+a30Z06ele+UHl06vU3v/p1/bsR6qJut0hPWr2NFHfSV/1vpVubiO9Hq5mS4h2Xp/dIa8wKbklCQhUBwIJt550kI6zKWq45yUkZN4U2nkpu/SJEU3GBAk0JLvnHFrOVoqPx7eqpK0Z3R+dnJWVSlcOgUC1K5D0Ifr+y1otJ9rAFqnhmzKFE2xSSF/36QN8RA81KTMKxBaIrcoWdxPVnDqUhH45HqJ9J9+SlOSSAwSq/cN4xnoU8rcghVHN/QfZX0L6rmfS8djPsw4aBeoqSM3ruwj0FfuQStjL5SI3d05KcskBAtX+W5h3XYeeRAfYdDXcpwfVtPwzf/D9d8r962wvjxgEuoov+oYeyPLQZu5jUyEp2SUFCFQXH6L/wkpIaNuf7/eyNnlE552jfKT2tR2oRBexn/goWSAfkwQaLAdONJshdL1TehectVamJinZJQUIVBcCzWe7iSYxfrz1oNR4lr0nP1jFZijRNfLiow9+R91uFxt7DALRVRfuYGuJDrMXpUcFW5OSXHKAQHUh0CL2pVi0jh0lRWpmNr1BvHN26rhevDvSo/U+pW/FKdf4Ja/2Us/e4kvVBKNAC9htXQLi0VyvcxyiRu0mJyW55ACB6kKg/7K3xNt1mU0uGTfi1+zCo1Lss4xm/e4bcUqTBWrnl9llT97ZfATRRHbL/OG/62IQ6EgT5TuAz5p3m3ZX584Hk5JccoBAdSHQT+xc6e7IA//Xst2lLyvfINK+sb9q0fX6LXrvd/q06TatmqjqzuxTh5ecaxCI+rEd8v2WQe07D91LKQQEws85bJGYQF6fiLJHfJwan2/Y5XLLT36fFjU0Ba3pMzQpoDUDhs4xEoBAqQJegSCQLSAQBLIFBIJAtoBAEMgWEAgC2QICQSBbQCAIZAsIVIsCaU++uqbEnBPuCAscVBphiTdCvILK4hxRRhURlkQaUaoWXoQ/RwgEgayPgEAQyAAEgkAGIBAEMgCBFCCQkicEMqkMBJIIjK1UGt/cM+Ylr3anl0nOEwIF0xAE4sbUskCfTLlBEah6RHFgZr56ZyiTnCcECgYCqXy/LU8RaMMMooIH1DtDmeQ8IVAwEEhnqCLQB/OIDo1W74iW5OTk7E6ouClMYM1htam+TUOgZAo0Sr0jKsrPz/9FvdqQ8TpGQTh9ERZ4KMIChz9C3EXVcY6oVi+zZHnEMbZIbVZCoOQKtOEJom/vV+8MZZLzbCRvYQfZfK3NnyMESopABz3OW48Iz+UTvzOUSc4TAgUDgXRkgQbvou0T750rfjDgd3qZ5DwhUDAQyHqZ5DwhkEllIJClMsl5QiCTykAgS2WS84RAJpWBQJbKJOcJgUwqA4EslUnOEwKZVAYCWSqTnCcEMqkMBLJUJjnPeAX6fddfnxWBsyPEu/66a62POIst0FLkzzHVBfowT2SwPNXE1Jvy8l7h4UYu0HE2cOrECEyJEJ88dVKcIyZNnRzniImPFGk58ueY6gJJbJUv7EYjq/VQoxfohZR8C2uYf413TZMnrnCNMMQgUBgQKJJAizbKdz+NnHXHM8fERkFubu7KgEwNBTSEQGBWa6VJNeINN6aGL+YP9c4qpLdrDE1b5hjLJJcBAplUpo4EOjRJuTru/iUVVW9IV+feN3PmzG1uGT+5NWrc7pmtlSb5xRtujI8v5g/1ziqCX2t69abPnjqGMsllgEAmlakjgZZ/rNx7/UQVQ/illvEWFgYEMhdIGF8m3R30rLnf6f3XozwKgcKAQOYC7R0v3w3eVfPayFFPq2k3IoH2Hw8PQyAVfJGo5BlRoHU9WPtpYWEIpAKBlDwjCbTvTGnylHmhYQikAoGUPCMJ9I48+07HK0KBQBwIpOQZSaB3ZYFOzw1l8JZGIJCwdPToGWWRz9mFQLGILVDxWZJAr4QvSM2/xscnUMGYSv8LCyOfswuBYqF9LekX3OZ4tl3E2j1rssBHJsHQ70CD8JInzhEe8sY5wk3q97JuB3+OUQQ6tJvcry0LO2e36tChQ6VlIsoeKVMo95aVDekjNyvIUabiqtSanoDWLPNprXJyau3qKq0Za9r2hiGQ9uTdQpk55d5jbI7ZgmoqjzDEFyHu0DdncUSlYUdZG1FO1WrzRGyBiDbkjXVGPmdX2SOG7sP7JqPqlmgYAln5HugX9rzZgsbwFibiXjQz7Jzd4jVr1hypElH2SBXHV1V186Vyy0kuNVjlcWpNX0BrVvm1lsPYuVpreqOmBYFMSD2BVn9BtO/2yOfs4jNQLNJcoA33uIU3ZlPEc3YhUCzSXCBh8e13zKqgiOfsQqBYpLlAsSoDgSyVSc4TAplUBgJZKpOcJwQyqQwEslQmOU8IZFIZCGSpTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok52ku0GXyr4FeNFsEgRQgkJKnuUBnXTFn3gsv/mi2CAIpQCAlzwgC3d3ALu8CgSCQAQgEgQxAoLQSaPVjIqdAIAgUs0xynmECXSUdfzWbDYEgUKwyyXmGCTTwD8rTh0DqqtNUIO1kJ/VafMYL8UGgSEAgTtDJTvK1+IwX4oNAkYBAnKAJCqVr8QVdiA8CRQICcbSTnSSka/FpF+LLz83N/UG7/J7hUnwK11wXelG9YGrCRhgu5ZekEcqlABMcoZ65B4HsCzRKacvX4tMuxPfN3LlzD7g4fsEVwtXXynduf+gCjpciLHAFIsQ95I5zhJs8cY5wkVdtqQWCQPbewgwnO8nX4gu6EB/ewiIBgTjqyU4HPfxafEEX4oNAECgW/GSnwbv4tfiCLsQHgSIBgayXSc4TAplUBgJZKpOcJwQyqQwEslQmOU8IZFIZCGSpTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPK1KdA/EJ9DXeyFQhUvwLxCyu6DNce9JWVPZGhNAVXmXoJx+HqRf34w/CLANa4tabDpTWdCdXFrExyGSCQSWXwFmapTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok5wmBTCqTbgIJiZVJzhMCmVQm3QQ6b9aBRMok5wmBTCqTbgI9eW6TAYsr4y6TnCcECsYjoewRD6fG4xl2mdzykk8NegJevSloTakzx9jZbxgXI4F6+QwkfPNgl1a3fOK3XCYIFLUy6fYKJHF8NGOdHvfEUyY5TwhkUpm0E+jIgkHNuk7ZuPg3N8VTJjlPCGRSmXQTqF+TrlO2SYdiK7PiKZOcJwQyqUy6CfTQNvVsnZ0Wy1Tt5PgEZwhXXyvfVftDF3A8FGGBMxAh7iZXnCNc5I5zhJM8agvnhcUt0CD5k/2RG62XqaqC4xEqQrjqj/JdpTd0AcdFlRGW+CPEnfrmLI6oImecIyrJpTbL+XOEQBYFmjWL/XWWyJiOcZZJzhNvYSaVSS+BrriC9ZdmdB+4NM4yyXlCIJPKpJdARDnWvwAylknOEwKZVCatBFqwidZy4iyTnCcEMqlMWgnEHqSWnDjLJOcJgUwqk1YCFZ+gWDNJRyiTnCcEMqlMWgkk0uG+r+P8RQcEilqZdBNoXv8m3eP7RQcEilqZdBOI6PDc3zcbtCTOMsl5QiCTyqSfQES+Je3jqBgEilqZtBPImT8yK2PoijjLJOcJgUwqk24CDW7V8qZ34jpjFQJFrUy6CZT7ZrynaoQIdOz8LI2TrlGePgRSV93IBUrGN9EH2aCJGh8pTx8Cqatu5AIl45vog+HTo0KgdBGo+ESiZZLzhEAmlUkrgSiRH5RBoKiVSS+BkvCDMggUXJn0EigJPyiDQMGVSS+BkvCDMggUXJm0EijSYbw2Y6E6VaEegEAQSCfCYbxhxkJlqsKgKQwhEARSiXAYr89YyKcqDJrCEAJFIv0Ektj4I3184+NBP0zUZyzkUxVqgf+MHDnyRz+nhqTbKvaKP5SasIhxhBlChHiAArU+wk9avuoegkCWBXqevV/dfvCZD4YJJM9YyKcq1ALrpk6dWhx8ZZJyttATgjcQGlGvVEIRFhiubBKMj7wRlkQaYbwyirURHvKrLfWvyhDIskBnzBZe7yG89ytjTJ+xkE9VaJzCEG9hEMhIy6004n76uoUxps9YyKcqVAMQKFUE4kfHFHyAXB8C9XxwX5tt9NzZQUFtxkJ1qkIegECpIpBydEwhB8j1IdAHzVk/+it7Ic4yyXlCIJPK1IlA/OiYDAfI/srKyhOlMtVCqYa3tHRGhtIUqsUbboyTL+YP9c4qNS6tWVmtNR0mz7p4jZPWfRFvmeQyQKD6EogfHZPhiHlzTk7OB6ZpzW5teMCNifAwEVx7ZawPgEBRK1MnAvGjYzIcMR/Lz8/f45DxCg4Nv8PxdGulKXjFG26Mhy9W39G0zipyZwWXR2u6w5/0ey2ZDASSCRcojt+71J1A/OiYjEfMVD+fgc4etsdYOQgULFBcv3epO4H40bF4nBx0gFwfAmV9b12dNBTI5Pcuq8fd9uhh7fA57M/MdSKQenQ8eFfQAXJ9CHTTezYEOn7f6NEjGrVA4b93OZR31L90inr4HP5n5nT7InFTryc/SfisjCJ2Zq9eOV+E7JDGJVDoUca3C4kO3KoePof/mTndBLJ1VkYRW1RiQqMSyOQowzt7oXr4rB1FlxYWFpaUiyh7pFyhwltePqSP3KwkR7mKu0pregNas9yntSrIqbVd+rhY14Kvr3Pj4yPNBAo/ytg09tWAevisHUUvycnJ2S0tDftiZXjfZFTdEvUiUNlHc8p2x3OZqTQTKPQoQ5j/kHQ1HH74rB1Fp+0rUGGnTk2LR5/zEwSSCRco9Cjjm/vkL4b44XP4n5nT7TPQNTd5M4vLrk3svLB0ECj0KOON3Ly8vJHa35fD/sycbgK12UyZxfSF1Yky0k+gOI4y0lKgM9ZKAq3qYk0erUxynmkhUBykpUD39D2eWVx4/p1xlknOMy0EClkSszLpJpDzxmYsk11dYdEeSjuBGLP81+a0FEg8Dnvv7W/judJvmgkkfQv93Wu9rEyGlaYCEVX5LFQnuExynmkhkMJ/B1itTHoJtPWubeQZyjKmxHGGfFoKVNDWamXSSqD1zQfsopmtXnkl81Ur6vAsqzhe4We2uMoEh88sKuKmCAuq/BHiLnLGOcJJ1XGOcJBbbaofBQ0C7ZRYf00PCGQi0FV3ih9+uo8nmtUbAkmYCKR8hO60GgKZCJS9jugXtp3o0/bWBUqztzD+E2HLlUkrgdp8TfRmVkD8jNjOsj/pJhDVrF3w8uc1liuTVgJdOJvo6sFiY/pF1uTRyiTnmRYCHb2w6dndml10zGpl0kqgxS2mjmNvk/OdNvMhkEy4QMMu20+0v/cI01qku0DCS92zHxRoCJsQxzdBaSZQp3XS7drOViuTVgJxCuM4qSftBMpWBOpktTLpKFB8pJlAwy49QHSgzy1WKwOBLJVJzjMtBDqa06xbt2Y5+BAtAYHMiHUYv27hwrU4jJeBQGZEF8j98G1EAyZWm9bCpDIQyFKZ5DzTQqB7sl8hWnbmRKuVgUCWyiTnmRYCZS+Tbt89zWplIJClMsl5poVA7TdJtxtPsVoZCGSpTHKeaSFQ3jUnxOf8x9S6PlAEIFAY9S/QL7/NyOnd9pwDVisDgSyVSc4zLQSiwEeznnrf0rnfEMgS6SZQnJVpGAKp4kCgMCAQBDIAgSCQAQik0OgF0q8cya8oqU/NAIEiA4E4+pUj+RUl9akZCAJFBgJx9CtH8itKuow/6IRAkYBAHH3GQlKuKKlNzRAy4dwv7A3TOd8w4RwEUmYs5FeU1KZmCJny8ihbZjqHJKa8TG+B9PkX+BUl9akZCG9hKSyQxycTIJ+G4PM901ppUkC8CRZIfah31sbVaE1/QGsGrBVCn7GQX1FSnZoBAqW2QKnyCqTPWMivKKlOzQCBIJB9IFDUykAgS2WS84RAJpWBQJbKJOcJgUwqA4EslUnOEwIF4/VphznqYYt4LDPscuVYhvzawUyNoWk88tGbZDjyMXSOkQAECqNBCYRXIOtlkvOEQCaVgUCWyiQ/s+fHQqCwykAgS2WS+Im17rTabI9AIAgUq0wS+9jrZvsDAkGg2GWSgEBmlYFAlsokAYHMKgOBLJVJAgKZVQYCWSqTBAQyqwwEslQmCQhkVhkIZKlMEhDIrDIQyFKZJCCQWWUgkKUySUAgs8pAIEtlkoBAZpWBQJbKJAGBzCoDgSyVSQICmVUGAsWiqoLzM1taYUql1zxe4aLKCEv8EeJOfXMWR1SRM84RleRSm+X8OUKgWhSo2snZz95ymlLtN487PRRhgTMQIe4mV5wjXOSOc4STPGpLLRAEwluY9RF4C4NABiAQBDIAgSCQAQikUJcCDR/+u2ZKQlEE4kCgEghUAoGMQCAIZAACKUAgGQhkVhkIZKlMEhDIrDIQyFKZJCCQWWUgkKUySUAgs8pAIEtlkoBAZpWBQJbKJAGBzCoDgSyVSQICmVUGAlkqkwQEMqsMBLJUJgkIZFYZCGSpTBIQyKwyEMhSmSQgkFll6kYgPg0XBc/E1cAEep69ab5HIFBtC6ROw0XBM3E1MIGmZf1ivkcgUG0LxKfhEgmaiStlBNJnLOQtPWAUqGOEPQKB6uAzkDQNl4g2E5ezsLDwcLmMWyjX8HGBxKbgFm+CjQl56NPH1Xi0psOlNavNn3go+oyFvKUHIBBRYGwlRf6vVUcCydNwiWgzcW3Oycn5wCRbLpD+0EjowyShz1jIW3qAINAnU26ojPJfq04E4tNwkWEmrlR6BdJnLOQtLfDN3LlzD7g4j3V0meP2R1jgpQgLXIEIcQ+54xzhJk+cI1zkVVtWzgv7flteZZT/WnUiEJ+Giw56gmbiSpXPQPqMhbylBfJzc3N/CHAOfRswp0aItIAiLAgkb0SAahIf4bYgENHQyvD/WsVr1qw5UiWi7Ioqjq+q6uZL5ZaTXGqwyuPUmr6A1qzyay2HsXO11lTfK4lPw0WDdwXNxJUqAukzFvKWHqCgK9WXmNO438IMAhn+ay0RP4LslhaGfZoY3tda1ZNAqgikz1jIW2pABgJJAg8gRncAAApTSURBVIX+1/JWVlaWlYoou6JU4YSntDSvj9wsp8pSFVeF1vT4tWapV2uVUZXWrjaMayAC6TMWqi1+B4E0gSL+16qTz0CpLlBUIJAkUMT/WhAoFhAoamUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok5wmBTCoDgSyVSc4TAplUBgJZJv/ueEesG+mN3SmInSN/iXPE4ZHfxznCO3J9aAgC1YVAiwbFO+LDHE+cI7bk/BzniOKcrXGOcOf8OzQEgSCQdSBQPQm0fGS8I9bkxvsWVpB7KM4RB3O/jXOEJ3dNaAgC1YVAjRgIBIFsAYEgkC0askAhTqScQFF/cB9jBD+byXgqU4wRvGvMbeg9PswTGXwi9kb4b5tNnwgEqjWBov/gPvoI9WymkTF+WmtYpdI15jZCemx9MfZG+G+bzZ8IBKo1gaL/4D76CH42U9CpTNFH8K4xtxHcwzXNHXsj/LfNZPpEIFCtCRT5B/exR5ByNpN2KlPsEbxrzG0E91i0kWJvhPjvekyfCASqXYFMf3AfewQ/m0k7lSn2CN415jaCehyaJFDsjVCwQMFPBALV3ltY1B/cRx/Bz2bSTmWKPYJ3jbmNoCyWf2xlI6QJZPJEIFCtCRT9B/fRR/CzmYJOZYo+gneNuQ3DEBLGl1nZCHGBTJ8IBKq9w/ioP7iPPoKfzRR0KlP0EWrXmNswpLV3vPQ49ka4QKZPBALhi0RbQCAIZAsIBIFsAYEgkC0gEASyBQSCQLaAQBDIFhAo9QXydzgSGhKW5LTt9IcNEYcUswW0/ow+5ew5Q6BWgEApL5D7YRYm0NyTnt32xZiTtkUac+LBTTT0uiOuB9caAlfMqoXsIFCqC/RSCxYuUI+p4o1w5V3RBl43PSQAgXTSSKBjO98OF6jjOOl21zYq6PDlpe2u+B+Rc8KZba/dTXRkaIfO97qp5dpBjPWhDv/RAzmMDXqonzjsqfOi/+U0LiBQqgtE9HW4QA+wP7wln4ha0OLstzdcn1VON17++aYbO5cFfvuHjUuzHxF9CVz7iF8USA/4+/81sK3JERK6J/OVCAI1SIFqludmsR6zvFTA3iRydXppd7PjRN7sjz7KOEH0ym2iL/JbWIf/GALiW5hw1gLa0eRAEpODQA1IoA8zMzN3qdHA1+NaDhUFkl6Ibhy3gonLMpvOmZWjLNUEMgSkz0BTBtGUAclMDgI1IIGcxcXF8q8oCoc4pbtFrKqAHRUbeXe8nVUsUfZUb6WrJpAhIAm0tdnxLouTmRwEakACaZSwd6W7VzJ8BSxfPNA/9flvWaG4W0YXrmhbQbRsgC6QISAJJJw1ulVlMpODQA1RILq3zaOfrJmd+aD4Fnbm+1/mZpYKV/VcvfZP3Tzec/60acWZ9+kCGQIDx4jrmcJuSWpyEKhBCuT7x+9OzspZ6BcF+rhX234F4i4Zc1pm7j6i/blZp06o1gUyBJZ2HEy0kX2S1OQgUOoLFI0C5o7dycjizv6kJtBABfL4RIKdELhA4gIKhC0N7ezTEGq0pj+gNQMJ1aXuiVOg8lW/eTy5CdgXiO8SvALVC3EKtDPrxjhfsWKRmEAeCS4O3yU1Hs+wy+S4l3welYBXbwpa01OjtYyd/YZxMRKAQKkCXoEgkC0gEASyBQSCQLaAQBDIFhAIAtkCAkEgW0AgCGSLxieQuTHhnaMshUDWgUAQyBYQCALZAgJBIFtAIAhkCwgEgWwBgSCQLSAQBLIFBIJAtoBAEMgWEAgC2QICQSBb1JpAShQCNXYgEASyBQSCQLaAQBDIFhAIAtkCAkEgW0AgCGQLCASBbAGBIJAtIBAEsgUEgkC2gEAQyBYQCALZAgJBIFskT6Dhw8/K1h9CoDShtgXSdwkEapRAIAhkCwgEgWwBgSCQLSAQBLKFdYG+uWfMS17ejl8gbc/EK5C+WWMCEChVsCxQ9YjiwMx8/qDuBNI3G5QABEoVLAu0YQZRwQP8Qd0JpG82KAEIlCpYFuiDeUSHRouNovz8/F8cIkqx+d1wvyKQ+tARvKPUzhy/2nA4ya2tarhLC/vCNqu3jokJ7NETUPEHCxSyNLxzlKXiupM8o0TjJT6BRomNJTk5ObtNuwzvm6ysTDartzaLCXxg2nl26+QnAKJj/S3sCaJv7+cP+B8oPD7tPae2pnvSNxuUgIOvXgha5+MZSlMwXG3VoTUdZJYArtJqD8sCOW89IjwX9CG6TgRSN3vQE5QABEoVrB/Gb59479ygw/g6EUjd7OBdQQlAoFTBxheJdSOQORAoVYBAEMgWEAgC2QICQSBbQCAIZAsIBIFsAYEgkC0gEASyBQSCQLaAQBDIFhAIAtkCAkEgW9gS6McfdIHE3TB5hNw8svOwvtPKtOa+PfpO0/fZsZ0H9Z2m21b8Y/QEuBY/7wpa5zzF4JJd+3UndJkP7DRLoKSwWGuW6zIf2lmTUGXSjsQE4jw0ziy6P2eTWfipEWbRspxPzcJ/v8FSAv+8wjTcb7FZ9N0cwSz8p7lm0U9yKi1lkPZAIAhkCwgEgWxhS6C1q8yilUsOm4U3fmQWdS8pNgtve99SAt+9ZRp+639m0d1LTDu/t90sum+J1ywMQrElEAAQCNjCjkDGc401hKWjR88oC++8/6HR00rDov+64/a/h56CFRgrffxYPe62R03fClMpAWBHoKBzjTUKxlT6X1gY1jlwR0HNa8+HRr+ZcNw9f2lw7JMpN4j771DeUf/SKSmeALAlUNC5xhqHdpP7tWVhnbdPJfKFvS4s/yfRD/cEx77flifuv29FBQ7cmuIJAFsC6WcdB7Mhb6wzLPjxk0+NefKX0OiWew5UvDwsNDpUOYL2zg5/HUmtBIB9gUaZLHAvmhkWWzGy0P3uQ6FRYcVd9755e2hU2X+bxr4aSPEEgL23MOO5xhqrvyDaF7ZL6PNZRJVDQr/Jc4t7atu00L7S/hPmP3Qg5RMAtgQKOtdYY8M9buGN2WGdy27f588P21M/jSj1PPxFaFTaf9/cF/t/f70nAOwdxhvPNdYQFt9+x6yK8M6bxo+ccSws+q9Rd70T9gcGaf+9kZuXlzcy1RMA+CIR2AMCAVtAIGALCARsAYGALSAQsAUEAraAQMAWDUQgtrm+MwDmQCBgCwgEbJGiAuUOFm/mdfDuvrpd2347JIEcbCfRXlZCzglntr3W/FL5oO5JUYHebOUk6j+BLuq/5rPfXxwk0I2Xf77pxs4mP3oG9UGKClTVMp8ON9lW8+wPRMs6GAXa3ew4kTfb9CQzUPekqEB000ia210g/8Z/3N4pSKAVLFOk6Zz6ThAopKpA72T5+j1D1f16TP/vP3WBvmMlb2cVS+AtLEVIVYEcGUua7aePMzxE/+ACrSd6jZV8ywqJykcX1neCQCFVBaKh7QcSrWXPb5yZ3WK7KJCQfU3Byt+xEuGqnqvX/qmbp77zAwopK9AKtoRImN6x/ZAf+w6Qvgf6tHvbK3eKR2HlY07LzN1X3+kBTsoKBBoGEAjYAgIBW0AgYAsIBGwBgYAtIBCwxf8DpDa8QWZG4mIAAAAASUVORK5CYII=" style="display: block; margin: auto;" /></p>
<p>When considering the optimality of a cutpoint, we can only make a judgement based on the sample at hand. Thus, the estimated cutpoint may not be optimal within the population or on unseen data, which is why we sometimes put the “optimal” in quotation marks.</p>
<div id="features" class="section level2">
<h2>Features</h2>
<ul>
<li>Calculation of optimal cutpoints in binary classification tasks</li>
<li>Tidy output, integrates well with functions from the tidyverse</li>
<li>Functions for plotting ROC-curves, metric distributions and more</li>
<li>Bootstrapping for simulating the cutpoint variability and for obtaining out-of-bag estimates of various metrics (as a form of internal validation)</li>
<li>Multiple methods for calculating cutpoints</li>
<li>Multiple metrics can be chosen for maximization / minimization</li>
<li>Standard/Nonstandard evaluation (<code>cutpointr_</code> and <code>cutpointr</code>)</li>
</ul>
</div>
</div>
<div id="calculating-cutpoints" class="section level1">
<h1>Calculating cutpoints</h1>
<div id="method-functions-for-cutpoint-estimation" class="section level2">
<h2>Method functions for cutpoint estimation</h2>
<p>The included methods for calculating cutpoints are:</p>
<ul>
<li><code>maximize_metric</code>: Maximize the metric function</li>
<li><code>minimize_metric</code>: Minimize the metric function</li>
<li><code>maximize_loess_metric</code>: Maximize the metric function after LOESS smoothing</li>
<li><code>minimize_loess_metric</code>: Minimize the metric function after LOESS smoothing</li>
<li><code>maximize_spline_metric</code>: Maximize the metric function after spline smoothing</li>
<li><code>minimize_spline_metric</code>: Minimize the metric function after spline smoothing</li>
<li><code>maximize_gam_metric</code>: Maximize the metric function after smoothing via Generalized Additive Models</li>
<li><code>minimize_gam_metric</code>: Minimize the metric function after smoothing via Generalized Additive Models</li>
<li><code>maximize_boot_metric</code>: Bootstrap the optimal cutpoint when maximizing a metric</li>
<li><code>minimize_boot_metric</code>: Bootstrap the optimal cutpoint when minimizing a metric</li>
<li><code>oc_manual</code>: Specify the cutoff value manually</li>
<li><code>oc_mean</code>: Use the sample mean as the “optimal” cutpoint</li>
<li><code>oc_median</code>: Use the sample median as the “optimal” cutpoint</li>
<li><code>oc_youden_kernel</code>: Maximize the Youden-Index after kernel smoothing the distributions of the two classes</li>
<li><code>oc_youden_normal</code>: Maximize the Youden-Index parametrically assuming normally distributed data in both classes</li>
</ul>
</div>
<div id="metric-functions" class="section level2">
<h2>Metric functions</h2>
<p>The included metrics to be used with the minimization and maximization methods are:</p>
<ul>
<li><code>accuracy</code>: Fraction correctly classified</li>
<li><code>abs_d_sens_spec</code>: The absolute difference of sensitivity and specificity</li>
<li><code>abs_d_ppv_npv</code>: The absolute difference between positive predictive value (PPV) and negative predictive value (NPV)</li>
<li><code>cohens_kappa</code>: Cohen’s Kappa</li>
<li><code>sum_sens_spec</code>: sensitivity + specificity</li>
<li><code>sum_ppv_npv</code>: The sum of positive predictive value (PPV) and negative predictive value (NPV)</li>
<li><code>prod_sens_spec</code>: sensitivity * specificity</li>
<li><code>prod_ppv_npv</code>: The product of positive predictive value (PPV) and negative predictive value (NPV)</li>
<li><code>youden</code>: Youden- or J-Index = sensitivity + specificity - 1</li>
<li><code>odds_ratio</code>: (Diagnostic) odds ratio</li>
<li><code>risk_ratio</code>: risk ratio (relative risk)</li>
<li><code>p_chisquared</code>: The p-value of a chi-squared test on the confusion matrix</li>
<li><code>cost_misclassification</code>: The sum of the misclassification cost of false positives and false negatives. Additional arguments: cost_fp, cost_fn</li>
<li><code>total_utility</code>: The total utility of true / false positives / negatives. Additional arguments: utility_tp, utility_tn, cost_fp, cost_fn</li>
<li><code>F1_score</code>: The F1-score (2 * TP) / (2 * TP + FP + FN)</li>
</ul>
<p>Furthermore, the following functions are included which can be used as metric functions but are more useful for plotting purposes, for example in plot_cutpointr, or for defining new metric functions: <code>tp</code>, <code>fp</code>, <code>tn</code>, <code>fn</code>, <code>tpr</code>, <code>fpr</code>, <code>tnr</code>, <code>fnr</code>, <code>false_omission_rate</code>, <code>false_discovery_rate</code>, <code>ppv</code>, <code>npv</code>, <code>precision</code>, <code>recall</code>, <code>sensitivity</code>, and <code>specificity</code>.</p>
<p><code>cutpointr</code> makes use of nonstandard evaluation for higher usability and to allow for easy transformation of the variables. The inputs to the arguments <code>method</code> and <code>metric</code> are functions so that user-defined functions can easily be supplied instead of the built-in ones.</p>
</div>
</div>
<div id="applications" class="section level1">
<h1>Applications</h1>
<p>To showcase the functionality, we’ll use the included <code>suicide</code> data set.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(cutpointr)
<span class="kw">data</span>(suicide)
<span class="kw">head</span>(suicide)</code></pre></div>
<pre><code>## age gender dsi suicide
## 1 29 female 1 no
## 2 26 male 0 no
## 3 26 female 0 no
## 4 27 female 0 no
## 5 28 female 0 no
## 6 53 male 2 no</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut</code></pre></div>
<pre><code>## # A tibble: 1 x 16
## direction optimal_cutpoint method sum_sens_spec acc
## <chr> <dbl> <chr> <dbl> <dbl>
## 1 >= 2. maximize_metric 1.75 0.865
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.889 0.863 0.924 yes no 0.0677 suicide
## predictor data roc_curve boot
## <chr> <list> <list> <lgl>
## 1 dsi <tibble [532 × 2]> <data.frame [13 × 10]> NA</code></pre>
<p>Alternatively, instead of supplying a data frame the raw vectors of the predictor and outcome can be given as <code>x</code> and <code>class</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">cutpointr</span>(<span class="dt">x =</span> suicide<span class="op">$</span>dsi, <span class="dt">class =</span> suicide<span class="op">$</span>suicide)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## # A tibble: 1 x 16
## direction optimal_cutpoint method sum_sens_spec acc
## <chr> <dbl> <chr> <dbl> <dbl>
## 1 >= 2. maximize_metric 1.75 0.865
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.889 0.863 0.924 yes no 0.0677 class
## predictor data roc_curve boot
## <chr> <list> <list> <lgl>
## 1 x <tibble [532 × 2]> <data.frame [13 × 10]> NA</code></pre>
<p><code>cutpointr</code> makes assumptions about the direction of the dependency between <code>class</code> and <code>x</code>, if <code>direction</code> and / or <code>pos_class</code> or <code>neg_class</code> are not specified. The same result as above can be achieved by manually defining <code>direction</code> and the positive / negative classes which is slightly faster, since the classes and direction don’t have to be determined:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">direction =</span> <span class="st">">="</span>, <span class="dt">pos_class =</span> <span class="st">"yes"</span>,
<span class="dt">neg_class =</span> <span class="st">"no"</span>, <span class="dt">method =</span> maximize_metric, <span class="dt">metric =</span> youden)
opt_cut</code></pre></div>
<pre><code>## # A tibble: 1 x 16
## direction optimal_cutpoint method youden_index acc
## <chr> <dbl> <chr> <dbl> <dbl>
## 1 >= 2. maximize_metric 0.752 0.865
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <chr> <chr> <dbl> <chr>
## 1 0.889 0.863 0.924 yes no 0.0677 suicide
## predictor data roc_curve boot
## <chr> <list> <list> <lgl>
## 1 dsi <tibble [532 × 2]> <data.frame [13 × 10]> NA</code></pre>
<p><code>opt_cut</code> is a tidy data frame that returns the input data in a nested tibble. Methods for summarizing and plotting the data and results are included:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(opt_cut)</code></pre></div>
<pre><code>## Method: maximize_metric
## Predictor: dsi
## Outcome: suicide
## Direction: >=
##
## optimal_cutpoint youden_index acc sensitivity specificity AUC n_pos
## 2 0.7518 0.8647 0.8889 0.8629 0.9238 36
## n_neg
## 496
##
## Cutpoint 2:
## observation
## prediction yes no
## yes 32 68
## no 4 428
##
##
## Predictor summary:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD
## 0 0 0 0 0.9211 1 5 11 1.8527
##
## Predictor summary per class:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max SD
## no 0 0.00 0 0 0.6331 0 4.00 10 1.4122
## yes 0 0.75 4 5 4.8889 6 9.25 11 2.5498</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(opt_cut)</code></pre></div>
<p><img 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foCAtWFQPnsdRKye9Yo0Z+a30Z06ele+UHl06vU3v/p1/bsR6qJut0hPWr2NFHfSV/1vpVubiO9Hq5mS4h2Xp/dIa8wKbklCQhUBwIJt550kI6zKWq45yUkZN4U2nkpu/SJEU3GBAk0JLvnHFrOVoqPx7eqpK0Z3R+dnJWVSlcOgUC1K5D0Ifr+y1otJ9rAFqnhmzKFE2xSSF/36QN8RA81KTMKxBaIrcoWdxPVnDqUhH45HqJ9J9+SlOSSAwSq/cN4xnoU8rcghVHN/QfZX0L6rmfS8djPsw4aBeoqSM3ruwj0FfuQStjL5SI3d05KcskBAtX+W5h3XYeeRAfYdDXcpwfVtPwzf/D9d8r962wvjxgEuoov+oYeyPLQZu5jUyEp2SUFCFQXH6L/wkpIaNuf7/eyNnlE552jfKT2tR2oRBexn/goWSAfkwQaLAdONJshdL1TehectVamJinZJQUIVBcCzWe7iSYxfrz1oNR4lr0nP1jFZijRNfLiow9+R91uFxt7DALRVRfuYGuJDrMXpUcFW5OSXHKAQHUh0CL2pVi0jh0lRWpmNr1BvHN26rhevDvSo/U+pW/FKdf4Ja/2Us/e4kvVBKNAC9htXQLi0VyvcxyiRu0mJyW55ACB6kKg/7K3xNt1mU0uGTfi1+zCo1Lss4xm/e4bcUqTBWrnl9llT97ZfATRRHbL/OG/62IQ6EgT5TuAz5p3m3ZX584Hk5JccoBAdSHQT+xc6e7IA//Xst2lLyvfINK+sb9q0fX6LXrvd/q06TatmqjqzuxTh5ecaxCI+rEd8v2WQe07D91LKQQEws85bJGYQF6fiLJHfJwan2/Y5XLLT36fFjU0Ba3pMzQpoDUDhs4xEoBAqQJegSCQLSAQBLIFBIJAtoBAEMgWEAgC2QICQSBbQCAIZAsIVIsCaU++uqbEnBPuCAscVBphiTdCvILK4hxRRhURlkQaUaoWXoQ/RwgEgayPgEAQyAAEgkAGIBAEMgCBFCCQkicEMqkMBJIIjK1UGt/cM+Ylr3anl0nOEwIF0xAE4sbUskCfTLlBEah6RHFgZr56ZyiTnCcECgYCqXy/LU8RaMMMooIH1DtDmeQ8IVAwEEhnqCLQB/OIDo1W74iW5OTk7E6ouClMYM1htam+TUOgZAo0Sr0jKsrPz/9FvdqQ8TpGQTh9ERZ4KMIChz9C3EXVcY6oVi+zZHnEMbZIbVZCoOQKtOEJom/vV+8MZZLzbCRvYQfZfK3NnyMESopABz3OW48Iz+UTvzOUSc4TAgUDgXRkgQbvou0T750rfjDgd3qZ5DwhUDAQyHqZ5DwhkEllIJClMsl5QiCTykAgS2WS84RAJpWBQJbKJOcJgUwqA4EslUnOEwKZVAYCWSqTnCcEMqkMBLJUJjnPeAX6fddfnxWBsyPEu/66a62POIst0FLkzzHVBfowT2SwPNXE1Jvy8l7h4UYu0HE2cOrECEyJEJ88dVKcIyZNnRzniImPFGk58ueY6gJJbJUv7EYjq/VQoxfohZR8C2uYf413TZMnrnCNMMQgUBgQKJJAizbKdz+NnHXHM8fERkFubu7KgEwNBTSEQGBWa6VJNeINN6aGL+YP9c4qpLdrDE1b5hjLJJcBAplUpo4EOjRJuTru/iUVVW9IV+feN3PmzG1uGT+5NWrc7pmtlSb5xRtujI8v5g/1ziqCX2t69abPnjqGMsllgEAmlakjgZZ/rNx7/UQVQ/illvEWFgYEMhdIGF8m3R30rLnf6f3XozwKgcKAQOYC7R0v3w3eVfPayFFPq2k3IoH2Hw8PQyAVfJGo5BlRoHU9WPtpYWEIpAKBlDwjCbTvTGnylHmhYQikAoGUPCMJ9I48+07HK0KBQBwIpOQZSaB3ZYFOzw1l8JZGIJCwdPToGWWRz9mFQLGILVDxWZJAr4QvSM2/xscnUMGYSv8LCyOfswuBYqF9LekX3OZ4tl3E2j1rssBHJsHQ70CD8JInzhEe8sY5wk3q97JuB3+OUQQ6tJvcry0LO2e36tChQ6VlIsoeKVMo95aVDekjNyvIUabiqtSanoDWLPNprXJyau3qKq0Za9r2hiGQ9uTdQpk55d5jbI7ZgmoqjzDEFyHu0DdncUSlYUdZG1FO1WrzRGyBiDbkjXVGPmdX2SOG7sP7JqPqlmgYAln5HugX9rzZgsbwFibiXjQz7Jzd4jVr1hypElH2SBXHV1V186Vyy0kuNVjlcWpNX0BrVvm1lsPYuVpreqOmBYFMSD2BVn9BtO/2yOfs4jNQLNJcoA33uIU3ZlPEc3YhUCzSXCBh8e13zKqgiOfsQqBYpLlAsSoDgSyVSc4TAplUBgJZKpOcJwQyqQwEslQmOU8IZFIZCGSpTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok52ku0GXyr4FeNFsEgRQgkJKnuUBnXTFn3gsv/mi2CAIpQCAlzwgC3d3ALu8CgSCQAQgEgQxAoLQSaPVjIqdAIAgUs0xynmECXSUdfzWbDYEgUKwyyXmGCTTwD8rTh0DqqtNUIO1kJ/VafMYL8UGgSEAgTtDJTvK1+IwX4oNAkYBAnKAJCqVr8QVdiA8CRQICcbSTnSSka/FpF+LLz83N/UG7/J7hUnwK11wXelG9YGrCRhgu5ZekEcqlABMcoZ65B4HsCzRKacvX4tMuxPfN3LlzD7g4fsEVwtXXynduf+gCjpciLHAFIsQ95I5zhJs8cY5wkVdtqQWCQPbewgwnO8nX4gu6EB/ewiIBgTjqyU4HPfxafEEX4oNAECgW/GSnwbv4tfiCLsQHgSIBgayXSc4TAplUBgJZKpOcJwQyqQwEslQmOU8IZFIZCGSpTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPK1KdA/EJ9DXeyFQhUvwLxCyu6DNce9JWVPZGhNAVXmXoJx+HqRf34w/CLANa4tabDpTWdCdXFrExyGSCQSWXwFmapTHKeEMikMhDIUpnkPCGQSWUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok5wmBTCqTbgIJiZVJzhMCmVQm3QQ6b9aBRMok5wmBTCqTbgI9eW6TAYsr4y6TnCcECsYjoewRD6fG4xl2mdzykk8NegJevSloTakzx9jZbxgXI4F6+QwkfPNgl1a3fOK3XCYIFLUy6fYKJHF8NGOdHvfEUyY5TwhkUpm0E+jIgkHNuk7ZuPg3N8VTJjlPCGRSmXQTqF+TrlO2SYdiK7PiKZOcJwQyqUy6CfTQNvVsnZ0Wy1Tt5PgEZwhXXyvfVftDF3A8FGGBMxAh7iZXnCNc5I5zhJM8agvnhcUt0CD5k/2RG62XqaqC4xEqQrjqj/JdpTd0AcdFlRGW+CPEnfrmLI6oImecIyrJpTbL+XOEQBYFmjWL/XWWyJiOcZZJzhNvYSaVSS+BrriC9ZdmdB+4NM4yyXlCIJPKpJdARDnWvwAylknOEwKZVCatBFqwidZy4iyTnCcEMqlMWgnEHqSWnDjLJOcJgUwqk1YCFZ+gWDNJRyiTnCcEMqlMWgkk0uG+r+P8RQcEilqZdBNoXv8m3eP7RQcEilqZdBOI6PDc3zcbtCTOMsl5QiCTyqSfQES+Je3jqBgEilqZtBPImT8yK2PoijjLJOcJgUwqk24CDW7V8qZ34jpjFQJFrUy6CZT7ZrynaoQIdOz8LI2TrlGePgRSV93IBUrGN9EH2aCJGh8pTx8Cqatu5AIl45vog+HTo0KgdBGo+ESiZZLzhEAmlUkrgSiRH5RBoKiVSS+BkvCDMggUXJn0EigJPyiDQMGVSS+BkvCDMggUXJm0EijSYbw2Y6E6VaEegEAQSCfCYbxhxkJlqsKgKQwhEARSiXAYr89YyKcqDJrCEAJFIv0Ektj4I3184+NBP0zUZyzkUxVqgf+MHDnyRz+nhqTbKvaKP5SasIhxhBlChHiAArU+wk9avuoegkCWBXqevV/dfvCZD4YJJM9YyKcq1ALrpk6dWhx8ZZJyttATgjcQGlGvVEIRFhiubBKMj7wRlkQaYbwyirURHvKrLfWvyhDIskBnzBZe7yG89ytjTJ+xkE9VaJzCEG9hEMhIy6004n76uoUxps9YyKcqVAMQKFUE4kfHFHyAXB8C9XxwX5tt9NzZQUFtxkJ1qkIegECpIpBydEwhB8j1IdAHzVk/+it7Ic4yyXlCIJPK1IlA/OiYDAfI/srKyhOlMtVCqYa3tHRGhtIUqsUbboyTL+YP9c4qNS6tWVmtNR0mz7p4jZPWfRFvmeQyQKD6EogfHZPhiHlzTk7OB6ZpzW5teMCNifAwEVx7ZawPgEBRK1MnAvGjYzIcMR/Lz8/f45DxCg4Nv8PxdGulKXjFG26Mhy9W39G0zipyZwWXR2u6w5/0ey2ZDASSCRcojt+71J1A/OiYjEfMVD+fgc4etsdYOQgULFBcv3epO4H40bF4nBx0gFwfAmV9b12dNBTI5Pcuq8fd9uhh7fA57M/MdSKQenQ8eFfQAXJ9CHTTezYEOn7f6NEjGrVA4b93OZR31L90inr4HP5n5nT7InFTryc/SfisjCJ2Zq9eOV+E7JDGJVDoUca3C4kO3KoePof/mTndBLJ1VkYRW1RiQqMSyOQowzt7oXr4rB1FlxYWFpaUiyh7pFyhwltePqSP3KwkR7mKu0pregNas9yntSrIqbVd+rhY14Kvr3Pj4yPNBAo/ytg09tWAevisHUUvycnJ2S0tDftiZXjfZFTdEvUiUNlHc8p2x3OZqTQTKPQoQ5j/kHQ1HH74rB1Fp+0rUGGnTk2LR5/zEwSSCRco9Cjjm/vkL4b44XP4n5nT7TPQNTd5M4vLrk3svLB0ECj0KOON3Ly8vJHa35fD/sycbgK12UyZxfSF1Yky0k+gOI4y0lKgM9ZKAq3qYk0erUxynmkhUBykpUD39D2eWVx4/p1xlknOMy0EClkSszLpJpDzxmYsk11dYdEeSjuBGLP81+a0FEg8Dnvv7W/judJvmgkkfQv93Wu9rEyGlaYCEVX5LFQnuExynmkhkMJ/B1itTHoJtPWubeQZyjKmxHGGfFoKVNDWamXSSqD1zQfsopmtXnkl81Ur6vAsqzhe4We2uMoEh88sKuKmCAuq/BHiLnLGOcJJ1XGOcJBbbaofBQ0C7ZRYf00PCGQi0FV3ih9+uo8nmtUbAkmYCKR8hO60GgKZCJS9jugXtp3o0/bWBUqztzD+E2HLlUkrgdp8TfRmVkD8jNjOsj/pJhDVrF3w8uc1liuTVgJdOJvo6sFiY/pF1uTRyiTnmRYCHb2w6dndml10zGpl0kqgxS2mjmNvk/OdNvMhkEy4QMMu20+0v/cI01qku0DCS92zHxRoCJsQxzdBaSZQp3XS7drOViuTVgJxCuM4qSftBMpWBOpktTLpKFB8pJlAwy49QHSgzy1WKwOBLJVJzjMtBDqa06xbt2Y5+BAtAYHMiHUYv27hwrU4jJeBQGZEF8j98G1EAyZWm9bCpDIQyFKZ5DzTQqB7sl8hWnbmRKuVgUCWyiTnmRYCZS+Tbt89zWplIJClMsl5poVA7TdJtxtPsVoZCGSpTHKeaSFQ3jUnxOf8x9S6PlAEIFAY9S/QL7/NyOnd9pwDVisDgSyVSc4zLQSiwEeznnrf0rnfEMgS6SZQnJVpGAKp4kCgMCAQBDIAgSCQAQik0OgF0q8cya8oqU/NAIEiA4E4+pUj+RUl9akZCAJFBgJx9CtH8itKuow/6IRAkYBAHH3GQlKuKKlNzRAy4dwv7A3TOd8w4RwEUmYs5FeU1KZmCJny8ihbZjqHJKa8TG+B9PkX+BUl9akZCG9hKSyQxycTIJ+G4PM901ppUkC8CRZIfah31sbVaE1/QGsGrBVCn7GQX1FSnZoBAqW2QKnyCqTPWMivKKlOzQCBIJB9IFDUykAgS2WS84RAJpWBQJbKJOcJgUwqA4EslUnOEwIF4/VphznqYYt4LDPscuVYhvzawUyNoWk88tGbZDjyMXSOkQAECqNBCYRXIOtlkvOEQCaVgUCWyiQ/s+fHQqCwykAgS2WS+Im17rTabI9AIAgUq0wS+9jrZvsDAkGg2GWSgEBmlYFAlsokAYHMKgOBLJVJAgKZVQYCWSqTBAQyqwwEslQmCQhkVhkIZKlMEhDIrDIQyFKZJCCQWWUgkKUySUAgs8pAIEtlkoBAZpWBQJbKJAGBzCoDgSyVSQICmVUGAsWiqoLzM1taYUql1zxe4aLKCEv8EeJOfXMWR1SRM84RleRSm+X8OUKgWhSo2snZz95ymlLtN487PRRhgTMQIe4mV5wjXOSOc4STPGpLLRAEwluY9RF4C4NABiAQBDIAgSCQAQikUJcCDR/+u2ZKQlEE4kCgEghUAoGMQCAIZAACKUAgGQhkVhkIZKlMEhDIrDIQyFKZJCCQWWUgkKUySUAgs8pAIEtlkoBAZpWBQJbKJAGBzCoDgSyVSQICmVUGAlkqkwQEMqsMBLJUJgkIZFYZCGSpTBIQyKwyEMhSmSQgkFll6kYgPg0XBc/E1cAEep69ab5HIFBtC6ROw0XBM3E1MIGmZf1ivkcgUG0LxKfhEgmaiStlBNJnLOQtPWAUqGOEPQKB6uAzkDQNl4g2E5ezsLDwcLmMWyjX8HGBxKbgFm+CjQl56NPH1Xi0psOlNavNn3go+oyFvKUHIBBRYGwlRf6vVUcCydNwiWgzcW3Oycn5wCRbLpD+0EjowyShz1jIW3qAINAnU26ojPJfq04E4tNwkWEmrlR6BdJnLOQtLfDN3LlzD7g4j3V0meP2R1jgpQgLXIEIcQ+54xzhJk+cI1zkVVtWzgv7flteZZT/WnUiEJ+Giw56gmbiSpXPQPqMhbylBfJzc3N/CHAOfRswp0aItIAiLAgkb0SAahIf4bYgENHQyvD/WsVr1qw5UiWi7Ioqjq+q6uZL5ZaTXGqwyuPUmr6A1qzyay2HsXO11lTfK4lPw0WDdwXNxJUqAukzFvKWHqCgK9WXmNO438IMAhn+ay0RP4LslhaGfZoY3tda1ZNAqgikz1jIW2pABgJJAg8gRncAAApTSURBVIX+1/JWVlaWlYoou6JU4YSntDSvj9wsp8pSFVeF1vT4tWapV2uVUZXWrjaMayAC6TMWqi1+B4E0gSL+16qTz0CpLlBUIJAkUMT/WhAoFhAoamUgkKUyyXlCIJPKQCBLZZLzhEAmlYFAlsok5wmBTCoDgSyVSc4TAplUBgJZJv/ueEesG+mN3SmInSN/iXPE4ZHfxznCO3J9aAgC1YVAiwbFO+LDHE+cI7bk/BzniOKcrXGOcOf8OzQEgSCQdSBQPQm0fGS8I9bkxvsWVpB7KM4RB3O/jXOEJ3dNaAgC1YVAjRgIBIFsAYEgkC0askAhTqScQFF/cB9jBD+byXgqU4wRvGvMbeg9PswTGXwi9kb4b5tNnwgEqjWBov/gPvoI9WymkTF+WmtYpdI15jZCemx9MfZG+G+bzZ8IBKo1gaL/4D76CH42U9CpTNFH8K4xtxHcwzXNHXsj/LfNZPpEIFCtCRT5B/exR5ByNpN2KlPsEbxrzG0E91i0kWJvhPjvekyfCASqXYFMf3AfewQ/m0k7lSn2CN415jaCehyaJFDsjVCwQMFPBALV3ltY1B/cRx/Bz2bSTmWKPYJ3jbmNoCyWf2xlI6QJZPJEIFCtCRT9B/fRR/CzmYJOZYo+gneNuQ3DEBLGl1nZCHGBTJ8IBKq9w/ioP7iPPoKfzRR0KlP0EWrXmNswpLV3vPQ49ka4QKZPBALhi0RbQCAIZAsIBIFsAYEgkC0gEASyBQSCQLaAQBDIFhAo9QXydzgSGhKW5LTt9IcNEYcUswW0/ow+5ew5Q6BWgEApL5D7YRYm0NyTnt32xZiTtkUac+LBTTT0uiOuB9caAlfMqoXsIFCqC/RSCxYuUI+p4o1w5V3RBl43PSQAgXTSSKBjO98OF6jjOOl21zYq6PDlpe2u+B+Rc8KZba/dTXRkaIfO97qp5dpBjPWhDv/RAzmMDXqonzjsqfOi/+U0LiBQqgtE9HW4QA+wP7wln4ha0OLstzdcn1VON17++aYbO5cFfvuHjUuzHxF9CVz7iF8USA/4+/81sK3JERK6J/OVCAI1SIFqludmsR6zvFTA3iRydXppd7PjRN7sjz7KOEH0ym2iL/JbWIf/GALiW5hw1gLa0eRAEpODQA1IoA8zMzN3qdHA1+NaDhUFkl6Ibhy3gonLMpvOmZWjLNUEMgSkz0BTBtGUAclMDgI1IIGcxcXF8q8oCoc4pbtFrKqAHRUbeXe8nVUsUfZUb6WrJpAhIAm0tdnxLouTmRwEakACaZSwd6W7VzJ8BSxfPNA/9flvWaG4W0YXrmhbQbRsgC6QISAJJJw1ulVlMpODQA1RILq3zaOfrJmd+aD4Fnbm+1/mZpYKV/VcvfZP3Tzec/60acWZ9+kCGQIDx4jrmcJuSWpyEKhBCuT7x+9OzspZ6BcF+rhX234F4i4Zc1pm7j6i/blZp06o1gUyBJZ2HEy0kX2S1OQgUOoLFI0C5o7dycjizv6kJtBABfL4RIKdELhA4gIKhC0N7ezTEGq0pj+gNQMJ1aXuiVOg8lW/eTy5CdgXiO8SvALVC3EKtDPrxjhfsWKRmEAeCS4O3yU1Hs+wy+S4l3welYBXbwpa01OjtYyd/YZxMRKAQKkCXoEgkC0gEASyBQSCQLaAQBDIFhAIAtkCAkEgW0AgCGSLxieQuTHhnaMshUDWgUAQyBYQCALZAgJBIFtAIAhkCwgEgWwBgSCQLSAQBLIFBIJAtoBAEMgWEAgC2QICQSBb1JpAShQCNXYgEASyBQSCQLaAQBDIFhAIAtkCAkEgW0AgCGQLCASBbAGBIJAtIBAEsgUEgkC2gEAQyBYQCALZAgJBIFskT6Dhw8/K1h9CoDShtgXSdwkEapRAIAhkCwgEgWwBgSCQLSAQBLKFdYG+uWfMS17ejl8gbc/EK5C+WWMCEChVsCxQ9YjiwMx8/qDuBNI3G5QABEoVLAu0YQZRwQP8Qd0JpG82KAEIlCpYFuiDeUSHRouNovz8/F8cIkqx+d1wvyKQ+tARvKPUzhy/2nA4ya2tarhLC/vCNqu3jokJ7NETUPEHCxSyNLxzlKXiupM8o0TjJT6BRomNJTk5ObtNuwzvm6ysTDartzaLCXxg2nl26+QnAKJj/S3sCaJv7+cP+B8oPD7tPae2pnvSNxuUgIOvXgha5+MZSlMwXG3VoTUdZJYArtJqD8sCOW89IjwX9CG6TgRSN3vQE5QABEoVrB/Gb59479ygw/g6EUjd7OBdQQlAoFTBxheJdSOQORAoVYBAEMgWEAgC2QICQSBbQCAIZAsIBIFsAYEgkC0gEASyBQSCQLaAQBDIFhAIAtkCAkEgW9gS6McfdIHE3TB5hNw8svOwvtPKtOa+PfpO0/fZsZ0H9Z2m21b8Y/QEuBY/7wpa5zzF4JJd+3UndJkP7DRLoKSwWGuW6zIf2lmTUGXSjsQE4jw0ziy6P2eTWfipEWbRspxPzcJ/v8FSAv+8wjTcb7FZ9N0cwSz8p7lm0U9yKi1lkPZAIAhkCwgEgWxhS6C1q8yilUsOm4U3fmQWdS8pNgtve99SAt+9ZRp+639m0d1LTDu/t90sum+J1ywMQrElEAAQCNjCjkDGc401hKWjR88oC++8/6HR00rDov+64/a/h56CFRgrffxYPe62R03fClMpAWBHoKBzjTUKxlT6X1gY1jlwR0HNa8+HRr+ZcNw9f2lw7JMpN4j771DeUf/SKSmeALAlUNC5xhqHdpP7tWVhnbdPJfKFvS4s/yfRD/cEx77flifuv29FBQ7cmuIJAFsC6WcdB7Mhb6wzLPjxk0+NefKX0OiWew5UvDwsNDpUOYL2zg5/HUmtBIB9gUaZLHAvmhkWWzGy0P3uQ6FRYcVd9755e2hU2X+bxr4aSPEEgL23MOO5xhqrvyDaF7ZL6PNZRJVDQr/Jc4t7atu00L7S/hPmP3Qg5RMAtgQKOtdYY8M9buGN2WGdy27f588P21M/jSj1PPxFaFTaf9/cF/t/f70nAOwdxhvPNdYQFt9+x6yK8M6bxo+ccSws+q9Rd70T9gcGaf+9kZuXlzcy1RMA+CIR2AMCAVtAIGALCARsAYGALSAQsAUEAraAQMAWDUQgtrm+MwDmQCBgCwgEbJGiAuUOFm/mdfDuvrpd2347JIEcbCfRXlZCzglntr3W/FL5oO5JUYHebOUk6j+BLuq/5rPfXxwk0I2Xf77pxs4mP3oG9UGKClTVMp8ON9lW8+wPRMs6GAXa3ew4kTfb9CQzUPekqEB000ia210g/8Z/3N4pSKAVLFOk6Zz6ThAopKpA72T5+j1D1f16TP/vP3WBvmMlb2cVS+AtLEVIVYEcGUua7aePMzxE/+ACrSd6jZV8ywqJykcX1neCQCFVBaKh7QcSrWXPb5yZ3WK7KJCQfU3Byt+xEuGqnqvX/qmbp77zAwopK9AKtoRImN6x/ZAf+w6Qvgf6tHvbK3eKR2HlY07LzN1X3+kBTsoKBBoGEAjYAgIBW0AgYAsIBGwBgYAtIBCwxf8DpDa8QWZG4mIAAAAASUVORK5CYII=" style="display: block; margin: auto;" /></p>
<p>To inspect the optimization, the function of metric values per cutpoint can be plotted using <code>plot_metric</code>, if an optimization function was used that returns a metric column in the <code>roc_curve</code> column. For example, the <code>maximize_metric</code> and <code>minimize_metric</code> functions do so:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<p>Predictions for new data can be made using <code>predict</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">predict</span>(opt_cut, <span class="dt">newdata =</span> <span class="kw">data.frame</span>(<span class="dt">dsi =</span> <span class="dv">0</span><span class="op">:</span><span class="dv">5</span>))</code></pre></div>
<pre><code>## [1] "no" "no" "yes" "yes" "yes" "yes"</code></pre>
<div id="separate-subgroups" class="section level2">
<h2>Separate subgroups</h2>
<p>Cutpoints can be separately estimated on subgroups that are defined by a third variable, <code>gender</code> in this case:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(opt_cut)</code></pre></div>
<pre><code>## Method: maximize_metric
## Predictor: dsi
## Outcome: suicide
## Direction: >=
## Subgroups: female, male
##
## Subgroup: female
## ---------------------------------------------------------------------------
## optimal_cutpoint sum_sens_spec acc sensitivity specificity AUC
## 2 1.8081 0.8852 0.9259 0.8822 0.9446
## n_pos n_neg
## 27 365
##
## Cutpoint 2:
## observation
## prediction yes no
## yes 25 43
## no 2 322
##
##
## Predictor summary:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD
## 0 0 0 0 0.8393 1 5 10 1.7452
##
## Predictor summary per class:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max SD
## no 0 0.0 0 0 0.5479 0 4 10 1.3181
## yes 0 1.3 4 5 4.7778 6 7 9 2.0444
##
## Subgroup: male
## ---------------------------------------------------------------------------
## optimal_cutpoint sum_sens_spec acc sensitivity specificity AUC
## 3 1.6251 0.8429 0.7778 0.8473 0.8617
## n_pos n_neg
## 9 131
##
## Cutpoint 3:
## observation
## prediction yes no
## yes 7 20
## no 2 111
##
##
## Predictor summary:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD
## 0 0 0 0 1.15 1 6 11 2.1151
##
## Predictor summary per class:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max SD
## no 0 0.0 0 0 0.8702 1 5.0 6 1.6286
## yes 0 0.4 3 4 5.2222 8 10.6 11 3.8333</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
</div>
<div id="bootstrapping" class="section level2">
<h2>Bootstrapping</h2>
<p>If <code>boot_runs</code> is larger zero, <code>cutpointr</code> will carry out the usual cutpoint calculation on the full sample, just as before, and additionally on <code>boot_runs</code> bootstrap samples, which offers a way of gauging the out-of-sample performance of the cutpoint estimation method.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">12</span>)
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">boot_runs =</span> <span class="dv">50</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut</code></pre></div>
<pre><code>## # A tibble: 1 x 16
## direction optimal_cutpoint method sum_sens_spec acc
## <chr> <dbl> <chr> <dbl> <dbl>
## 1 >= 2. maximize_metric 1.75 0.865
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.889 0.863 0.924 yes no 0.0677 suicide
## predictor data roc_curve boot
## <chr> <list> <list> <list>
## 1 dsi <tibble [532 × 2]> <data.frame [13 × 10]> <tibble [50 × 23]></code></pre>
<p>The returned object has the additional column <code>boot</code> which is a nested tibble that includes the cutpoints per bootstrap sample along with the metric calculated using the function in <code>metric</code> and various default metrics. The metrics are suffixed by <code>_b</code> to indicate in-bag results or <code>_oob</code> to indicate out-of-bag results:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut<span class="op">$</span>boot</code></pre></div>
<pre><code>## [[1]]
## # A tibble: 50 x 23
## optimal_cutpoint AUC_b AUC_oob sum_sens_spec_b sum_sens_spec_oob acc_b
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 4. 0.941 0.900 1.79 1.60 0.923
## 2 2. 0.910 0.927 1.71 1.80 0.857
## 3 2. 0.962 0.880 1.81 1.68 0.855
## 4 3. 0.946 0.906 1.76 1.62 0.906
## 5 2. 0.940 0.895 1.79 1.70 0.891
## 6 4. 0.940 0.932 1.82 1.56 0.929
## 7 2. 0.917 0.918 1.75 1.73 0.844
## 8 2. 0.862 0.925 1.63 1.76 0.831
## 9 3. 0.970 0.846 1.82 1.48 0.882
## 10 1. 0.912 0.920 1.71 1.67 0.782
## # ... with 40 more rows, and 17 more variables: acc_oob <dbl>,
## # sensitivity_b <dbl>, sensitivity_oob <dbl>, specificity_b <dbl>,
## # specificity_oob <dbl>, kappa_b <dbl>, kappa_oob <dbl>, TP_b <dbl>,
## # FP_b <dbl>, TN_b <int>, FN_b <int>, TP_oob <dbl>, FP_oob <dbl>,
## # TN_oob <int>, FN_oob <int>, roc_curve_b <list>, roc_curve_oob <list></code></pre>
<p>The summary and plots include additional elements that summarize or display the bootstrap results:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">summary</span>(opt_cut)</code></pre></div>
<pre><code>## Method: maximize_metric
## Predictor: dsi
## Outcome: suicide
## Direction: >=
## Nr. of bootstraps: 50
##
## optimal_cutpoint sum_sens_spec acc sensitivity specificity AUC
## 2 1.7518 0.8647 0.8889 0.8629 0.9238
## n_pos n_neg
## 36 496
##
## Cutpoint 2:
## observation
## prediction yes no
## yes 32 68
## no 4 428
##
##
## Predictor summary:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max. SD
## 0 0 0 0 0.9211 1 5 11 1.8527
##
## Predictor summary per class:
## Min. 5% 1st Qu. Median Mean 3rd Qu. 95% Max SD
## no 0 0.00 0 0 0.6331 0 4.00 10 1.4122
## yes 0 0.75 4 5 4.8889 6 9.25 11 2.5498
##
## Bootstrap summary:
## Variable Min. 5% 1st Qu. Median Mean 3rd Qu. 95%
## optimal_cutpoint 1.0000 1.4500 2.0000 2.0000 2.1400 2.0000 3.5500
## AUC_b 0.8621 0.8913 0.9168 0.9327 0.9296 0.9466 0.9586
## AUC_oob 0.8311 0.8541 0.8983 0.9142 0.9134 0.9338 0.9644
## sum_sens_spec_b 1.6285 1.6894 1.7478 1.7747 1.7702 1.7995 1.8385
## sum_sens_spec_oob 1.4764 1.5551 1.6510 1.7085 1.7068 1.7631 1.8324
## acc_b 0.7613 0.8164 0.8571 0.8712 0.8679 0.8816 0.9052
## acc_oob 0.7200 0.7976 0.8455 0.8618 0.8546 0.8721 0.8921
## sensitivity_b 0.7949 0.8358 0.8777 0.9077 0.9049 0.9316 0.9683
## sensitivity_oob 0.5833 0.6958 0.8031 0.8571 0.8519 0.9215 1.0000
## specificity_b 0.7520 0.8095 0.8545 0.8691 0.8653 0.8822 0.9091
## specificity_oob 0.7059 0.7866 0.8442 0.8628 0.8549 0.8722 0.8934
## kappa_b 0.2214 0.3289 0.3786 0.4221 0.4238 0.4673 0.5310
## kappa_oob 0.2145 0.2505 0.3198 0.3808 0.3814 0.4430 0.4866
## Max. SD
## 4.0000 0.6064
## 0.9705 0.0214
## 0.9737 0.0320
## 1.8555 0.0471
## 1.8876 0.0874
## 0.9286 0.0296
## 0.9091 0.0325
## 0.9762 0.0426
## 1.0000 0.0951
## 0.9313 0.0322
## 0.9389 0.0373
## 0.6033 0.0720
## 0.5003 0.0748</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<p>If a subgroup is given, the bootstrapping is carried out separately for every subgroup which is also reflected in the plots and output.</p>
<div id="parallelized-bootstrapping" class="section level3">
<h3>Parallelized bootstrapping</h3>
<p>Using <code>foreach</code> and <code>doRNG</code> the bootstrapping can be parallelized easily. The <strong>doRNG</strong> package is being used to make the bootstrap sampling reproducible. It may be preferable for long running tasks to specify <code>direction</code> and <code>pos_class</code> and / or <code>neg_class</code> manually to speed up <code>cutpointr</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="cf">if</span> (<span class="kw">suppressPackageStartupMessages</span>(<span class="kw">require</span>(doParallel) <span class="op">&</span><span class="st"> </span><span class="kw">require</span>(doRNG))) {
cl <-<span class="st"> </span><span class="kw">makeCluster</span>(<span class="dv">2</span>) <span class="co"># 2 cores</span>
<span class="kw">registerDoParallel</span>(cl)
<span class="kw">registerDoRNG</span>(<span class="dv">12</span>) <span class="co"># Reproducible parallel loops using doRNG</span>
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">pos_class =</span> <span class="st">"yes"</span>,
<span class="dt">direction =</span> <span class="st">">="</span>, <span class="dt">boot_runs =</span> <span class="dv">30</span>, <span class="dt">allowParallel =</span> <span class="ot">TRUE</span>)
<span class="kw">stopCluster</span>(cl)
opt_cut
}</code></pre></div>
<pre><code>## Running bootstrap...</code></pre>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method sum_sens_spec acc
## <chr> <chr> <dbl> <chr> <dbl> <dbl>
## 1 female >= 2. maximize_metric 1.81 0.885
## 2 male >= 3. maximize_metric 1.63 0.843
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <chr> <fct> <dbl> <chr>
## 1 0.926 0.882 0.945 yes no 0.0689 suicide
## 2 0.778 0.847 0.862 yes no 0.0643 suicide
## predictor grouping data roc_curve
## <chr> <chr> <list> <list>
## 1 dsi gender <tibble [392 × 2]> <data.frame [11 × 10]>
## 2 dsi gender <tibble [140 × 2]> <data.frame [11 × 10]>
## boot
## <list>
## 1 <tibble [30 × 23]>
## 2 <tibble [30 × 23]></code></pre>
</div>
</div>
</div>
<div id="more-robust-cutpoint-estimation-methods" class="section level1">
<h1>More robust cutpoint estimation methods</h1>
<div id="bootstrapped-cutpoints" class="section level2">
<h2>Bootstrapped cutpoints</h2>
<p>It has been shown that bagging can substantially improve performance of a wide range of types of models in regression as well as in classification tasks. In the setting of generating a numerical output, a number of bootstrap samples is drawn and the final result is the average of all models that were fit to the bootstrap samples. We make this pricinple available for cutpoint estimation via the <code>maximize_boot_metric</code> and <code>minimize_boot_metric</code> functions. If one of these functions is used as <code>method</code>, <code>boot_cut</code> bootstrap samples are drawn, the cutpoint optimization is carried out in each one and a summary (e.g. the mean) of the resulting optimal cutpoints on the bootstrap samples is returned as the optimal cutpoint in <code>cutpointr</code>. Note that if bootstrap validation is run, i.e. if <code>boot_runs</code> is larger zero, an outer bootstrap will be executed. In the bootstrap validation routine <code>boot_runs</code> bootstrap samples are generated and each one is again bootstrapped <code>boot_cut</code> times. This may lead to long run times, so activating the built-in parallelization may be advisable. The advantages of bootstrapping the optimal cutpoint are that the procedure doesn’t possess parameters that have to be tuned, unlike the LOESS smoothing, that it doesn’t rely on assumptions, unlike the Normal method, and that it is applicable to any metric that can be used with <code>minimize_metric</code> or <code>maximize_metric</code>, unlike the Kernel method. Furthermore, like Random Forests cannot be overfit by increasing the number of trees, the bootstrapped cutpoints cannot be overfit by running an excessive amount of <code>boot_cut</code> repetitions.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">100</span>)
<span class="kw">cutpointr</span>(suicide, dsi, suicide, gender,
<span class="dt">method =</span> maximize_boot_metric,
<span class="dt">boot_cut =</span> <span class="dv">30</span>, <span class="dt">summary_func =</span> mean,
<span class="dt">metric =</span> accuracy, <span class="dt">silent =</span> <span class="ot">TRUE</span>)</code></pre></div>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method accuracy acc
## <chr> <chr> <dbl> <chr> <dbl> <dbl>
## 1 female >= 5.59 maximize_boot_metric 0.957 0.957
## 2 male >= 7.93 maximize_boot_metric 0.957 0.957
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.444 0.995 0.945 yes no 0.0689 suicide
## 2 0.333 1.00 0.862 yes no 0.0643 suicide
## predictor grouping data roc_curve boot
## <chr> <chr> <list> <list> <lgl>
## 1 dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 dsi gender <tibble [140 × 2]> <data.frame [11 × 9]> NA</code></pre>
</div>
<div id="loess-smoothing-for-selecting-a-cutpoint" class="section level2">
<h2>LOESS smoothing for selecting a cutpoint</h2>
<p>When using <code>maximize_metric</code> and <code>minimize_metric</code> the optimal cutpoint is selected by searching the maximum or minimum of the metric function. For example, we may want to minimize the misclassification cost. Since false negatives (a suicide attempt was not anticipated) can be regarded as much more severe than false positives we can set the cost of a false negative <code>cost_fn</code> for example to ten times the cost of a false positive.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">method =</span> minimize_metric,
<span class="dt">metric =</span> misclassification_cost, <span class="dt">cost_fp =</span> <span class="dv">1</span>, <span class="dt">cost_fn =</span> <span class="dv">10</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut)</code></pre></div>
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" style="display: block; margin: auto;" /></p>
<p>As this “optimal” cutpoint may depend on minor differences between the possible cutoffs, smoothing of the function of metric values by cutpoint value might be desirable, especially in small samples. The <code>minimize_loess_metric</code> and <code>maximize_loess_metric</code> functions can be used to smooth the function so that the optimal cutpoint is selected based on the smoothed metric values. Options to modify the smoothing, which is implemented using <code>loess.as</code> from the <strong>fANCOVA</strong> package, include:</p>
<ul>
<li><code>criterion</code>: the criterion for automatic smoothing parameter selection: “aicc” denotes bias-corrected AIC criterion, “gcv” denotes generalized cross-validation.</li>
<li><code>degree</code>: the degree of the local polynomials to be used. It can be 0, 1 or 2.</li>
<li><code>family</code>: if “gaussian” fitting is by least-squares, and if “symmetric” a re-descending M estimator is used with Tukey’s biweight function.</li>
<li><code>user.span</code>: the user-defined parameter which controls the degree of smoothing.</li>
</ul>
<p>Using parameters for the LOESS smoothing of <code>criterion = "aicc"</code>, <code>degree = 2</code>, <code>family = "symmetric"</code>, and <code>user.span = 0.7</code> we get the following smoothed versions of the above metrics:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender,
<span class="dt">method =</span> minimize_loess_metric,
<span class="dt">criterion =</span> <span class="st">"aicc"</span>, <span class="dt">family =</span> <span class="st">"symmetric"</span>,
<span class="dt">degree =</span> <span class="dv">2</span>, <span class="dt">user.span =</span> <span class="fl">0.7</span>,
<span class="dt">metric =</span> misclassification_cost, <span class="dt">cost_fp =</span> <span class="dv">1</span>, <span class="dt">cost_fn =</span> <span class="dv">10</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## fANCOVA 0.5-1 loaded</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<p>The optimal cutpoint for the female subgroup changes to 3. Note, though, that there are no reliable rules for selecting the “best” smoothing parameters. Notably, the LOESS smoothing is sensitive to the number of unique cutpoints. A large number of unique cutpoints generally leads to a more volatile curve of metric values by cutpoint value, even after smoothing. Thus, the curve tends to be undersmoothed in that scenario. The unsmoothed metric values are returned in <code>opt_cut$roc_curve</code> in the column <code>m_unsmoothed</code>.</p>
</div>
<div id="smoothing-via-generalized-additive-models-for-selecting-a-cutpoint" class="section level2">
<h2>Smoothing via Generalized Additive Models for selecting a cutpoint</h2>
<p>In a similar fashion the function of metric values per cutpoint can be smoothed using Generalized Additive Models with smooth terms. Internally, <code>mgcv::gam</code> carries out the smoothing which can be customized via the arguments <code>formula</code> and <code>optimizer</code>, see <code>help("gam", package = "mgcv")</code>. Most importantly, the GAM can be specified by altering the default formula, for example the smoothing function could be configured to apply cubic regression splines (<code>"cr"</code>) as the smooth term. As the <code>suicide</code> data has only very few unique cutpoints, it is not very suitable for showcasing the GAM smoothing, so we will use two classes of the <code>iris</code> data here. In this case, the purely empirical method and the GAM smoothing lead to identical cutpoints, but in practice the GAM smoothing tends to be more robust, especially with larger data. An attractive feature of the GAM smoothing is, that the default values tend to work quite well and usually require no tuning, eliminating researcher degrees of freedom.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">exdat <-<span class="st"> </span>iris
exdat <-<span class="st"> </span>exdat[exdat<span class="op">$</span>Species <span class="op">!=</span><span class="st"> "setosa"</span>, ]
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(exdat, Petal.Length, Species,
<span class="dt">method =</span> minimize_gam_metric,
<span class="dt">formula =</span> m <span class="op">~</span><span class="st"> </span><span class="kw">s</span>(x.sorted, <span class="dt">bs =</span> <span class="st">"cr"</span>),
<span class="dt">metric =</span> abs_d_sens_spec)</code></pre></div>
<pre><code>## Assuming the positive class is virginica</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">ggplot</span>(opt_cut<span class="op">$</span>roc_curve[[<span class="dv">1</span>]] <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">gather</span>(metric, value, m, m_unsmoothed, <span class="op">-</span>x.sorted, <span class="dt">na.rm =</span> <span class="ot">TRUE</span>),
<span class="kw">aes</span>(<span class="dt">x =</span> x.sorted, <span class="dt">y =</span> value, <span class="dt">color =</span> metric)) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_line</span>()</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
</div>
<div id="spline-smoothing-for-selecting-a-cutpoint" class="section level2">
<h2>Spline smoothing for selecting a cutpoint</h2>
<p>Again in the same fashion the function of metric values per cutpoint can be smoothed using smoothing splines. By default, the number of knots is automatically chosen using the <code>cutpoint_knots</code> function. That function uses <code>stats::.nknots.smspl</code>, which is the default in <code>stats::smooth.spline</code> to pick the number of knots.</p>
<p>Alternatively, the number of knots can be set manually and also the other smoothing parameters of <code>stats::smooth.spline</code> can be set as desired. For details see <code>?maximize_spline_metric</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender,
<span class="dt">method =</span> minimize_spline_metric, <span class="dt">spar =</span> <span class="fl">0.4</span>,
<span class="dt">metric =</span> misclassification_cost, <span class="dt">cost_fp =</span> <span class="dv">1</span>, <span class="dt">cost_fn =</span> <span class="dv">10</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## nknots: 10
## nknots: 10</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div id="parametric-method-assuming-normality" class="section level3">
<h3>Parametric method assuming normality</h3>
<p>In addition to these general methods, which are applicable for all metrics, two methods to only maximize the Youden-Index robustly are included, the “normal method” and a method based on kernel smoothing. The “normal method” in <code>oc_youden_normal</code> is a parametric method for maximizing the Youden-Index or equivalently the sum of <span class="math inline">\(Se\)</span> and <span class="math inline">\(Sp\)</span>. It relies on the assumption that the predictor for both the negative and positive observations is normally distributed. In that case it can be shown that</p>
<p><span class="math display">\[c^* = \frac{(\mu_P \sigma_N^2 - \mu_N \sigma_P^2) - \sigma_N \sigma_P \sqrt{(\mu_N - \mu_P)^2 + (\sigma_N^2 - \sigma_P^2) log(\sigma_N^2 / \sigma_P^2)}}{\sigma_N^2 - \sigma_P^2}\]</span></p>
<p>where the negative class is normally distributed with <span class="math inline">\(\sim N(\mu_N, \sigma_N^2)\)</span> and the positive class independently normally distributed with <span class="math inline">\(\sim N(\mu_P, \sigma_P^2)\)</span> provides the optimal cutpoint <span class="math inline">\(c^*\)</span> that maximizes the Youden-Index. If <span class="math inline">\(\sigma_N\)</span> and <span class="math inline">\(\sigma_P\)</span> are equal, the expression can be simplified to <span class="math inline">\(c^* = \frac{\mu_N + \mu_P}{2}\)</span>. However, the <code>oc_youden_normal</code> method in cutpointr always assumes unequal standard deviations. Since this method does not select a cutpoint from the observed predictor values, it is questionable which values for <span class="math inline">\(Se\)</span> and <span class="math inline">\(Sp\)</span> should be reported. Here, the Youden-Index can be calculated as</p>
<p><span class="math display">\[J = \Phi(\frac{c^* - \mu_N}{\sigma_N}) - \Phi(\frac{c^* - \mu_P}{\sigma_P})\]</span></p>
<p>if the assumption of normality holds. However, since there exist several methods that do not select cutpoints from the available observations and to unify the reporting of metrics for these methods, <strong>cutpointr</strong> reports all metrics, e.g. <span class="math inline">\(Se\)</span> and <span class="math inline">\(Sp\)</span>, based on the empirical observations. If better estimates of the metrics are sought, the user is referred to the available bootstrapping routine that will be introduced later. If a method is superior, for example if the assumption of normality is appropriate, this should lead to a better performance in the bootstrap validation.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">method =</span> oc_youden_normal)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method sum_sens_spec acc
## <chr> <chr> <dbl> <chr> <dbl> <dbl>
## 1 female >= 2.48 oc_youden_normal 1.72 0.895
## 2 male >= 3.17 oc_youden_normal 1.54 0.864
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.815 0.901 0.945 yes no 0.0689 suicide
## 2 0.667 0.878 0.862 yes no 0.0643 suicide
## predictor grouping data roc_curve boot
## <chr> <chr> <list> <list> <lgl>
## 1 dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 dsi gender <tibble [140 × 2]> <data.frame [11 × 9]> NA</code></pre>
</div>
<div id="nonparametric-kernel-method" class="section level3">
<h3>Nonparametric kernel method</h3>
<p>A nonparametric alternative is the “kernel method” <span class="citation">[@fluss_estimation_2005]</span>. Here, the empirical distribution functions are smoothed using the Gaussian kernel functions <span class="math inline">\(\hat{F}_N(t) = \frac{1}{n} \sum^n_{i=1} \Phi(\frac{t - y_i}{h_y})\)</span> and <span class="math inline">\(\hat{G}_P(t) = \frac{1}{m} \sum^m_{i=1} \Phi(\frac{t - x_i}{h_x})\)</span> for the negative and positive classes respectively. Following Silverman’s plug-in “rule of thumb” the bandwidths are selected as <span class="math inline">\(h_y = 0.9 * min\{s_y, iqr_y/1.34\} * n^{-0.2}\)</span> and <span class="math inline">\(h_x = 0.9 * min\{s_x, iqr_x/1.34\} * m^{-0.2}\)</span> where <span class="math inline">\(s\)</span> is the sample standard deviation and <span class="math inline">\(iqr\)</span> is the inter quartile range. It has been demontrated that AUC estimation is rather insensitive to the choice of the bandwith procedure <span class="citation">[@faraggi_estimation_2002]</span> and thus the plug-in bandwith estimator has also been recommended for cutpoint estimation. Indeed, as our preliminary simulations have shown, the choices of the bandwidth and the kernel function do not seem to exhibit a considerable influence on the variability (or bias) of the estimated cutpoints. Thus, the <code>oc_youden_kernel</code> function in <strong>cutpointr</strong> uses a Guassian kernel and the direct plug-in method for selecting the bandwidths. The kernel smoothing is done via the <code>bkde</code> function from the <strong>KernSmooth</strong> package <span class="citation">[@wand_kernsmooth:_2013]</span>.</p>
<p>Again, there is a way to calcualte the Youden-Index from the results of this method <span class="citation">[@fluss_estimation_2005]</span> which is</p>
<p><span class="math display">\[\hat{J} = max_c \{\hat{F}_N(c) - \hat{G}_N(c) \}\]</span></p>
<p>but as before we prefer to report all metrics based on applying the cutpoint that was estimated using the kernel method to the empirical observations.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">method =</span> oc_youden_kernel)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method sum_sens_spec acc
## <chr> <chr> <dbl> <chr> <dbl> <dbl>
## 1 female >= 1.18 oc_youden_kernel 1.81 0.885
## 2 male >= 1.32 oc_youden_kernel 1.59 0.807
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.926 0.882 0.945 yes no 0.0689 suicide
## 2 0.778 0.809 0.862 yes no 0.0643 suicide
## predictor grouping data roc_curve boot
## <chr> <chr> <list> <list> <lgl>
## 1 dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 dsi gender <tibble [140 × 2]> <data.frame [11 × 9]> NA</code></pre>
</div>
</div>
</div>
<div id="additional-features" class="section level1">
<h1>Additional features</h1>
<div id="calculating-only-the-roc-curve" class="section level2">
<h2>Calculating only the ROC curve</h2>
<p>When running <code>cutpointr</code>, a ROC curve is by default returned in the column <code>roc_curve</code>. This ROC curve can be plotted using <code>plot_roc</code>. Alternatively, if only the ROC curve is desired and no cutpoint needs to be calculated, the ROC curve can be created using <code>roc()</code> and plotted using <code>plot_cutpointr</code>. The <code>roc</code> function, unlike <code>cutpointr</code>, does not determine <code>direction</code>, <code>pos_class</code> or <code>neg_class</code> automatically and does not support nonstandard evaluation, so the function arguments have to be enclosed in quotation marks.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">roc_curve <-<span class="st"> </span><span class="kw">roc</span>(<span class="dt">data =</span> suicide, <span class="dt">x =</span> <span class="st">"dsi"</span>, <span class="dt">class =</span> <span class="st">"suicide"</span>,
<span class="dt">pos_class =</span> <span class="st">"yes"</span>, <span class="dt">neg_class =</span> <span class="st">"no"</span>)
<span class="kw">plot_cutpointr</span>(roc_curve, fpr, tpr, <span class="dt">aspect_ratio =</span> <span class="dv">1</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" style="display: block; margin: auto;" /></p>
</div>
<div id="midpoints" class="section level2">
<h2>Midpoints</h2>
<p>So far - which is the default in <code>cutpointr</code> - we have considered all unique values of the predictor as possible cutpoints. An alternative could be to use a sequence of equidistant values instead, for example in the case of the <code>suicide</code> data all integers in <span class="math inline">\([0, 10]\)</span>. However, with very sparse data and small intervals between the candidate cutpoints (i.e. a ‘dense’ sequence like <code>seq(0, 10, by = 0.01)</code>) this leads to the uninformative evaluation of large ranges of cutpoints that all result in the same metric value. A more elegant alternative, not only for the case of sparse data, that is supported by <strong>cutpointr</strong> is the use of a mean value of the optimal cutpoint and the next highest (if <code>direction = ">="</code>) or the next lowest (if <code>direction = "<="</code>) predictor value in the data. The result is an optimal cutpoint that is equal to the cutpoint that would be obtained using an infinitely dense sequence of candidate cutpoints and is thus usually more efficient computationally. This behavior can be activated by setting <code>use_midpoints = TRUE</code>, which is the default. If we use this setting, we obtain an optimal cutpoint of 1.5 for the complete sample on the <code>suicide</code> data instead of 2 when maximizing the sum of sensitivity and specificity.</p>
<p>Assume the following small data set:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">dat <-<span class="st"> </span><span class="kw">data.frame</span>(<span class="dt">outcome =</span> <span class="kw">c</span>(<span class="st">"neg"</span>, <span class="st">"neg"</span>, <span class="st">"neg"</span>, <span class="st">"pos"</span>, <span class="st">"pos"</span>, <span class="st">"pos"</span>, <span class="st">"pos"</span>),
<span class="dt">pred =</span> <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>, <span class="dv">8</span>, <span class="dv">11</span>, <span class="dv">11</span>, <span class="dv">12</span>))</code></pre></div>
<p>Since the distance of the optimal cutpoint (8) to the next lowest observation (3) is rather large we arrive at a range of possible cutpoints that all maximize the metric. In the case of this kind of sparseness it might for example be desirable to classify a new obsevation with a predictor value of 4 as belonging to the negative class. If <code>use_midpoints</code> is set to <code>TRUE</code>, the mean of the optimal cutpoint and the next lowest observation is returned as the optimal cutpoint, if direction is <code>>=</code>. The mean of the optimal cutpoint and the next highest observation is returned as the optimal cutpoint, if <code>direction = "<="</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(dat, <span class="dt">x =</span> pred, <span class="dt">class =</span> outcome, <span class="dt">use_midpoints =</span> <span class="ot">TRUE</span>)</code></pre></div>
<pre><code>## Assuming the positive class is pos</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_x</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<p>A simulation demonstrates more clearly that setting <code>use_midpoints = TRUE</code> avoids biasing the cutpoints. To simulate the bias of the metric functions, the predictor values of both classes were drawn from normal distributions with constant standard deviations of 10, a constant mean of the negative class of 100 and higher mean values of the positive class that are selected in such a way that optimal Youden-Index values of 0.2, 0.4, 0.6, and 0.8 result in the population. Samples of 9 different sizes were drawn and the cutpoints that maximize the Youden-Index were estimated. The simulation was repeated 10000 times. As can be seen by the mean error, <code>use_midpoints = TRUE</code> eliminates the bias that is introduced by otherwise selecting the value of an observation as the optimal cutpoint. If <code>direction = ">="</code>, as in this case, the observation that represents the optimal cutpoint is the highest possible cutpoint that leads to the optimal metric value and thus the biases are positive. The methods <code>oc_youden_normal</code> and <code>oc_youden_kernel</code> are always unbiased, as they don’t select a cutpoint based on the ROC-curve or the function of metric values per cutpoint.</p>
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" style="display: block; margin: auto;" /></p>
</div>
<div id="finding-all-cutpoints-with-acceptable-performance" class="section level2">
<h2>Finding all cutpoints with acceptable performance</h2>
<p>By default, most packages only return the “best” cutpoint and disregard other cutpoints with quite similar performance, even if the performance differences are miniscule. <strong>cutpointr</strong> makes this process more explicit via the <code>tol_metric</code> argument. For example, if all cupoints are of interest that are achieve at least an accuracy within <code>0.05</code> of the optimally achievable accuracy, <code>tol_metric</code> can be set to <code>0.05</code> and also those cutpoints will be returned.</p>
<p>In the case of the <code>suicide</code> data and when maximizing the sum of sensitivity and specificity, empirically the cutpoints 2 and 3 lead to quite similar performances. If <code>tol_metric</code> is set to <code>0.05</code>, both will be returned.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">metric =</span> sum_sens_spec,
<span class="dt">tol_metric =</span> <span class="fl">0.05</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Multiple optimal cutpoints found</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(optimal_cutpoint, sum_sens_spec) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>unnest</code></pre></div>
<pre><code>## # A tibble: 2 x 2
## optimal_cutpoint sum_sens_spec
## <dbl> <dbl>
## 1 2. 1.75
## 2 1. 1.70</code></pre>
</div>
<div id="manual-and-mean-median-cutpoints" class="section level2">
<h2>Manual and mean / median cutpoints</h2>
<p>Using the <code>oc_manual</code> function the optimal cutpoint will not be determined based on, for example, a metric but is instead set manually using the <code>cutpoint</code> argument. This is useful for supplying and evaluating cutpoints that were found in the literature or in other external sources.</p>
<p>The <code>oc_manual</code> function could also be used to set the cutpoint to the sample mean using <code>cutpoint = mean(data$x)</code>. However, this may introduce a bias into the bootstrap validation procedure, since the actual mean of the population is not known and thus the mean to be used as the cutpoint should be automatically determined in every resample. To do so, the <code>oc_mean</code> and <code>oc_median</code> functions can be used.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">100</span>)
opt_cut_manual <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">method =</span> oc_manual,
<span class="dt">cutpoint =</span> <span class="kw">mean</span>(suicide<span class="op">$</span>dsi), <span class="dt">boot_runs =</span> <span class="dv">30</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">100</span>)
opt_cut_mean <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">method =</span> oc_mean, <span class="dt">boot_runs =</span> <span class="dv">30</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
</div>
<div id="nonstandard-evaluation-and-transforming-variables" class="section level2">
<h2>Nonstandard evaluation and transforming variables</h2>
<p>The arguments to <code>cutpointr</code> do not need to be enclosed in quotes. This is possible thanks to nonstandard evaluation of the arguments, which are evaluated on <code>data</code>. As an example of a transformation of the <code>x</code>, <code>class</code> and <code>subgroup</code> variables consider:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">12</span>)
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, <span class="kw">log</span>(dsi <span class="op">+</span><span class="st"> </span><span class="dv">1</span>), suicide <span class="op">==</span><span class="st"> "yes"</span>,
<span class="dt">subgroup =</span> dsi <span class="op">%%</span><span class="st"> </span><span class="dv">2</span> <span class="op">==</span><span class="st"> </span><span class="dv">0</span>, <span class="dt">boot_runs =</span> <span class="dv">30</span>)</code></pre></div>
<pre><code>## Assuming the positive class is TRUE</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut</code></pre></div>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method sum_sens_spec acc
## <chr> <chr> <dbl> <chr> <dbl> <dbl>
## 1 FALSE >= 1.79 maximize_metric 1.61 0.849
## 2 TRUE >= 1.10 maximize_metric 1.81 0.892
## sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <lgl> <lgl> <dbl>
## 1 0.750 0.865 0.851 TRUE FALSE 0.140
## 2 0.917 0.891 0.923 TRUE FALSE 0.0538
## outcome predictor grouping data
## <chr> <chr> <chr> <list>
## 1 "suicide == \"yes\"" log(dsi + 1) dsi%%2 == 0 <tibble [86 × 2]>
## 2 "suicide == \"yes\"" log(dsi + 1) dsi%%2 == 0 <tibble [446 × 2]>
## roc_curve boot
## <list> <list>
## 1 <data.frame [7 × 10]> <tibble [30 × 23]>
## 2 <data.frame [7 × 10]> <tibble [30 × 23]></code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">predict</span>(opt_cut, <span class="dt">newdata =</span> <span class="kw">data.frame</span>(<span class="dt">dsi =</span> <span class="dv">0</span><span class="op">:</span><span class="dv">5</span>))</code></pre></div>
<pre><code>## [1] FALSE FALSE TRUE FALSE TRUE TRUE</code></pre>
<p>Functions that use nonstandard evaluation are often not suitable for programming with. The use of nonstandard evaluation often leads to scoping problems and subsequent obvious as well as possibly subtle errors. <strong>cutpointr</strong> offers a variant that uses standard evaluation which is suffixed by <code>_</code>. It gives the same results as <code>cutpointr</code>, of course, but does not support transforming variables as above.</p>
</div>
<div id="roc-curve-and-optimal-cutpoint-for-multiple-variables" class="section level2">
<h2>ROC-curve and optimal cutpoint for multiple variables</h2>
<p>Alternatively, we can map the standard evaluation version <code>cutpointr_</code> to the column names. In this case, we would like to determine the optimal cutpoint along with the AUC of multiple variables in a data set.</p>
<p>If <code>direction</code> and / or <code>pos_class</code> and <code>neg_class</code> are unspecified, these parameters will automatically be determined by <strong>cutpointr</strong> so that the AUC values for all variables will be <span class="math inline">\(> 0.5\)</span>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">dat <-<span class="st"> </span>iris <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>dplyr<span class="op">::</span><span class="kw">filter</span>(Species <span class="op">%in%</span><span class="st"> </span><span class="kw">c</span>(<span class="st">"setosa"</span>, <span class="st">"virginica"</span>))
purrr<span class="op">::</span><span class="kw">map_df</span>(<span class="kw">colnames</span>(dat)[<span class="dv">1</span><span class="op">:</span><span class="dv">4</span>], <span class="cf">function</span>(coln) {
<span class="kw">cutpointr_</span>(dat, <span class="dt">x =</span> coln, <span class="dt">class =</span> <span class="st">"Species"</span>,
<span class="dt">pos_class =</span> <span class="st">"setosa"</span>, <span class="dt">use_midpoints =</span> T) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">variable =</span> coln)
}) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>dplyr<span class="op">::</span><span class="kw">select</span>(variable, direction, optimal_cutpoint, AUC)</code></pre></div>
<pre><code>## Assuming the positive class has lower x values</code></pre>
<pre><code>## Multiple optimal cutpoints found</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Assuming the positive class has lower x values
## Assuming the positive class has lower x values</code></pre>
<pre><code>## # A tibble: 4 x 4
## variable direction optimal_cutpoint AUC
## <chr> <chr> <dbl> <dbl>
## 1 Sepal.Length <= 5.65 0.985
## 2 Sepal.Width >= 3.35 0.834
## 3 Petal.Length <= 3.20 1.00
## 4 Petal.Width <= 1.00 1.00</code></pre>
<p>To make this task more convenient, the built-in <code>multi_cutpointr</code> function can be used to achieve the same result.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">multi_cutpointr</span>(dat, <span class="dt">class =</span> <span class="st">"Species"</span>, <span class="dt">pos_class =</span> <span class="st">"setosa"</span>,
<span class="dt">use_midpoints =</span> <span class="ot">TRUE</span>, <span class="dt">silent =</span> <span class="ot">TRUE</span>) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>dplyr<span class="op">::</span><span class="kw">select</span>(variable, direction, optimal_cutpoint, AUC)</code></pre></div>
<pre><code>## # A tibble: 4 x 4
## variable direction optimal_cutpoint AUC
## <chr> <chr> <dbl> <dbl>
## 1 Sepal.Length <= 5.65 0.985
## 2 Sepal.Width >= 3.35 0.834
## 3 Petal.Length <= 3.20 1.00
## 4 Petal.Width <= 1.00 1.00</code></pre>
</div>
<div id="accessing-data-roc_curve-and-boot" class="section level2">
<h2>Accessing <code>data</code>, <code>roc_curve</code>, and <code>boot</code></h2>
<p>The object returned by <code>cutpointr</code> is of the classes <code>cutpointr</code>, <code>tbl_df</code>, <code>tbl</code>, and <code>data.frame</code>. Thus, it can be handled like a usual data frame. The columns <code>data</code>, <code>roc_curve</code>, and <code>boot</code> consist of nested data frames, which means that these are list columns whose elements are data frames. They can either be accessed using <code>[</code> or by using functions from the tidyverse.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Extracting the bootstrap results</span>
<span class="kw">set.seed</span>(<span class="dv">123</span>)
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">boot_runs =</span> <span class="dv">20</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Using base R to summarise the result of the first bootstrap</span>
<span class="kw">summary</span>(opt_cut<span class="op">$</span>boot[[<span class="dv">1</span>]]<span class="op">$</span>optimal_cutpoint)</code></pre></div>
<pre><code>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 1.75 2.00 2.05 2.00 4.00</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Using dplyr</span>
opt_cut <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(boot) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>unnest <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(optimal_cutpoint) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>summary</code></pre></div>
<pre><code>## optimal_cutpoint
## Min. :1.00
## 1st Qu.:1.75
## Median :2.00
## Mean :2.05
## 3rd Qu.:2.00
## Max. :4.00</code></pre>
<p>If subgroups were given, the output contains one row per subgroup and the function that accesses the data should be mapped to every row or the data should be grouped by subgroup.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">123</span>)
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">boot_runs =</span> <span class="dv">20</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(subgroup, boot) <span class="op">%>%</span>
<span class="st"> </span>unnest <span class="op">%>%</span>
<span class="st"> </span><span class="kw">group_by</span>(subgroup) <span class="op">%>%</span>
<span class="st"> </span><span class="kw">summarise</span>(<span class="dt">mean_oc =</span> <span class="kw">mean</span>(optimal_cutpoint),
<span class="dt">mean_accuracy =</span> <span class="kw">mean</span>(acc_oob))</code></pre></div>
<pre><code>## # A tibble: 2 x 3
## subgroup mean_oc mean_accuracy
## <chr> <dbl> <dbl>
## 1 female 2. 0.866
## 2 male 3. 0.811</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <span class="op">%>%</span>
<span class="st"> </span><span class="kw">select</span>(subgroup, boot) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">mutate</span>(<span class="dt">summary_b =</span> <span class="kw">map</span>(boot, <span class="cf">function</span>(x) {
<span class="kw">data.frame</span>(<span class="dt">min =</span> <span class="kw">min</span>(x<span class="op">$</span>optimal_cutpoint),
<span class="dt">mean =</span> <span class="kw">mean</span>(x<span class="op">$</span>optimal_cutpoint),
<span class="dt">max =</span> <span class="kw">max</span>(x<span class="op">$</span>optimal_cutpoint))
})) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(<span class="op">-</span>boot) <span class="op">%>%</span>
<span class="st"> </span>unnest</code></pre></div>
<pre><code>## # A tibble: 2 x 4
## subgroup min mean max
## <chr> <dbl> <dbl> <dbl>
## 1 female 1. 2. 4.
## 2 male 1. 3. 8.</code></pre>
</div>
<div id="user-defined-functions" class="section level2">
<h2>User-defined functions</h2>
<div id="method" class="section level3">
<h3>method</h3>
<p>User-defined functions can be supplied to <code>method</code>, which is the function that is responsible for returning the optimal cutpoint. To define a new method function, create a function that may take as input(s):</p>
<ul>
<li><code>data</code>: A <code>data.frame</code> or <code>tbl_df</code></li>
<li><code>x</code>: (character) The name of the predictor variable</li>
<li><code>class</code>: (character) The name of the class variable</li>
<li><code>metric_func</code>: A function for calculating a metric, e.g. accuracy. Note that the method function does not necessarily have to accept this argument</li>
<li><code>pos_class</code>: The positive class</li>
<li><code>neg_class</code>: The negative class</li>
<li><code>direction</code>: <code>">="</code> if the positive class has higher x values, <code>"<="</code> otherwise</li>
<li><code>tol_metric</code>: (numeric) In the built-in methods, all cutpoints will be returned that lead to a metric value in the interval [m_max - tol_metric, m_max + tol_metric] where m_max is the maximum achievable metric value. This can be used to return multiple decent cutpoints and to avoid floating-point problems.</li>
<li><code>use_midpoints</code>: (logical) In the built-in methods, if TRUE (default FALSE) the returned optimal cutpoint will be the mean of the optimal cutpoint and the next highest observation (for direction = “>”) or the next lowest observation (for direction = “<”) which avoids biasing the optimal cutpoint.</li>
<li><code>...</code>: Further arguments that are passed to <code>metric</code> or that can be captured inside of <code>method</code></li>
</ul>
<p>The function should return a data frame or tibble with one row, the column <code>optimal_cutpoint</code>, and an optional column with an arbitraty name with the metric value at the optimal cutpoint.</p>
<p>For example, a function for choosing the cutpoint as the mean of the independent variable could look like this:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">mean_cut <-<span class="st"> </span><span class="cf">function</span>(data, x, ...) {
oc <-<span class="st"> </span><span class="kw">mean</span>(data[[x]])
<span class="kw">return</span>(<span class="kw">data.frame</span>(<span class="dt">optimal_cutpoint =</span> oc))
}</code></pre></div>
<p>If a <code>method</code> function does not return a metric column, the default <code>sum_sens_spec</code>, the sum of sensitivity and specificity, is returned as the extra metric column in addition to accuracy, sensitivity and specificity.</p>
<p>Some <code>method</code> functions that make use of the additional arguments (that are captured by <code>...</code>) are already included in <strong>cutpointr</strong>, see the list at the top. Since these functions are arguments to <code>cutpointr</code> their code can be accessed by simply typing their name, see for example <code>oc_youden_normal</code>.</p>
</div>
<div id="metric" class="section level3">
<h3>metric</h3>
<p>User defined <code>metric</code> functions can be used as well. They are mainly useful in conjunction with <code>method = maximize_metric</code>, <code>method = minimize_metric</code>, or one of the other minimization and maximization functions. In case of a different <code>method</code> function <code>metric</code> will only be used as the main out-of-bag metric when plotting the result. The <code>metric</code> function should accept the following inputs as vectors:</p>
<ul>
<li><code>tp</code>: Vector of true positives</li>
<li><code>fp</code>: Vector of false positives</li>
<li><code>tn</code>: Vector of true negatives</li>
<li><code>fn</code>: Vector of false negatives</li>
<li><code>...</code>: Further arguments</li>
</ul>
<p>The function should return a numeric vector, a matrix, or a <code>data.frame</code> with one column. If the column is named, the name will be included in the output and plots. Avoid using names that are identical to the column names that are by default returned by <strong>cutpointr</strong>, as such names will be prefixed by <code>metric_</code> in the output. The inputs (<code>tp</code>, <code>fp</code>, <code>tn</code>, and <code>fn</code>) are vectors. The code of the included metric functions can be accessed by simply typing their name.</p>
<p>For example, this is the <code>misclassification_cost</code> metric function:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">misclassification_cost</code></pre></div>
<pre><code>## function (tp, fp, tn, fn, cost_fp = 1, cost_fn = 1, ...)
## {
## misclassification_cost <- cost_fp * fp + cost_fn * fn
## misclassification_cost <- matrix(misclassification_cost,
## ncol = 1)
## colnames(misclassification_cost) <- "misclassification_cost"
## return(misclassification_cost)
## }
## <environment: namespace:cutpointr></code></pre>
</div>
</div>
</div>
<div id="plotting" class="section level1">
<h1>Plotting</h1>
<p><strong>cutpointr</strong> includes several convenience functions for plotting data from a <code>cutpointr</code> object. These include:</p>
<ul>
<li><code>plot_cut_boot</code>: Plot the bootstrapped distribution of optimal cutpoints</li>
<li><code>plot_metric</code>: If <code>maximize_metric</code> or <code>minimize_metric</code> was used this function plots all possible cutoffs on the x-axis vs. the respective metric values on the y-axis. If bootstrapping was run, a confidence interval based on the bootstrapped distribution of metric values at each cutpoint can be displayed. To display no confidence interval set <code>conf_lvl = 0</code>.</li>
<li><code>plot_metric_boot</code>: Plot the distribution of out-of-bag metric values</li>
<li><code>plot_precision_recall</code>: Plot the precision recall curve</li>
<li><code>plot_sensitivity_specificity</code>: Plot all cutpoints vs. sensitivity and specificity</li>
<li><code>plot_roc</code>: Plot the ROC curve</li>
<li><code>plot_x</code>: Plot the distribution of the predictor variable</li>
</ul>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">102</span>)
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender,
<span class="dt">boot_runs =</span> <span class="dv">50</span>, <span class="dt">silent =</span> F, <span class="dt">tol_metric =</span> <span class="fl">0.05</span>, <span class="dt">metric =</span> accuracy)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Multiple optimal cutpoints found
## Multiple optimal cutpoints found</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">method =</span> minimize_metric,
<span class="dt">metric =</span> abs_d_sens_spec, <span class="dt">boot_runs =</span> <span class="dv">50</span>, <span class="dt">silent =</span> <span class="ot">TRUE</span>)
opt_cut</code></pre></div>
<pre><code>## # A tibble: 2 x 18
## subgroup direction optimal_cutpoint method abs_d_sens_spec
## <chr> <chr> <dbl> <chr> <dbl>
## 1 female >= 2. minimize_metric 0.0437
## 2 male >= 2. minimize_metric 0.0314
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <fct> <fct> <dbl>
## 1 0.885 0.926 0.882 0.945 yes no 0.0689
## 2 0.807 0.778 0.809 0.862 yes no 0.0643
## outcome predictor grouping data roc_curve
## <chr> <chr> <chr> <list> <list>
## 1 suicide dsi gender <tibble [392 × 2]> <data.frame [11 × 10]>
## 2 suicide dsi gender <tibble [140 × 2]> <data.frame [11 × 10]>
## boot
## <list>
## 1 <tibble [50 × 23]>
## 2 <tibble [50 × 23]></code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_cut_boot</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric</span>(opt_cut, <span class="dt">conf_lvl =</span> <span class="fl">0.9</span>)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_metric_boot</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_precision_recall</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_sensitivity_specificity</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_roc</span>(opt_cut)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<p>All plot functions, except for the standard plot method, return <code>ggplot</code> objects than can be further modified. For example, changing labels, title, and the theme can be achieved this way:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">p <-<span class="st"> </span><span class="kw">plot_x</span>(opt_cut)
p <span class="op">+</span><span class="st"> </span><span class="kw">ggtitle</span>(<span class="st">"Distribution of dsi"</span>) <span class="op">+</span><span class="st"> </span><span class="kw">theme_minimal</span>() <span class="op">+</span><span class="st"> </span><span class="kw">xlab</span>(<span class="st">"Depression score"</span>)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div id="flexible-plotting-function" class="section level2">
<h2>Flexible plotting function</h2>
<p>Using <code>plot_cutpointr</code> any metric can be chosen to be plotted on the x- or y-axis and results of <code>cutpointr()</code> as well as <code>roc()</code> can be plotted. If a <code>cutpointr</code> object is to be plotted, it is thus irrelevant which <code>metric</code> function was chosen for cutpoint estimation. Any metric that can be calculated based on the ROC curve can be subsequently plotted as only the true / false positives / negatives over all cutpoints are needed. That way, not only the above plots can be produced, but also any combination of two metrics (or metric functions) and / or cutpoints. The built-in metric functions as well as user-defined functions or anonymous functions can be supplied to <code>xvar</code> and <code>yvar</code>. If bootstrapping was run, confidence intervals can be plotted around the y-variable. This is especially useful if the cutpoints, available in the <code>cutpoints</code> function, are placed on the x-axis. Note that confidence intervals can only be correctly plotted if the values of <code>xvar</code> are constant across bootstrap samples. For example, confidence intervals for TPR by FPR (a ROC curve) cannot be plotted, as the values of the false positive rate vary per bootstrap sample.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">500</span>)
oc <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, <span class="dt">boot_runs =</span> <span class="dv">20</span>,
<span class="dt">metric =</span> sum_ppv_npv) <span class="co"># metric irrelevant for plot_cutpointr</span></code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_cutpointr</span>(oc, <span class="dt">xvar =</span> cutpoints, <span class="dt">yvar =</span> sum_sens_spec, <span class="dt">conf_lvl =</span> <span class="fl">0.9</span>)</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_cutpointr</span>(oc, <span class="dt">xvar =</span> fpr, <span class="dt">yvar =</span> tpr, <span class="dt">aspect_ratio =</span> <span class="dv">1</span>, <span class="dt">conf_lvl =</span> <span class="dv">0</span>)</code></pre></div>
<p><img src="data:image/png;base64,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" style="display: block; margin: auto;" /></p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot_cutpointr</span>(oc, <span class="dt">xvar =</span> cutpoint, <span class="dt">yvar =</span> tp, <span class="dt">conf_lvl =</span> <span class="fl">0.9</span>) <span class="op">+</span><span class="st"> </span><span class="kw">geom_point</span>()</code></pre></div>
<p><img src="data:image/png;base64,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" style="display: block; margin: auto;" /></p>
</div>
<div id="manual-plotting" class="section level2">
<h2>Manual plotting</h2>
<p>Since <code>cutpointr</code> returns a <code>data.frame</code> with the original data, bootstrap results, and the ROC curve in nested tibbles, these data can coveniently be extracted and plotted manually. This offers additional ways of tweaking these plots as well as the possibility to plot results that are not included in <code>plot</code> or one of the other plotting functions. The relevant nested tibbles are in the columns <code>data</code>, <code>roc_curve</code> and <code>boot</code>. The following is an example of accessing and plotting the grouped data.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">set.seed</span>(<span class="dv">123</span>) <span class="co"># Some missing values expected</span>
opt_cut <-<span class="st"> </span><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">boot_runs =</span> <span class="dv">50</span>)</code></pre></div>
<pre><code>## Assuming the positive class is yes</code></pre>
<pre><code>## Assuming the positive class has higher x values</code></pre>
<pre><code>## Running bootstrap...</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">head</span>(opt_cut<span class="op">$</span>data)</code></pre></div>
<pre><code>## [[1]]
## # A tibble: 392 x 2
## dsi suicide
## <dbl> <fct>
## 1 1. no
## 2 0. no
## 3 0. no
## 4 0. no
## 5 0. no
## 6 0. no
## 7 0. no
## 8 1. no
## 9 0. no
## 10 0. no
## # ... with 382 more rows
##
## [[2]]
## # A tibble: 140 x 2
## dsi suicide
## <dbl> <fct>
## 1 0. no
## 2 2. no
## 3 1. no
## 4 0. no
## 5 0. no
## 6 0. no
## 7 1. no
## 8 0. no
## 9 0. no
## 10 0. no
## # ... with 130 more rows</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">opt_cut <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(data, subgroup) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span>unnest <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x =</span> suicide, <span class="dt">y =</span> dsi)) <span class="op">+</span><span class="st"> </span>
<span class="st"> </span><span class="kw">geom_boxplot</span>(<span class="dt">alpha =</span> <span class="fl">0.3</span>) <span class="op">+</span><span class="st"> </span><span class="kw">facet_grid</span>(<span class="op">~</span>subgroup)</code></pre></div>
<p><img src="data:image/png;base64,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" style="display: block; margin: auto;" /></p>
</div>
<div id="benchmarks" class="section level2">
<h2>Benchmarks</h2>
<p>To offer a comparison to established solutions, <strong>cutpointr</strong> will be benchmarked against <code>optimal.cutpoints</code> from the <strong>OptimalCutpoints</strong> package and custom functions based on the <strong>ROCR</strong> and <strong>pROC</strong> packages. By generating data of different sizes the benchmarks will offer a comparison of the scalability of the different solutions. When selecting cutpoints, the <code>optimal.cutpoints</code> and <code>cutpointr</code> functions are more convenient and offer additional features in comparison to the functions based on <strong>ROCR</strong> and <strong>pROC</strong> but the latter ones are still useful for benchmarking purposes.</p>
<p>Using <code>prediction</code> and <code>performance</code> from the <strong>ROCR</strong> package and <code>roc</code> from the <strong>pROC</strong> package, we can write functions for computing the cutpoint that maximizes the sum of sensitivity and specificity:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Return cutpoint that maximizes the sum of sensitivity and specificiy</span>
<span class="co"># ROCR package</span>
rocr_sensspec <-<span class="st"> </span><span class="cf">function</span>(x, class) {
pred <-<span class="st"> </span>ROCR<span class="op">::</span><span class="kw">prediction</span>(x, class)
perf <-<span class="st"> </span>ROCR<span class="op">::</span><span class="kw">performance</span>(pred, <span class="st">"sens"</span>, <span class="st">"spec"</span>)
sens <-<span class="st"> </span><span class="kw">slot</span>(perf, <span class="st">"y.values"</span>)[[<span class="dv">1</span>]]
spec <-<span class="st"> </span><span class="kw">slot</span>(perf, <span class="st">"x.values"</span>)[[<span class="dv">1</span>]]
cut <-<span class="st"> </span><span class="kw">slot</span>(perf, <span class="st">"alpha.values"</span>)[[<span class="dv">1</span>]]
cut[<span class="kw">which.max</span>(sens <span class="op">+</span><span class="st"> </span>spec)]
}
<span class="co"># pROC package</span>
proc_sensspec <-<span class="st"> </span><span class="cf">function</span>(x, class,
<span class="dt">levels =</span> <span class="kw">c</span>(<span class="st">"no"</span>, <span class="st">"yes"</span>), <span class="dt">algo =</span> <span class="dv">2</span>) {
r <-<span class="st"> </span>pROC<span class="op">::</span><span class="kw">roc</span>(class, x, <span class="dt">algorithm =</span> algo)
sens <-<span class="st"> </span>r<span class="op">$</span>sensitivities
spec <-<span class="st"> </span>r<span class="op">$</span>specificities
cut <-<span class="st"> </span>r<span class="op">$</span>thresholds
cut[<span class="kw">which.max</span>(sens <span class="op">+</span><span class="st"> </span>spec)]
}</code></pre></div>
<p>The benchmarking will be carried out using the <strong>microbenchmark</strong> package and randomly generated data. The values of the <code>x</code> predictor variable are drawn from a normal distribution which leads to a lot more unique values than were encountered before in the <code>suicide</code> data. Accordingly, the search for an optimal cutpoint is much more demanding, if all possible cutpoints are evaluated.</p>
<p>Benchmarks are run for sample sizes of 1000, 1e4, 1e5, 1e6, and 1e7. For low sample sizes <strong>cutpointr</strong> is slower than the other solutions. While this should be of low practical importance, <strong>cutpointr</strong> scales more favorably with increasing sample size. The speed disadvantage in small samples that leads to the lower limit of around 25ms is mainly due to the nesting of the original data and the results that makes the compact output of <code>cutpointr</code> possible. For sample sizes > 1e5 <strong>cutpointr</strong> is a little faster than the function based on <strong>ROCR</strong>. Both of these solutions are generally faster than <strong>OptimalCutpoints</strong> and <strong>ThresholdROC</strong> with the exception of small samples. <strong>OptimalCutpoints</strong> and <strong>ThresholdROC</strong> had to be excluded from benchmarks with more than 1e4 observations and <strong>pROC</strong> from benchmarks with more than 1e5 observations due to high memory requirements and/or excessive run times, rendering the use of these packages in larger samples impractical.</p>
<p><img 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KBdggAGAACgXbLOyXyFQqFSqdRxZ3t7ewzD6urqTNqlZtutr683c6N8Pp/H49XU1Ji5XVtbW4lEolKpzNkol8u1s7Orrq42882OPB6Ppmm5XG7ORkmSdHR0rKurUygU5myXoiiSJCUSiTkbRQi5urqKRCKpVKrXIabrD7AI6wxgOI4TBKHjzuyk9brv31owDDN/o+xyjhZ5seZfSVL9Ys0cwCzyJrON6vXJb612zd+oumnd21UvTQCsiXUGML0W+GD/BmxsbEzWnae2a/5GSZLEMMwi7fJ4PDMHEvX/rPnbZRhG3+VgjMT+DuNyuU+ufmdSbABrYeki06EoSvdfRWY+IQbmYZ0BTCqV6juEKBKJTNqlZts1f6PsEKL527XUECJFUSKRqIMMIXK5XIlE0kGGEHk8nkwm02sIEVgfSOIAAADQLkEAAwAA0C5BAAMAANAuQQADAADQLkEAAwAA0C6ZPAtRpVK9/fbb69evt7e3Z0sSExPz8/PZvNuRI0fOnj0bIZSamrpjxw6pVBoREREfH8/mweteCAAAoKMx7RnY8ePHExMTy8vLNQvv3r27c+fOQ4cOHTp0iI1eYrE4KSlp0aJF27ZtE4lEx44d06sQANDR7NxtgTvPQFtj2gDm4+MzefJkzTsrJRIJTdN8Pl9zt5SUlKCgID8/P4IgRo8efenSJb0KAQAd0JGjdpbuArAw0w4hhoWFof/OqVNeXo7j+Jo1awoLCwMCAmbOnOnu7l5VVeXm5sbu4ObmVlVVhRDSvZD1999/Hz9+nH0cHx/v5eWlYyfZGRPs7Mz9x0CSpEUaxTDMIu3iOG6RKZ3s7OwsMhMHl8s1Z6PsmDyfzzfznEnsNBxmnnbkwCEe+0D3TzLMxGGVzD0TB0EQw4YNGzduHI7jhw8fTkpKWrt2bZN9mv260Vook8nUc+MyDKPXzHsWmakPPfqGNScMwyzyYrFHzNko+zLN3y7bnJnfZLZR8//nWuoTxTpwiPfSJJ0ik0UmuwKmZu4A5unpOX36dPb32gsvvHD06FGGYVxdXTMyMtgdqqqq2EmjdS9kjRgxYsSIEexjoVCo++zyHXA2evO/WAvORl9fX99BppJydHRsbGy0+qmkTvzlprmp+4fZ1tbWBN0BlmTu300XLlz44IMPGhsb5XL5uXPnQkJCMAzr1atXQUFBeXk5wzCnTp2KiYlBCOleCADoIJpEr2ZLQMdh7jOwuLi40tLS+Ph4DMO6deuWkJCAEBIIBO+///7q1atVKlVwcPCYMWP0KgQAdGQn/nIbOaLS0r0AFoCZeXTFPGBBy6eBBS3NABa0NJEWTrZ0CWCwoKX1gZk4AADtHgwkdkwQwAAA7QCEKPAkCGAAAGsAEa4Dss5rYHK5XPfbPgiCwDBM92tmrYUkSfM3ShAEjuNmvkzCtkvTtPlvZCYIwvwvlr0pysw3FLN3EyuVSjO/yex9YOZ5sUXFP/x7/a3oPlu7+r9BUZRKpdK9XZlMBmn01sfcWYjmIRaLIYmjWXAfmBnAfWCm0NCQk3rjPU/PcS7OE+vq6lxdXSUSiVQq1b0GCGDWB4YQAQBtnUolTs+YxeV69Qj9wtJ9AW2IdZ6BAQCsSXbOIrGktH/fEyQJE/iCxyCAAQDatLI7P9+9t79n2EY7ux6W7gtoWyywoKWRa1fCgpYAdBwiUU5u3sdenhM6dZpm6b6ANsfcC1oauXYlLGgJQMehUjXeSJ/J43qHhSZZui+gLTL3gpZGrl0JC1oC0HFkZS+SSG5HRuwgSUggBM0w94KWRq5d2cKClleuXDl37hz7eMaMGe7u7jp2kl3bxfwptiRJWqRRDMPM3y5FURhm7psO2Q+era2tRRa0NPPgNnvjo42NjZkX0sRxnL3frtVrvlW0/d79A316b/Py6tvsDlwuV/eFNGFBS6tk4SQOw9aubLawuro6JyeHfaxQKHT/ZLN/+WZeUhY9uvPUzI1aZP1c9OjFmv8eW/Tf30/mwa49bZEFLdkb1c3crik+UXV1mRk3F/v6Tg0MeP1p+7BTEOhYoZnvQQTmYe4vMiPXrmxhQcsxY8aoV1cRCoVCoVDHLnXAG5l1f3NaiwVvZK6rq+s4NzKLRCIruJFZpWq8fHUy38a3W+Dap31WXV1dxWKxXjcyCwSCVuogaCvMfSOzkWtXwoKWAFi9rOyFUundiPDvCMLG0n0BbZq5z8CMXLsSFrQ0gFvmVy08W9ljntl6AoBWt8u+v3f/YM+wTba2wZbuC2jrrHMyX1jQUlNbCGCwoKWpWceClg2i7CtXn/P2mtgjbEPLe7q6uopEIr2GEGFBS+sDcyECANoEpVKUlj5TIPAP6b7a0n0B7QNMJQUAaBOychZKpff69zsFl76AjiCAAQAsr/T2d/fvH+rZY7OtoJul+wLaDRhCBABYWENDVl7+ss6dX+7k/ZKl+wLaEwhgAABLUijqUtNeFQi6hgR/bum+gHYGhhABAJaUmfWeXF7Vu9dfcOkL6AsCGADAYkpvb3tQcSy85zdw6QsYAIYQAQCWUVd3Iy9veZfOr3p7TbJ0X0C7BGdg1o+9VXnRvXPH6gsLo+ba2Qhqamos3SnQ0SkUdWkZs/iCgJDuKy3dF9BeWWcAs7HRYzCdnUjbzs7OZN15artma1RKK3+rL3zVPcKWx8cwzCIvlp2j3ZyNsvOy29nZWWQ5FTMva8LOy87n82maNme7hq5vwFy5OluhqBk86Hc7OzfDmubxeJprDbYMllOxStYZwKRSqe5TSdnZ2WEYJhKJTNqlZts1W6MHhXm1Ssl4foBcLudyueZ/sQKBQCqVmn8qKYqiRCJRR5hKiiAIDocjkUjaxVRSxSVb7tw9EhG+FcM6GfZpfDcHX9hF7oL0mEoKWB/rDGAMw+j7nWWROSHN1uju2qzefM9QngvboqVerJnbVb9Y87dr/kY1mzZ/i3o1Wld3I79ghU+X1708Jxrc2+wGulbBOJNWOJUr0B0kcVi/Mnl9sujOVMcQS3cEAKRQCNMyZgn4gd2DP7N0X0C7BwHM+u0V5nAwYpwDpCkDi2MysxLk8urIiB04zrN0Z0C7Z51DiECNQcx+Ye4YhwAHwqw5BQA8qaRky4OKPyN6bhUIAi3dF2AN4AzMyl0U3SmR1011DLV0R0BHV1eXml/4ua/PLC+viZbuC7AScAZm5fYIs7tQdjGCzpbuCOjQFAphWvosgSAouNun+h4rpbE8MdaksEGJchuRiPjPT3BXiunEhbSODgQCmDWrV8n+qL/1rmtvHGv69w+AGTE3s+YplLV9+hww4NLXxTp87W2OZkmNErsrpT8vIvj4fwbGewhUGwLhfq8OBAKYNTtcly+lVZMf5R/arfsMIaRAyA6hhkWfWLRroAMpLvm6ouJ4VOQPAn6AAYcPd1INd3p8n9k/9cSETK4rF/3SUxVAwn1gHRoEMGu2R5gzyLazL8cePYpeauwmhDFgasK6lILC1b4+sz3cxxhfW5kMfy2XG2FLkxSFkFnviwdtkAUCWGJiYn5+PjvzzciRI2fPno0QSk1N3bFjh1QqjYiIiI+P53A4ehWCJxXIalPE5Vs6P4eeiF4AmIdCIUxPn21nGxocvMz42kQqbHo214ZAP4XIZhfqOokUsGIWyEK8e/fuzp07Dx06dOjQITZ6icXipKSkRYsWbdu2TSQSHTt2TK9C0KydtVn2BPd5+5YGbSCwAVNibmbNU6rqIyO+wzFjf2jSDHo7n3tbhu0MkbpRkKkBEDJ/AJNIJDRN8/l8zcKUlJSgoCA/Pz+CIEaPHn3p0iW9CsGTlAx9UJg7waGbDU5ClAIWUVT8VUXFibDQDTY2vsbX9lkp569aYks3WSjfrLMVg7bM3EOI5eXlOI6vWbOmsLAwICBg5syZ7u7uVVVVbm4PZ6R2c3OrqqpCCOleyMrPz8/MzGQf9+/fX/cJ19nptHk8c88LgOO46Rr9Q1hYoRS/5hHJ4/EUS1dRK5Y8bU/zvHCCILhcrpknSmenSOfxeGaeHpCiKIZh2LnwzYZtjsPhEARhznYJgmj2k1xb+2/hrbUBAe/4+b5ofCu772Nf38WXBzLjvSmEHg4ekiSp+6dX99m9QTti7gBGEMSwYcPGjRuH4/jhw4eTkpLWrl3bZJ9mv260Fl65cmXTpk3s4507d3p5eenVMVtbW732bxWma3RPSXaYwH2wRxC7KbNEH5rQfeWL1iUQCCzSrkXotZBQK2qydoxcXnM99XUnp8i+0V/guLGDh5dr6Hm5ssmdiKVhHPXtIIlBqhAngq9zsNZ3vnzQLpg7gHl6ek6fPp39afzCCy8cPXqUYRhXV9eMjAx2h6qqKldXV4SQ7oWsqVOnjh8/nn2sUqmqq6t17BK7nEp9fX0rvDx92NnZNTQ0mKLmSqX4z+qCpZ4D1G/C02KU6INPRTq/UcawtbWVSCTmX07F1ta2pqamgyyn4ujoWF9f3waWU2FSbrwslwv79Pq1ttbYT3iZFHshnRfCZ77wldRUP/5/HOPp0tjYWC3VI43eUtEdmI65r4FduHDhgw8+aGxslMvl586dCwkJwTCsV69eBQUF5eXlDMOcOnUqJiYGIaR7IYvD4dg/gmEYozP2cN33by2ma3RfbQ6DmIkOweqSZtPlGxZ9YqIOtB0W+Z+1CEt9jJ90q2hDRcXJHqEbbWx8jKxKpETTs7kkhn4OkXIxWvMpA16sab/agCWY+wwsLi6utLQ0Pj4ew7Bu3bolJCQghAQCwfvvv7969WqVShUcHDxmzBi9CkET+2pzRtj5u5P/yZSRD4ylrl6k53/Ec3auqamxVN+AdautvVJQuNbPN97D43kjq2LTDouk2O89pV4cCD+gGZhV/jARCoW6X7Nlz9jq6upM2qVm2zXFuGWKuHxk0f5ffMaMtO/6uJRhbLdvUnXywSZN4/F45g9glhpCtLOzq66uNvOH3CJDiCRJOjo61tXVWXAIUa6ovnxlCJfr1Tf6d+Mvfa0o5Wy6Q20Plr3g2szfsqurq0gkkuozhKh5xQFYB5iN3trsEea4kfyhdv9JXCaLC7E6oTyil6V6Bawew9AZGW+rVJLIiO+Mj177K8iv7lAf+iqajV4AsCCAWRUpozxSl/+SYwiF/Sc9i0pLoZ1dVZ26WKpjwOoVFW+oqj7fI2yjDc/Yj9m/9fj7hZz/uSjf6wwz84KWQACzKr/XFdapZFMezd7LwhrqyeJCRWRvBHPSA9Ooqb1ceOv//P3meLiPNrKqOzLs1VxeiIDZ3E0On1fQMghgVmWPMKcP3yuY56xZyLl5g8FwRWi4pXoFrJtMVpme8ZaDfWRQ4IdGViWlsddzeQSGfgmR2uBWeHketC4IYNajTNFwSXRn6n9PvxDDUJnpqu6hDNwEA0yAYejrqbNoWhoRsd3IS18MQnMLOLli7OcQSDsEOoEAZj321GZzMOIFhyDNQrKoAKsTyiN6W6pXwLoVFK6rqDjbI+wr4y99rSrlHK0ivwqSR9nCbIdAJxDArASDmP3CnP85BDoQ/5nUh0pPpV1cVd6dLdUxYMVqai/nF/xft6D3PdxHGVnV0Wpy4x1qsY9iPKQdAp1BALMSF0RlpfL6qU6hmoUP0zciIH0DtD65vCo94y1Hx14h3ZcaWVW6CJ+bzxnjopzfBdIOgR4ggFmJPcKcLpTdAH4nzUIq4waDQ/oGaH0MQ2fcfJumZb2jvsdxo6ZpLpdjL+fwgmyYryHtEOgJApg1qFfJ/qy/Nc0pDNc806JpTmaaKjgM0jdAq7tVtL6q+u+eYV/Z2Bh16UtKY6/k8GgEaYfAEOaeCxGYwqG6PBmtesmxu2YhWVyI1dfB7Bug1dXUJN8q+iKga4K7+0hj6mEQereAk92IHe0p9eZC9AJ6gwBmDfbU5jxr26ULx16zENI3gCnI5ZXpN+MdHKICun5gZFVrSqnfqsit3WS97CDtEBgChhDbvVxp9Q3Jg+bTNyL7QPoGaEXspS+GVkaGG3vp6/dq8ss7nIVd5BPcIO0QGAjOwNq93cJse4I7yq6rZuHD9I2QnpbqFb+7ljkAACAASURBVLBKhbf+r7rmYu9ee3k8/VY8byKjEZ+Tz3neRbXIx6xz5wMroyWA3bp168yZM//++295eTlN015eXtHR0cOGDQsICDBP/0DLlAx9SJj3omOwDa7xX8mmb3SH9A3QmmpqkouKN/j7Jbi6DDGmngdy7OUcXqAN83U3GYwPAGM8dQjxxIkTcXFxkZGRW7dura+vj4iI6NWrl0gk2rZtW1RUVFxc3IkTJ8zZUdCskw3FFUpxk+mjyKICrL4OZt8ArUgur0zPeMvJsW9QoFGXvqQ09kouT0mjX0KkfEg7BMZp/gzsxRdfvH37dkJCwokTJzicpvObyeXygwcPfvrpp999993BgwdN30nwVHtqs0N4LpE2HpqFkL4BWhfD0Ok34xlER4R/i2GGX3dgEEoo5GSJsN96SjtB2iEwWvOfxQULFvTr1w97yvV/Doczbdq0qVOnXr161ZR9A1pUKsVnRbc/8RygWYjV15Elt2RDnrNUr4D1KShcXVOT3DtqL5fraUw9625ThyvJb7rJekPaIWgNzQ8h9u/fXx29amtrf//99y+//LK2tjY3N1e9UDqGYf379zdTN0Fz9tbmMIiZ4BCsWUjdZGff6GGpXgErU11zsbhkU1f/+a6uRl36OlZNri/jvN9Z/iKkHYJWomU0ICcnJzY2FiFUVVU1fvz41atXX758+a+//vL39zdH70CL9gpzRtp3dSf5j4tompOZruwexvAgfQO0Apm8IiMj3smxb2DAQmPqudmIz8nnjHZRLYa0Q9B6tNwH9v777w8cOLCsrMzOzg4htGHDhqCgoPnz55ulb6Al/4rv58tqmk/fCIfZN0ArYBhlWvrMR5e+CIPreSDHZuTwutow33ST4ZB3CFqPljOw5OTk06dPq/M4nJycFi1aNGHCBNN3DGixpzbbjeQPsfXRLKTSU1Su7nQnY1dmAgAhVFC4Rii81rvXPmMufckY7NVcnpJGOyHtELQ2LWdgTk5OUqlUs0QulwsEAlN2CWgnZZRH6wunOIVQGr+Lsfo6sqRIAZMfgtZQVXWmuGRTQNeFri6xBlfCIJRQwMkUYT+FQNohaH1aAtj//ve/jz/+uLKykt3MyclZuHDhqFHGLl4HjPSbsKBOJZvy3/FDdvYNZSjMvgGMJZXeS7/5jpNT/4CuRl0vSCrj/FpJfhko7wNph8AEtASw//u//3Nzc/Py8qqrq4uMjAwNDfXy8lq/fr15OgeeZo8wJ5rv1Y3r/LiIpjmZN5Tde0D6BjASwyjTM97EMCKip1GXvo5VE+vKqITO8knukHYITELLNTCBQHD48OGcnJzMzEyVShUSEhIeHv60+8OAedxW1F9pvJvUKU6zkLyVjzU0wOIpwHgFhauEdf/27rWfy/XQvvdTZDbic/K5I51VH0LaITCZ5gPYk3cod+nSBSEkkUj++ecfhFC/fv1M3TPwNLtrsjkYMdY+ULOQSk9VubrTMPsGME5l1emi4s1BgYtdXQYbXEmFApuRw+vCYzYHQdohMKHmA5jWO5QZBq7HWgbNMPvrcl9wDHIguOpCrL6OLC2SxsHsG8AoUum9jJtznJ0HdvV/z+BKZAz2ag5PokK/9ZDZEfBFAUyo+QDW3uMTjuMEoevYPTsiqvv+rQXDMAMavdBQWiavn95lhOaxVGYag+NMjwitFeI4jiz0YtmmzUn9Ys38ebbIm8w2qtcnvwmGUabffBPDiF6R20my6QyoLbSr2SiD0Pu5VEYjfqiHvKsAQ8iEb4JeL5amIYvECuk9L2dKSsqiRYvOnj1rit60licnIG4B+zdgY/aVRwiCMKDRvXdy/biOw9yCMPRoaIamsZs3UM8onpNzi4cihBBJkhiGmf/FkiTJ4/HMHEjU/7Pmb5dhGJI062J77O8wLpdLUQauM5lx80Oh8N9BA485OvrpfhQbwNTXxdcWoQMVzDdhaJgXt+UDjUdRlO6/itRz4AFrouVv7MaNG2+++WZxcbG6pKGhITo62sS9MpZUKlUqdU18sre3xzBMJBKZtEvNtqtvo/Uq2e81+e+7RzeKGtWFZEGuTX19Y2g4rUNtfD6fx+OZ/8Xa2tpKJBKVSmXORtlvc5FIZOYAxuPxaJo28zcmSZJcLlcikSgUhiRNVFadyi/Y2C3oQz4/Wq+PB0VRJElKJBKE0B/VxGeFvHmdFZMc5ab+iPF4PJlM1uQuVdDRaPn9Mm/ePB6Pt2HDBoIg1q1b99lnn9nb2//000/m6Rxo4qAwT86oJjt01yyk0lNUbu60dydL9Qq0d1Lp3ZuZc12cY/z95hlcSVYj/k4+d4ijaokPnOsAM9F+Bnb06NG4uLgzZ854enqOGjWqtrY2MTHxwIED5ukf0LRHmDPYzqczx05dgtXXkaXFkL4BDEbTirT02Rgiw8O3GnzXV+WjtMNt3aQEpB0Cc9FyBoZhGHvxs0+fPpcuXUIIxcbGnjt3zhxdA/+VI61OkzxoMnsvlZ7C4LgyBGbfAAbKL/isrj41PHwrl+NuWA1yGs3M5YppbGeIzN6sF/5AR6clgPXt23fFihUFBQWRkZG//vprTU3N1atXzZ/DBhBCu2qzHAjuKPuuj4vYxVNCejA8nuX6Bdqxysq/Skq/DQxIdHEeZHAl7+dh10XE98FSPx5k+gGz0hLANm3a1NDQ8Ouvv/bt29fFxcXT03PhwoVvvfWWeToH1OS06qAw70XH7jyNBd3JwnxM1CAP723BjoH2SyK5czPrXVfXuK7+hl/6+vI28dNdbG1X2UAHs2boAIC0XgMLCQlJTU2laRrH8ZMnT547d04gEAwebPgt+sAwfzUUV6skTccPMyB9AxiIphUZN9/EcV5Ez28wzMBb9M7UEiuLiQRf5mUPmO0QWICWD65UKv3www/feOMNhBCfz09KSjp8+DCbMgvMaY8wJ4TnEmHz+CoFm76hiIDTL2CIvPxlwrobET2/pSjttw82X4MYn53HHeLEfBbYvuc9AO2XlgC2YMGCHTt2DBw4kN184403jhw58uGHH5q+Y+CxSqX4rKh0ulOYZiGVnsLgBKRvAANUVJ4svb09KHCJk5OBk5rWKLHpOVwvLvN9qALSDoGlaAlgBw4c+OKLL2bPns1uzpgxY926dZBDb2Z7arNxDHvRMfhxEaRvAENJJHduZrKXvuYaVoOCRq/nchtUOKQdAsvS8ulTqVQBAQGaJZ07d4a7381snzB3hK2fC/F4/ieyMA8TNcDiy0Bf7KUvgrCJ6PkNQgaeOi0u4v7bQOwPlfrzaJPOdghAy7ScgcXGxi5fvrympobdFAqFK1asgCQOc/pXfD9fVjOt6fhhqsrNXeUF6RtAP7l5nwjrbkSGbzf40tfmu9QvD8jV/rIYSDsElqblDGzz5s3Dhw/v3LlzaGgoQRDZ2dmenp5tfCZfK7O7Ntud5A+x9VGX4HVCsrRIOmyUBXsF2qOKihO3y3YEd/vU0fEZw2o4KyRWlnLivRWvekLaIbA8LQHMy8srPT39zz//zMrKUigUH3zwwdixY/Wa6x0YQ0wrfqsveMM5nNRIdCYzUhmShPQNoBexpCQjc46b61B/v3cMqyFfjM/O4z3roPrUD2Y7BG2C9vs//vnnn9DQ0MTExF69eu3cufPzzz+HhQnM5mhdYYNK/pLm7V/q9A2uyZerAFaDZuRp6bNI0i6859eGXfqqUaDpOVwPit4eLCUh7RC0DVoCWFJS0sCBA9PS0sRi8SuvvMIwzI8//rhkyRLzdA7sEWY/w/cK4jqpS6iH6Rtw+xfQQ17eJw0NWZHh2wy79KWg0Rt5vDoVvitU5gBph6DN0BLANmzYsHbt2gkTJuzfv9/Dw+Pw4cPr16/fv3+/eTrXwd1W1F9pvNc0fSMjVeXmofL0tlSvQLtT/uBo6e0dwd0+MfjSV2Ix91oDsSOYTTsEoK3QEsAqKytjY2MxDDt16tTIkSMxDPP393/w4IF5OtfB7arJssHJFxwC1SV4nZAoKVJEwukX0JVYXJyZ9b6b2wg/33jDavjmLvVzObnKXzYI0g5BG6NlOKBbt2779+93dXX97bff2FVUzp8/36kTZG+bHM0w++ty/2cfaIs/TpmhMlIZkoL0DaAjmpGnZcwiSbueYZsMu/R1Tkh8VsqZ7aV4DdIOQduj5Qxs+fLlGzduDAgI6NWrV3R09Oeff75o0aK5cw28gR/o7u/GsjvyhmlOoY+LaJqC9A2gj9zcj0SinMiI7RyOIZe+CiT47DzeIAfVZ/6QtwXaIi1nYOPHjy8oKCgsLOzfvz9CKCYm5uzZs0OGDDFL3zq03bVZPpR9P8Hja10UzL4B9FH+4LfbZT+GBK90dIg24PBaBZqezXWj6O8g7RC0Vdozivz8/Pz8/NjHMAeHedQqpcfrixa4P4NpDPtQ6ZC+AVqyczc29nkh+1h96cvX900DqmLTDoUq/ES4BNIOQZtl4DpAwKQO1eUpGHqyY3d1CV4nJEqLFFF9LNgr0F7QtCwtfSZFOYT32GzYpa8Pi7lX64nvukm7QtohaMMggLVFe4TZsbY+nSg7dQmVnsqQlLJ7Dwv2CrRlx/50Qgj9/ocjQignd4moMTe85zaKctJ2XDO+vUf9VE6u8pc96whph6BNgwDW5uTIqjMklf9J31CpqMw0ZSikbwDtysuPlN35uXvwZ06Ohlz6OldLLCvhzPJSvu4FaYegrdMyvJ2ZmdmkhCAId3d3JycnHIfgZxI7a7KcSN5I+67qEqowD2sUwewb4GlO/OWmfpyWMdvd7TmfLjMNqKdQgs/O5w10UK3wl7Ve7wAwFS0BrF+/fhKJhKYfj4MTBMEwDI/He+WVV9asWePg4GDiHnYsclp1SJg30SGYiz1eZunh7BseXhbsGGizNKMXq6LypAGXvti0Q1dIOwTth5azqOPHj/v7+//www/5+fmFhYU7d+7s3r17SkrK5cuXMzIyFi5caJ5edhwnRcXVKsk058fjh3idkCgtVkQZMhwEgI4UNJqVz6tUYD92lzpC2iFoJ7R8VBMSEtatWzd+/Hh2MyAgQCAQzJ07Nzk5eevWraNHjzZ9DzuW3bXZIVyXnrzHv6mp9BSGpJTdw1o4CnRYT55+qctHjqjUvZ6PSriX6oidIdLufKaVugaAyWkJYEVFRV5e/xm58vDwuHnzJkLIycmpurrasFZVKtXbb7+9fv16e3t7tiQ1NXXHjh1SqTQiIiI+Pp5dckz3QutQoRSfF93+zHPQ4yKVispMh/QNYFLf3ad+uE+u6Sob5gRph6A90TKEOHDgwM8//7y+vp7drK+vX7VqVd++fRmG2bVrV48ehmR1Hz9+PDExsby8XF0iFouTkpIWLVq0bds2kUh07NgxvQqtxu7aLBzDJjh2U5dA+oa+mIsU/S9BpxB0CqG4hsSXFOxjOoVQJZMoh9BeRfvxtNMvXZ5VOy8klhZzpnsoZkLaIWhvtASwrVu35ubmdu7cOSYmZtCgQV26dLl58+bWrVsPHz68bNmyVatWGdCkj4/P5MmTKYpSl6SkpAQFBfn5+REEMXr06EuXLulVaDX2C3NH2vq7EDbqEio9ReXpDekbulNdwpnLFKrGUS3O1GCqKoapwVAtju7jzN+k6kbHSp3VGsMKJfjsPF60ner/usJsh6D90TKE2KVLl+zs7CNHjmRlZSmVynfeeWfChAlcLpfP5xcXF3t6ehrQZFhYGEKIIB7/Fq6qqnJze/iX5ubmVlVVpVchKzU1VR3Pxo0b5+rqqmN/CILAMEwgEBjwWoxBEIRmo5cbygpktev8RzwurK3Bb5cwYye0Yt8oirLIiyVJ0sbGhmFMfn1FZEsT/oiuJvivEiSP4HA4lJRW1TKN39JUbwwjMBuBycec2UxdzZ9oJjJxvDgl9Z3bZbtiBh7zcB/M5XJlMplmznDLhEr0ShpypND+3oQTZeBHAn/EsMONweVyNb9GWqZQKEzaGWAR2vONCIJwc3Pz9PRUKpUeHh7sn6VhoUtHzX7NaS0sKSk5ffo0+3jkyJG6Xxtj//bMfy0Nx3HNRnfVZHXi2o9y7UZgD78L6BvXaYpDRUWj1usbjuMYhlnkxeI4boYAhuEyu7Ec8Sml9BfaYRaJEMJFZMM2uWAUhWikLKM5HJPHFQzD0FM+sa0rL39TSemP0X2+6eQ9lG2Uoigd21UyaEaq4oGMSY6hvASGZ81jGIZhmEUCGEEQurere1xvRRiGXblypV+/flr3LCkp8ff337JlS3y8gcu2dUxaAtiDBw9GjRqVnp7u6+uL43hJSUlERMTx48fd3d1bsROurq4ZGRns46qqKvbkSfdC1oQJEyZMmMA+FgqFtbW1OrZub2+PYVhdXV1rvBQ92Nvbqy8uimnFgYqsWS4R9cJH3VCpbK9fVYb0aBCLkVjcWo3y+Xwej6f7m9NabG1tJRKJSmXyHAGViltXX4fiGPo4VfOtymmqbc0mCR6rlASI6TSCkWKKWpGp+8Dj8WialstNOyhXK/wnLX2xT5fXXJwn1dbWkiTp6OjY0NCg46nG4iLu39XkLyFSL0WjMR8HiqJIkpRIJIZXYRBXV1exWCyVSnU/xPwDD1rFxsaOHDkyMTHR3t5+wYIFERERlu5RO6Pl90tCQgKPxysuLi4qKiosLCwqKiJJ8v3332/dTvTq1augoKC8vJxhmFOnTsXExOhVaAV+qy8U0XLN2XupwjxM3AiLpxgIQ/goBWKw6tWNxLMqPNzakuskkrIbN161t4voHvy5AYfvekB9f59c4S8fDmmHbYOzs/P69evZVauA7rQEsHPnzq1evdrHx4fd9PHxWbt27ZkzZ1q3EwKB4P3331+9evW7777L5XLHjBmjV6EV2F2T1Y/vHcR9PPUqpG8YiSnD6UKEcTEmC0dKq5pYgqalN9Jfx3AqKvJ7HNd7NPhKPfFBEWequ2K2F1wW0tuRI0ciIyNtbGx8fX2TkpLYwoqKiqlTp3p4eHh6ek6dOvXBgweah4hEIgzD1NPyFRYWYhhWVVXVp0+fv//++8MPPxw2bBhCiMfjnT9/voXaeDzelStXJkyY4OTkFBAQcPDgQbO96jZLyxCi7pej9LV//37Nzd69e/fu3TRZXPfCdq1UXv+P+P7GzsPUJbiwlrhdIh1hJeHZ/JhqXPUzhdkg1yX8qsP1qr0kMcVqcsSZm5nzRKLcvtG/c7l6X4ouleKv5XB72arWB0Daod5KSkomTZo0b968bdu2nTt3buHChf379+/Xr9/zzz9PEMS+ffswDEtMTBw1atT169e1Xp+7evXq0KFDR4wYkZiYqC6kabqF2uLj45csWfLZZ5+tXLlyxowZzz//vI2NzdNbsH5aAlhcXFxiYuL+/fu7dOmCECorK0tMTIyLizNL3zqKnbWZNjg51j5AXQKzbxiDacBUP3IQjXhvINwOI0YrVX+Sqr0kFmINc0wUFX91v/xwzx5fOThE6XtsgwqbkcOzJZgfu8s4HeuGgtZRWFioVCrnzJnTtWvX6OjowMBADw+Pixcv3rhxo6ioiB2p2rdvn7+//4ULF2JjY1uujSRJDMMIgtDMpWy5tokTJ7700ksIoeXLl+/bt+/u3buBgYEme7ntgJZP8caNGxUKhb+/f2BgYGBgoL+/v1Kp3Lhxo3k61xHQDHNAmPeCfaCteiyInX0jLJyxoklGzIfGVL9QSIbw5xV4Jwahh9fDMGfEXMNRO1+dsarqXEHhaj+/dzp5T9X3WBWD3szj3pGhnSFSF8oaYrn59e/ff+DAgeHh4TNmzPj5559HjRoVEBCQm5vr5+eneZ3F19c3NzfXsCZari06+uGcqC4uLsa9FCuh5QzMw8Pj2rVrFy9eZN/B4ODgZ599FhZSaUXnG2/fVTRMc358skUV5GLiRkW43r+vAUKIaWSQHMMIxJymxKeRBGtkmIezcDEyhNpcGpoeGsW30m/OdnGOCQ5aasDhHxdzzwqJX7pLQwQQvQwkEAiSk5OvXbu2Z8+eNWvWLFiw4Oeff35yNxzHlcqnDlmL9Uwq1qytgw8YPqn5AHb16lXNTS6Xq87vvHbtGkJIlzsbgC5212Z35Tj25T9O1qDSUyF9wzCMBCE+Qk40MUuBKIbL5drZ2VZXV5vhlixTUypFaWmvkYR9RPg2DNN7uvjdFdR398kV/vIRzpB2aLi///47OTn5o48+euaZZ7744ovx48dv3749ISGhpKTkzp07nTt3RgiVlZWVlJSEhoY2ObampoZ98O+//7bQRHBwsC61AVbzfwlaszmt4BuhLahVSo/XFy1yfwZ7tHoTLqwlyiB9wyAMog9RmBQjXpUj6xoiYxg642a8WFLWv+9xinLW9/Cr9cSiW5wp7op4b0g7NIpKpfr44495PF5sbGxRUVFaWtqrr7767LPPRkRETJo0ac2aNQihxMTE8PBwzQtgAoHAzc1t1apV9vb25eXlmzdvVj9FEAR7X5B6agittQFNzQ8GMtqYuZfW6lB9npKhJ2ne/pWewlCQvmEI+jzJ3CKwF+TIydo+n4W31lZU/tWzx0Zb2xB9j70tw1/L5UbZqpICIXoZKy4ubv369Zs3bx4wYMD8+fMnTpy4ZMkSHMf//PNPX1/fyZMnT5482c/P7/jx45rXWTAM27lzZ2lp6aBBg9auXfvLL7+on3rttdeOHj2qOfuG1tqAJswqo5FQKGxhDLoJC87E0Sf1W3eSv9fvhYdFKpXt1g3KbiHS4aZaaI2diUM9mmE2pp6JgynCVTs52EAlMfTx/zuXy7WzszP/EGLrzsTxoOLPG2mvBXRdEBS4uIXd2Jk46urqNGfiEKmw0TdtRErmrwipq2nOSi04E4dIJNJrJg7d50cF7QUEdovJFFfclFY2k74Bs2/oianDVAcpzJcmhljNzV4PiRrzb2bOdXd/LjBgkb7Hqhj0Vj63TIp2hcpMFL0AsCwIYBbz/YMbzqTNSDt/dQmVnqLy6qRyN+FEyVZIhdH7KEQgYqLCyj7OCkVt6o0ZXK5HeI+vMUz7a1ua859Bwk+KOadria3dZCH8dn73AABPYV1/8e2HnFbtq8qa6NCNgz28hxEX1hJlpXD6pS/6T5J5gBOTFMjWqk4yGEaVfvNtubwqKvInkrTX5ZBNxSr1W7Cngtp2n/rUV/4cpB0C66V3Pi5oFSdExVUK8TQnjfHDtOsMRSmDIX1DD3QGQacQ+CgF5mNtJxl5+cuqq8/1itppK+imfe//+qeeWHiLM8Vd+U4nSNwA1kzvM7AvvvgiMjIyPj7+8uXLpuhQB7G7JitS4NmD9+iqskpFZWUowyJg9g09PMDp30mshwrva20nGffuHygp3RoU+LGb63B9jy2T4a/mciMEqqRAmO0QWDm9A5idnZ2np+eWLVv++ecfU3SoI7ivEJ1vLHvV4/HaP1R+Dsy+oRdGipR7KcwBEWOt7SSjvuFmVvYCD/cxXf3n6nusSIVNz+byCfRziIyDWdWYahuhMo5F1tW0YnoPIc6ePXv27NkIoVZfFazj2CfMJTBssksYkjzMmqPSU2lvSN/QGYOY3zioEcNnyxDX0p1pVXJ5ZeqNl/n8ruE9v0ZI71VgZmcTt2XYn+GmSprv4BiG0XciqCY4HA6Xa10fWYvSfgZ2+fLlW7duIYT++OOP8ePHf/rpp6Zeatbq7RfmjLLr6krx2U28ppq4UyoPt6o1YkyKSSbpXJwYp8DcrOprmqYVaemzaFrSK/InguDre7hUxfxVg2/pJguFtEPQMWg5A0tKSlq4cOHBgwe9vLxeeeWVQYMG/fjjj42NjevXrzdP/6zPVfG9AlntSq9n1SVURirD4cLsGzpiinHVORLvr8RCre3SV07uh7XCa9G9D9jY+La8Z1IZZ+s9SrNERiMZjWxwNK+Ap1n+sqfiE1/4xQmsk5YAtmHDhrVr106YMOGnn37y8PA4fPjwwYMHFyxYAAHMYLtrsrwo28GCLg+32cVTQnsyFNXicQAhhJh6THWAwjox+FBru2f5dtmPZXd+Cum+xtk5RuvOC7rIF3R5HJb2VlDzCjgcHLv3rEypsLaLggA8jZYhxMrKytjYWAzDTp06NXLkSAzD/P39myyYDXQnphW/19+a4hhCPLovlcrPxiRiSN/QiQrRByiEIWKyHBHad29HhHX/5uZ91Mn7JV+fmfoe+3s1+V4hZ4qHysa63hMAtNISwLp167Z///6ioqLffvtt6tSpCKHz58936tTJLH2zQkfqCkS0fPJ/Zu9Npb07Q/qGLui/KOYuTkxSIDuruvQlk5XfSHvD3j48LOwLfY89XkO8mccd5az6KtjaTkkB0ErLEOLy5csnT56clJQ0aNCg6Ojozz///OOPP05KSjJP56zP7trs/oJOgVwndhOvqSbu3JaOHGvZXrULTCZB/0PgI5SYn1VlKNC0LDXtFcTQkeHf45h+dwH+LSRm53IHOai+DZaRGJx/WRJn5Ueam/KPP7dUTzoULWdg48ePLygoOHXq1PHjxxFCMTExZ8+enT9/vln6Zm2K5MJr4vvTnB6vTUelpzAcLsy+oRVThal+p7DuNN7f2s4zsrIXNdRnRUX9zOPpt4Tpvw3EKzncvg70L6Fwy5eFNYlezZY0S6lUrl+/PioqysPDIzQ0dPHixY2NjS3sv3LlSoTQsWPHDJ5Z//r16zExDy+yqlSqNWvWREZGurq6BgcHb9myRWvTutPaSX0rbFbzAey0hsLCQoTQlStXTp8+rVAoVCrV6dOnjW+4A9pTm8PHybH2gQ+3lUoqKwPSN7STI3ofBwkYYpxc/zuj2rSSkm/u3tsTGrrW0UG/myhuNuJTs3lhtszP3WVciF4W9bRYpUsMe+WVV86cOXPw4MHy8vJz585VVFTExcW1sOoQ+6UfGxt75coVgzusFh8fn5ycfOLEifLy8p9++mn9+vUHDx5suWndae2kCQPYOA0jRowYPnz48OHD2Qfjxo17vBZtiAAAIABJREFU7733jG+4o6EZ5oAwd5xDkAB/GK6YrAxMIlaEw+y9LWKQ6gjFCDFiihzxtO/ejlRV/51XsMLXZ3bnTjP0OjBHjL+YZdOZS+8OkQiIx9Er3o+wrvjeVoka8PJ76n8t7Ki5G1Z+v8mzly5dunDhwoEDBwICAjAM8/Dw2LFjB03TO3fu3Llz58yZM0ePHu3r6zto0KDc3FyE0Ouvvy6Xy4cOHVpSUsJmJGRmZg4aNGj69OkBAQFDhgz55Zdfevfu7ezs/MUXXyCEGIZZunSpt7d3QEDA888/X1JSotl6fn7+oUOHdu7c6enpSZJkv379vv322/r6+uTk5GHDhrH7HDlyZMqUKZpNN9sxhNDGjRuDgoK6du06YcIENstPs5PDhw+fP39+VFTUgAEDLl68qFlhY2PjSy+91LlzZ29v788/13vctfkAJnpk165d7JKgEolEIpGcOnXKy8vLgGbAWVHpXUWD5uy92PWrdKcuKncPC/aq7aOvkEw2gT+vwNyt6jxDIi1Lz3jT0aF3cLdleh1YJMUnZfGcSfpAmNTxv5ew14TCqbw5EGkp5Hdfq/+1sKfmbuTP25o8e/Xq1WHDhtna2qpLcBwfO3Yse+Kya9euVatWlZSUTJgw4eWXX0YI/fDDDxwO58yZM5qVJCcnv/fee/n5+WKx+JdffklOTj58+DAbwMrKyk6ePJmdnV1YWOjj4/PTTz9pHnj9+vVevXo5OjqqS4YNG/bGG280+0I0m36yY3///femTZsuXbp069atwMDAJydpOnfu3IQJE27cuDFmzBi2b+oK9+7dW1FRUVpampKScvTo0YaGhhbez2be4Zaf/vjjj7/44ouRI0eqX+H69euXLl36wgsvtHygZdnY2Oi+M0mSCCE7OzuTdQchhA7cLwiycY7zCMLYUbCqSqa0GB832dTtNkGSJIZhZm6UbRfHcX1XRlaVMPVnlNwYnD9I72kpEELsQux2dnZmXpGZIAiGYVqYMUipFF355xWKsh006BCX46J7zXekaFIqbUuiU30JL66t5lMYhiGE+Hy+mWfbw3EcwzD2j8jMeDwepfPweyvOH0T3iKC9O6s3qd0/PG1PxbTXH2/gTc8WFArFk+8bh8Nhl7ceNmxYZGQkQmjevHlLliwRCoWawUYtJCQkOjoaIdSzZ88BAwbY2NhERESwC1X7+Pj89ddfN27cSE9Pv3jx4pgxYzQPlMvlBGFI4s+THTtz5sy0adPc3d0RQgkJCb17Nx0PDwwMZC+8PfPMMxcuXNB8KiIiYvny5fPnzx82bNjFixc5es5mruVjV1pa6uzsrFni6Oh4+/ZtvdowP4lEolTqerXf3t4ewzB9I79eapSSYzX5H7j3FTWI2BLu5QscLk/k15UxZbtP4vP5PB7PpC+2Wba2thKJpIXB/WY0YsofOZgXUg4RG9ZfLpdLUVRDQ4OZAxiPx6Np+unfmExa+uyGhsJ+zxyTy7hyma6vrVKB/e8mT0ljR3pKbeV0w3+rJ0mSw+GIxWKFeW9kpiiKJEn2O9ecuFyuVCplv6l11Fq/2xhHJ+TopNOeXQNbeDY6Onr79u1SqZTHezg4zjDMiRMnJk2ahBBSRxcMw3Acf9rvEs1v/Cbf/unp6VOmTJk5c2ZMTAw7oqb5bERExMKFCxsaGtRvy4EDB9atW8eeIbGaHMJqtmPs7yf2wZNd1TzLbKJPnz55eXm///77sWPH5s2bd/nyZS8vPbKZtGQhPvPMMytXrqyvr2c36+vrV65c2bdvX90bAAihg3V5KsRMenT7F6ZSUVkZKKIXQ8KYz1PQSLWfwlQY8aLcyvLDbxUllT842rPHV/b2Edr3fqRGiY3P5AmV2MEwaReuVd1I0N4ZnDEfFxcXFhY2ZcqUkpIShmEqKirmzJlTXV09a9YshNDp06ezs7MZhtm8eXNwcDB7IqHXfPZnz54NCwtbsGCBn5/f6dOnm/yiioqKGjx48PTp0+/cuYMQKigo+OSTT1599VUbG5vMzMzGxka5XL5r1y71/uqmn+zY0KFDd+/eXVlZyTDMhg0b1JfQWsZWuGrVqtdee+3FF1/cvHmzg4PDtWvXdHx1LC0BbPPmzenp6X5+fs8999xzzz3n5+d38+bNTZs26dUG2FObHWfr4009/BlC5GVjEjHWG34HPBV9imRu49gEOXK0qktfFRUnCm+tC+ia4OU5Xvej6pVochavXI4fCJMG2UD0anOejGHyjz/XGtgwDDtw4EB0dPTYsWPd3NwGDRrE5XKTk5PZwecBAwYkJCT4+Pjs3btXHUji4uKionSdtWfy5MllZWXe3t7jx4+fNm3a/v37m4SH3bt39+zZc/jw4a6urqNHj541a9Y777wTERExfvz48PDwkSNHDh/+eDk6ddNPdmzw4MFz5swZMGBAQEBAYWHhhg0bdOkeW+GsWbOqqqq8vb39/f379es3atQoHV8dC9M6utLQ0LBr166cnBySJENCQqZOnSoQCPRqw/yEQqG+Q4h1dXUm6kyGpHLorT0/+Dw/xj6ALeHv+RFjGCI+QX1qazbsEGJNTY2Z29VrCJHJxVX7OEScEhtk1F1fXC7Xzs6uurq6jQwhNjYWXvnnOUfH3r2j9mA6n1dKaGxyFjerEf+1hzTS9qnRiyRJR0fHurq6DjKE6OrqKhKJ9BpCNPjeKTWGYZodVdOdjsup7Ny58/Tp0z/++KMxbZlCW+uY9kuvJEkOGzZMfVZ4//59hFBgYEtju0DTHmG2M2kzws6P3cRrqoi7ZZKR/zMkLaEjqMFURzhYEI3FWNU9y0plw420V7kct4ie23WPXnIavZrDTRfh+8JkLUQvADomLQHswIEDL7/8skwma1Ju5p+07ZecVv0qzJvk2J3z6DuLSkthOFxV99CWD+ygFEi1l4PxGNy67llmGDo94y2p7F7fZ45TlIOORylo9Hoe71I98XN3aX97a1s7BrRgxowZM2bod3egebS1jmm5BrZ48eJx48bl5uZW/pd5OmcF/mwoqlFJpz6aPgpTqajsDEVYT0jfaBb9B8XUIPwlBWZd56cFhSurqs+E99xqZ9td+94IIYRUDJpTwD1TS2ztJhvqBNELgGZoOQOrra1dunRpcHCweXpjfXbXZkXYuIfxHg6+E3lZmESihNk3msNcI+k0ghinwLysaqzsQcWxouLNQYGJ7m7P6XgIg9DCW9zfqsktQbKxLlY1lApAK9JyBjZkyJDs7GzzdMX63FeILjTemeoYoi7hpKeqvDur3GD2jaaYOxh9ksR7q7BIqzrbaGjIyrg5x8N9VEDXptMTtOCTYs6uB+S6rrIJbhC9AHgqLWdgixYtevvtt3NycqKjozWnt4iNjTVtv6zCHmEOgWHjHR+ev6rTNyzbq7aoEaP3c5AbjY+yqu9rubwmNe1VG17nnj02I52v6a0o5Wy9Ry33k7/iaVXvhhXAMKyFe3KB+WkJYEOGDEEIrVq1qkm5XtmrHRODmL212c/bBTgTD2+zp9JSGC6kbzyBQfRhCikwYoockdaTHMQwyrSMmUplfXTfkySp6xwQ68s4X92hPvJVvNPJrNnwQEdGztSFYZh60gpgPC0BDAKVwa403iuW1631imU3MZWSys5QhIZD+kYT9FmKvoUT0xVWds9ybt7HtbVXekft4vP9dTxk+31q7W0q3lvxXudWm7gPtCKGYcRisTE16HgfGNCR9vvAaJq+cOFCbm6uUqkMDQ2NjY3Fn5iVEjxpjzDbm7J91rYLu0nkZmMSCSye0gSTj9PJBD5YiQVa1aWvsjt7Sm/v6B68wtV1qI6H7KmgPirizPJSrvCH6AWATrQEsAcPHowaNSo9Pd3X1xfH8ZKSkoiIiOPHj7MTD4OnaaQVv9cVvuUSSWAPgz0nPUXVqQvtBu+bBiFGH+Fg/jT+rFVd7Kmt/TcjI8Hba5Kfb7yOh/xeTb5fyHnJXfm5f9N7LgEAT6PlXCohIYHH4xUXFxcVFRUWFhYVFZEk+eRyL6CJI3UFYlo55dHtX3h1FXHvjhxOvzQpMdU+ClEM8aJC28ewPZHJK65dn2FrGxwWmqTjIX9WE2/mcUc5K78MlOFwfQQAnWn55jh37tzq1at9fHzYTR8fn7Vr1zZZUQ08aXdt1gBBJ3/OwzkXqHRI32hKdYxkKjB8sgLxrefSF03L09LeoGll32f2EoROi9L9LSRm53EHOai+7SYjIXq1c7/9bm/pLnQsWgJYs1NGwTxSLbslE/4rLlff/oUplVR2hiIsAtI31OjrBJNG4KOUWCerumc5O2dxXX1qdJ+feLxOuuz/bwPxSg63nwP9S6iMY0WnoR0TG70ghpmTlj+auLi4xMTEsrIydrOsrCwxMTEuLs70HWvHdguz+Tg5xuHhfMdEbhYmkSh66roIgtVjynH6BImHq/A+VpW4UXp7+527O0O6r3Z1idFl/9QGfHIWN8yW+bm7jIvBj0LrATHMbLQEsI0bNyoUCn9//8DAwMDAQH9/f6VSuXHjRvN0rj1SMvR+Yc54h24C/OH5FicjFdI31BgJUu2lkDODj7WuxA3hP3n5y3y6vNal86u67J8jxqfm2PjxmN0hEgEB0avdMyxoeXp6uri4eHp6enh4uLm5TZs2rbGxESGkVCr/n70zj4uqev/4c+4yM+y7IIqCC4jI5k5qkqKpqaW5a1kupVkqLt8sra9ppSmWpl+1+llZKCYupZYrYeaWG4gsCgjixg7DOjN35t7z++MakQ7MgMwMM5z3iz9mLuee89yZO+dzzznPeZ6oqKjQ0FB3d/euXbu+++674nEA4Hl+7dq1ISEhrq6ufn5+27Ztq78qy0aHgLm7u1+6dCkuLm7p0qVLly49derUpUuXiAtiPcRX3s1TV015zH0juIdprWouYBD2s6BA9AQ1sJbTaysU9xISptvbBXfx0ys5b5aSGpcsc5fg/QEKR907WQjmh/56FhcXl5eXl5+ff/v27YSEBDFd8KuvvhoXF7dv3768vLz4+PiCgoJBgwaJ6fTmzJlz9uzZY8eO5eXl7dy5Myoqat++ffVUZdno3sj80Ucf5ebmihnMBg0aFBgYuGbNGmtry4oW3nTsLk3pKHXsae0hvmUTr2CplPfzr/+sFoLwB4Nv09R4DrlajnoJgjLh+uuIYkNDvqUoic7y91VoXIrMhsaxXZXOZFXUDFGry9Tq0tpHTsYFPVmsuvrOv94jytqqXT3V2tvbP//88/fv3z937py49VYMW+Xu7r5jx44+ffpER0eHhYXt378/KyvL0dERAPr27fvVV1/dvXu3rqoac3lmhQ4BW7x4cWxs7CefPHqunDFjxvLlywGAzCJqpUSjOFFx591WfRAgEN030m4Q9w0RnEUJZ2iqP091tSTHDXwjeX5l5c0+vQ5LpR46S+dy6KVkGY/hl0CVu8RyVLxFkX3n67Sbq3UWe0zVGMb2heEP6yqMMU5PTz9//vzq1asvXrwYERFRO+giRVGjRo26cOECy7Ldu3cX1UukJtWw1qr0vSSzRXdCy88//7wmg9m0adMkEsnChQuJgGkltuyWAHjC3/6Hj9w3goj7BghyUO+lUXuBes6iQvzdztqUm3cwsNuXDg66v+USDRqfIqvi0aFApZfUklS8ZdG2zQRHx541by9cfLGewmF9fxFfUHWk4R48eDDLsoIgFBYWTp06dciQIQkJCQzzeM8skUgUCgXHcTRdZzrvJ6vS95LMFh1rYDzPd+zYsfaRtm3bkgCJdRFTmjrItr0HayO+lVy/yrdtJ7i2+CVDHlXt1GCE6bEWtWe5qCg+8/Zab++32nhO1lm4XAMTUmSFHDoQoOhsRdTLjLG2bt/K7Tnxr371AoCakq6uz2otIC5cFRQUPHjw4NKlS0ePHu3Vq1d8fHztbhZjfOzYsd69ewcHB1+9erWioqLmX7Gxsb17966rqqe+1uaOju4kPDz8o48+KikpEd/K5fLVq1cPHDjQ8IaZH9cVBSnKoprtX3+7b5DoGyD8xvAPgZ3Eg53lTJpVVd++fmO2i3N/v84f6CysENDUNFmWAv0UoPS3sZwPgaAT/b05PD09n3322aSkpEGDBgUEBEyaNOnOnTsY44KCgnnz5hUXF8+aNSs0NHTgwIFTp04V17cyMjI+/PDD6dMfd3ytqaqJL6b5oWMKccuWLUOGDGnbtm3Xrl1pmk5NTfXw8Pj999+b3I6TJ0/u379fqVR6eXnNnTvX09MTAJYtW5aeni5mHxg2bNjs2bMB4Nq1azt27FAqlcHBwXPmzJFIdC+bG4cYeZozYzXU/lHocTbxMpbJeN+W7r4hJNHCVdrqJUpoj3lL2fel0VQmJr7G0PbBQV8jpMsTSkBTUqXXK6mfAlQhtmTsZVG8OKq8CWvr1KnTiRMn3nvvvdjY2KioqFGjRuXm5rq4uIwYMeLs2bNiGPvdu3evWrVqyJAhhYWFTk5Oc+bMeeutt+qpqgnNa4YgnWE1eJ7/7bffUlJS1Gp1165dR40a1eSa8eDBg/nz52/dutXFxSUmJiYpKWn9+vUA8Morr3z11Ve1PR6rq6tnz579ySefeHl5ffbZZ126dBk7duyTFcrlco1G321G9vb2CKGysrKnuQQV5rvd3DHJ0X916wEAgDQam21fqLsFq54bWk+75eVNeffrg7W1tUwmqxlSG5x8SvN/LPIVHF6XKhQK3rgKJpVK7ezsiouLmzZ2DMZCQuKrxSVnw/octbXV8oAik8kEQeA4DgDUArx2S3ZaTv/QRTnYyYCXzzCMo6NjWVmZWm3UVUaWZRmGUSgUxmwUAFxdXSsrKxu0nOHq6vqUjWKMKysrn6YGkk6ladG9CUXsZKVS6Ztvvpmfn28II4qKioYOHeru7g4A4eHhx48fBwCFQiEIwmP++levXu3cubO3tzcAjBgx4scff6wRMI7jau5mjHFDs8Y9ZZa5o+VZcl45yclfrIe5mYKUCk1QaP3VGj+1ndiicdrFStDsYZEDMC9qEJIZP5WfgS428/a6gsITIcHf2NlpD26J/obHMC9TGi+nv++iinAW9E/K3GhM8iGbKkkjSQ5J0CFgaWlp4eHhAFBUVDRmzJg1a9acP3/+xIkTPj765ujTh+Dg4ODgYADgOC4mJmbAgAEAkJeXR1HU2rVrMzMzO3bsOHPmzFatWhUVFbm5uYlnubm5FRUV1VQSExNTs3EvOjq6S5cuDbLBxcXlaS4h9kFGT7s2A9s+alSdmgQ+HZ10bf96ykYbjTHaxSDfoeSreZelVoyHHQCY6sHT2dm5CWu7d//nzNufB3b7oFvAzPpLYoDZidwvRXx0d8nktnoF9n167O1NE8TIJBtDbWxsbGxs9Cxs/DEiwQjoELDIyMh+/frt2bNHjL6xcePGqVOnLlq06ODBg01uyoULF7777rvevXu//vrrAEDTdERExEsvvURR1MGDBzds2PDZZ589dkrtqaGBAwe2afMogqqjo2NtR536sbKygqe7vx9wFXGlWevaDhIbRQV5bE625qUJynptsLKyMv6PSiqVsiz7lNMg+qA+DVwikk7BCpsqqACZTMZx3FOmY28oLMvKZLLKysqmmkKsqLx17vyrHh7DfbwX1XODsSwrYLwwFX97H23040c6VOt9MzYeiqJsbGyqq6uNPE9L0zRN0+J8qTGxs7NTKpX6z5fyPC/+0gmWhA4BO3v27KlTp2oWvZycnJYuXap12elpwBhv3749Ozv7gw8+8PJ6lMLYw8Nj6tSp4n6IF1988dChQxhjV1fXGteaoqKi2pPa3t7e4tQiAMjlcpVK38SAUqkUIaR/+SfZWZjIABpt20GsRHblL7CyVnbohOutUyqVPk2jjYOmaYZhDN0uzqb4kxIqTMP7angVAADLshzHGblvBQCZTKZSqZpEwNTq0ot/TZBK3bt13cxx9fWbCKEPMuCb+/RH3twUV7VxvmTxl6JWq42/BoYxNv6dbGdnp9FojN8uoVmhw43eycnpsWVSjuP0H7brSUJCQlpa2po1a2rUCwDOnDnzn//8p6qqiuO4+Ph4f39/hFD37t0zMjLy8vIwxidPnuzfX6+w3wYFA95TmvaCfUdHWgYASKNhUm9wAUGYbqlB7ioRf4BFbTCKsJxwvRjz12/M5bii0JCdDKNjmm5NNrXxLr28PfdWG4vatU0gNDd0dLKjR49esWJFzYRhWlrakiVLhg8f3rRGJCcn5+TkTJgwQXxrbW39448/Dho0KCcnZ86cOQghX1/fBQsWAICNjU1kZOSaNWt4nvfz8xs5cmTTWtIIzlc9uMOVrfd8Tnwrum+03OQpPPB7WRCAGs/VEXnALLmVvrK4OL57aLStjW/9Jb/JZT/NQkva8wvbEvWyNBBCT/n4TrxOmhYdbvRVVVXTpk07fPgwz/MODg5lZWVDhgyJjY11cHAwmomNwJhu9G8/OPln5b1rvq/RiAIAm13fYoqqnvyaPu1anhs9/xuDrzD0qxzy/tdyl62trfm60T/MjU268ZZv5w87+LxTf8mYAnZBhuSNtnhdZ42Rl4WIG70+pzx9u095D1MURTSsCdExArOxsTl48GBaWlpycjLP8/7+/kFBQeQLqKFKUB8py5zrGiqqF11UQD28rxw5xtR2mQacTONLDDVU85h6mTXlFTdSUhe7txrZweft+kvGFjALMyUTW2nW+SIg0TYsEYxxdXX109RA9oE1Lboj050/f14ikYwfP97Ozm7lypUrV640vsdRs+VAWXq1oJn4d/goNvEqWFlrWmT0DVyE+MMs8hOoMMtZ+uK4wmsJr1hbdwgK/F/9u7h+K6bnZ0pHOGu+6KSiyAMegWAUdAjYhg0b+vXrl5iYWF1d/eqrr2KMv//++/fff984xjV/YkpT+9m08ZY4gOi+kZbcQt03OBB+koANpsdwht+tayQEQZ14fZYgKLqH7KTp+vY5nZbTs29JI5z4r31VjKVcPoHQ/NEhYBs3bvzss8/Gjh27d+9ed3f3gwcPRkVF7d271zjGNXNuq+RXqvMm/518mbmZ3ELdNzDwP7O4FOgJapCZ2pimI+3me6XySyFBO6ys2tdT7HIFPT1N2tdB+L8uKtaCYu0TCM0fHT+4wsLC8PBwhNDJkyeHDRuGEPLx8TFQQCmzY5c8xZZmR9l3Et9Krl/jvdoLrm6mtcr4CBcYnEpTIzXIw3KWvu7e+/7e/Z1d/D52dq5vq8a1CmpCijTAFv/QRSVFZOGLQDAqOia7fH199+7d6+rq+ssvv8THxwPA6dOnawJetGQ0WNhbenOMg68VxQAAXdhC3TfwPYTjGKo3T4VYSqh5AHnZ5Zu3lrfxnNi+XX3xotKqqUlpVt4yYbe/wsaC9gwQCOaCDgH76KOPJkyYsGHDhgEDBvTq1euTTz5ZsWLFhg0bjGNccyauMidfU1WT/Yu93iLdN6qQECsBD0w9bzmOGypVXkLiDHv7oICAz+splqWkxiXLPCR4f4DCseUtehJqsL+6vq5/lfdYakxLWiA6phDHjBmTkZFx8uRJMbln//79f//990WLFhnFtmZNTGlqJ6lTD2sPeOS+cYPrFtyy3DcE4GNZUCN6PAe0hcyeCYLqWuKrgIWQoG8pVGfaoPsqNC5FZkPj2K4KZ9aYBhIsh7Fjx3p4eHh4eCCEXF1dPTw8OnTokJyc3LNnz6evXP96rly58mRIo+Tk5JCQEPG1h4eHi4uLh4eHu7u7m5vblClTqqqqAECj0URFRYWGhrq7u3ft2vXdd98VjwMAz/Nr164NCQlxdXX18/Pbtm3b01+RVrQL2Pbt2y9cuAAAp0+fvnPnDsMwly9fPn36tJim5PTp0wayxlwo0ShOVt6Z6tQVAQIAJi0ZKZUtzX1DOMXgHIoapwZHC1EvAEhJXVpRnhIa+oNM1rquMrkceilZJmDY303lLrGcaycYmQMHDuTl5eXl5Tk4OJw9ezYvLy8rK8vURmknLi4uLy8vPz//9u3bCQkJYt6PV199NS4ubt++fXl5efHx8QUFBYMGDRI3es+ZM+fs2bPHjh3Ly8vbuXNnVFTUvn37DGGY9hHD3LlzFy9eHBYWNmzYMK0FGrQB3vL4SX5TwHi846PkKZKkq7yXt+DSBPv8zQV8kxIuMNQgDepoOUtfd+5sffAwplvAF44OPeoqU6xG41NkVTw6FKj0klqO0wpBf8p4ValGrw7wjuqf+D4UQu0keiW7UalU8+bNO3v2rLW19fr16/v375+cnLxo0aKOHTump6fHxcXFxMSsXLlSpVIFBAR8/fXXbdq0qaqqmjFjxrlz5wRBmDdv3vLly7XWAwCbNm3asmULz/MhISHbtm0TszCKCILw/vvv79q1y87ObsSIEVpts7e3f/755+/fv3/u3LkzZ87cvHnT1tYWANzd3Xfs2NGnT5/o6OiwsLD9+/dnZWU5OjoCQN++fb/66qu7d+/qc+0NRfsILDs7W9zspawDQ5hiRuyRp0bYebszNvDIfeOBOri7qY0yIiWI/1mCOgtUf8tZ+ioq/uNWxur27Wa3bTOtrjLlGpiYKivk0MFuis5WRL1aKF8XXAtK/rrmr56StYv1TflOz/pTUlKmTJly/fr1F154YdOmTeLB06dPh4eH//rrrzdu3Fi1atWZM2du3779/PPPT5kyBQD27NlTUFCQk5Nz9erVQ4cOibl+nqznjz/+2Lx587lz527fvt2pU6fIyMja7e7evfv48ePXr19PTEzUOhbEGN+6dev8+fOjRo26ePFiRESEqF4iFEWNGjXqwoULV65c6d69u6heIhERETNmzNDz8huE9hGYOLCt57S+ffsawhqzIEGRn6osfrfVo0/gb/eNhuXPNGPUwP8kQTJMvWQ5e5YVynvXk95wdOjh57uyzjICmpImzVKgA92UXazJzGHLZbSTbyfZP1lSp2cdqqvkzg6ja14zSN9Ngr6+vv369QNPDSjgAAAgAElEQVSAvn37Xrx4UTzo4+MzceJEADh+/HhZWdmLL74IAIIgVFRUYIyDg4M/+uijRYsWRURE/Pnnn2ICrCfriYuLmzJlipjcccGCBT16/GumIS4u7s033xQTwM6fP3/hwoU1/xo8eDDLsoIgFBYWTp06dciQIQkJCWIGn9pIJBKFQsFxHE0byStXu4CFhYXVf1pTZQg0R2JK01wZqyF23gCANGom7QYXGNpy3DeEX1lcDPQMNTJBDl6DwPNVV69NZRib0NCdFKXdcUMpoCmp0qRK6qcAVYgtGXu1aPxkLn6yf3KaT6+75Bgnv0bUX3tYU4OdnZ34guf5sWPHbtmyRXxdUlKCEOrZs+etW7cOHz585MiR+fPnnz9/vq56aiLZIoQeSzBbO9DwYwFv4+LiRJ+Ohw8fhoeHHz16tFevXt98841SqZTJHgUvwBgfO3Zs/PjxwcHBS5YsqaioqLE5NjZ2/fr1ly5dasSnUT/au11z1ycxQraehcWvreZrqB+loDlYlv6qW5CdlQ0AUInJSKmkevbV8/Ta0DTdiLOeEoZh9L/YJ1GfB00iyMYB06FODz2t0DQtlUqNnJFZvAdkMlm99zO+fOVNheLOgH7H7e20b3BUCzD7BnWpAsUE8s+5sgA6/A7FHI8UZdSwHGJzEonEaA+/ImJGZpP0GCzbAAdQ/dNTNHMGDx78wgsvLFmypF27dqtWrbp58+ZPP/306aefXr9+PSYmZsyYMb169bp06VLHjh21njtr1qy3337b1dV148aNERERtf8bERGxbt26CRMm2NraigL5JJ6ens8++2xSUtKyZcsCAgImTZq0cePG9u3bFxYWrly5sri4eNasWVKpdODAgVOnTt26dWvbtm0zMjI+/PDDt9/WEQu7cWjv5WvGrXXRzKcQBUHQv68Uf3t6Zkn4ueSmnFdOdPQXy9NXLwntfTROztDwJAsYY+NnKG7QxT6GcA+432imF0ahQkMrEC/WyAIm9uk8z9fTvaZnfPbg4cHuof9nZxek9WPhMcxOY+JK0I8BmsFOel242KEb/8sFAEEQjNwuQggh1Pwv1twfymvo2bPnJ598MnToUIVCERISsmPHDgCYNWvW5MmTPT09GYYZOXLk8OHD09PTnzx34MCB8+bNe+aZZ0Qnju3bt9f+78SJE5OSkoKCguzs7N58882MjAytBnTq1OnEiRPvvfdebGxsVFTUqFGjcnNzXVxcRowYcfbsWTHW/u7du1etWjVkyJDCwkInJ6c5c+a89dZbBvgw6sgHpjNhSjO/GwyXD2zcnZ8rBO54hwkAQBcWWH+/XTnqZXWXgEYYaV75wLAC+K+kIMXMbDUwDf72m2c+sIKCYwnXp3fwmd+503KtBTBAZKZkTwG7tbNqrJu+d5RMJhMEgeQDMygmyQeGMa6srHyaGkg6laZF+ywH1oWRrWwmPFRXnq26/0/0jcQr2MpK07kFuG9gEPaxSIWYSY1Rr+ZJVVVmUvI8F5eBnTou01oAA7ybJd2dz67v2AD1IhAIRkP7FOL27duDg4PDwsLq2rMcHh5uOJuaLbtLUxlALzl0BgCkVjNpN9TBPbBxlxxMAv87g7NoeooanCxEvTSaioTE6VKJW3DgNwhp/wY/zpF8l8t85M294k7Ui0BojpCNzPqCAf8kTxvl0MmRloEYfYPj1EGWH30Dp1P4LEM9q0GdLWTPMsbC9aQ3laqHfXofZVkHrWXW35N8eZ9d3p57q41RZ+QIBIL+aBew7Oxse3t7aJFCVRdnK+/f4co2eA4S37LXr/Je3oKTS/1nmTtYjoSfJchHoAZazigkI/PjouK40JAf7Gy1T/9+k8uuu8tGtuUWtiXqRSA0X7QLmLe3d83r8vLyhw8fPlagS5cWsPDzb2LkaV4S+/42bQGALiyg8x4qR71saqMMjAYJP7HAYnqcWlfYZ7Mhv+BIVvaWzp2WtXJ7XmuBmAJ2eZZkVmvN++2JehEIzRodm6W+/PLLyMjIJ72fW5ofRwXPHSnPfNu1B4UQtBj3Df5XBhdQzGscWErgiYqKlKQb89xbDe/YIVJrgdgCZmGmZGIrzSc+KiPbRmj+IIRsbGyesoamMoYAOtOprFq1asaMGVlZWaX/xjjGNR8OlqUrBX6CYxcAQGqOSbuhDuxu2e4bwlUaJ9DUcDV4mXHgiejd//QXHFdyLXG6laxtYLctoC0K1m/F9PxM6QhnzcZOKor0MwRCs0fHCIym6SVLlvj4+BjHmmZLjDytv21bb4kD/OO+EWJqowxJPiUcZVAgT/W0GMcNTWLSTI2mvFef4wxj92SB03J69i1phBP/ta+KJupF0AbGuCblVeMg+8CaFh0jsMmTJ0dHR7e0CcPHyFSVXqnOrZV8+RrfzpLdN7ACNHtYcMb0aPN23PjlsD0AHD3uCgA3b60oLb0QHLjN2lrL09jlCnp6mrSvg/B/XVSspaz2EQgWj44R2OLFi319fQ8cOODt7V179vbIkSMGNqwZEV2aYk9LR9p3AgC6MJ/Oe6gcPc7URhkMDMIBFqoRPZsD1owfXI6dcKt5/eDhTzl3d3TxW+3qOvjJktcqqAkp0gBb/EMXlRSZ8SUTCC0NHQI2bdo0Jyen8PBwJycn4xjU3NBgYZ/81hgHXyuKAQA24Qq2stJ0akyQabNA+IPBmTQ9QY1cLacrv5H8tmfr8d7t5zz5r7RqalKalbdM2O2vsLHkNU2CMfilAIU7Y4eWkprC9Oj4pBMSEg4dOtQy426InKq4k6+pEucPkZpjbiarg3taqvsGzqKEMwzVn0f+5r30VXv4JfIwNzYocOtjB7OU1LhkmYcE7w9QOJJOh/DU7HhIeVkJ3e0s5+GvmaPjVxsaGmrk7AzNjRh5WiepUw9rD7D06Bu4DPH7WNROoJ5rEfuf7qvQuBSZDY1juyqdG5CXg0AgNBd0CNi77747Z86cyMjI9u3b114DeyyRTJPA8/zcuXOjoqLEICAAcO3atR07diiVyuDg4Dlz5ohpRrUeNBBFGsXJijvL3R+l92QTr/LtfQQn5/rPMkt44PexQAH9stnvWX5y+FVzfNjQQvF1LodeSpYJGPYHqtwl5HmZQDBLdPRVEyZMyMnJWbhw4ZgxY16qRZPbcfTo0WXLluXl5dUcqa6u3rBhw9KlS7/++uvKykrRbUTrQcOxV56GAY937AKi+0Z+rjqou0FbNBXCURYeUvQENZj57Edd6lWbYjUanyKr4tG+AKWX1Ix3uRFaCB9//HGDyh85cqT+3DENrbDZokPAKuugye1o167dhAkTaqdYvXr1aufOnb29vWmaHjFixLlz5+o6aDh+kqcNsfNuxVgDAJtw2VLdN/ANWrhC00M1qJ2F9+bHTriVa2BiqqyQQwe7KTpZWfj1EiyDhupNeHj4hQsXmrDCZov2KcTCwkI3N91PsnoW04eAgAAAqL3eVlRUVFO5m5tbUVFRXQdFkpOTr169Kr6OiIhwdHTUs2mxUSsrq8eOX6l8mKos/rDtQCsrK6TmqJspuGdfma1tI66urnafbNTQsCyLEKrdrpAH1YcxEwRW4SyAodaCGIYR0zwaqH6Rg7/o+HY4ZD3tlnWWAn7tgUPtZQYyg2VZjLGRF4/F9NNSqZRhjOqOQtO02LTxkUgk+kdm0j/DrU6UAijruJE1GCp4kGtrCgE86Z0YFRUlTiaNGDFi+/btFy9eXLly5alTpwDg559/3rNnz549e15//XWO4wYPHvz666/Hx8fn5uampKS0a9fum2++EWPSbtq0acuWLWKS5W3btrm7u9+5c+e11167cuVKcnJyZGRkYGBgfHy8lZXVZ599NmDAgJoKN23atGjRoo4dO6anp8fFxTXV52NMtN/rI0aMCAoKWrBgQVBQkNYCSUlJmzZtSkpKunz5siHN+wetm6lrH7xx48bOnTvF13379vX09NSzZvE3YG1t/djxPQ9utpLYjPHsxiKa/yuR5zhJ2AD0RLFGgxB6slFD89jFYiUu2a2knZDzKzIkM2z8CSN06FMnCxhr4n4fUiq/Mfz5y3Lae9hFLvm5R4EPFDyM/Iu7Xir81lfS38Xgfa5BV2frwlRRHmrPnRizUf3bbcKc0ZvvUquz6rx/zpZqv89tafxw4L+ce48fP/7DDz9cvnyZZdnnn39+165dHTt2fPLE7777LiYmJi4uLjo6eteuXRcvXgwODt64ceMrr7xy+fLlP/74Y/PmzefPn3dzc3v33XcjIyN3795d+/T4+Pj//ve/n3/++aeffvr5558PGDCgpsLk5OTTp0/PnDnziy++aNQnYXq0C9i5c+c2bdo0fPjw1q1bBwQEdO7cuXPnzgihjIyMjIyMlJSUBw8eREZGbtu2zXCWubq6JiUlia+LiorEKV2tB0UmT548efJk8bVcLi8uLtazIXt7e4RQWVlZ7YNKrInJT5rmFFBeIgcA6/NnoL1PBaJA72r1abe8vLypatMTa2trmUxWUlICAIBBiJUIpRQ9W1VSVQ1PFSJHB7a2tgqFgucN7p2fdmtFQeGfPbrHqFT2VbgKgC0pKcEYqwWYflN2roz+0V8ZAFVN9zVqQRxrchxnwDaegGEYR0fH8vJytdqoTqQsyzIM04TyoCeurq5VVVUNyvfUVM+Lo91wJ2teg6FU/fgz31f30Qg37PXvpwgZhe0YYJ54Pjx69Oi0adMcHBwA4Pjx4xjjhISE+puOiIgICQkBgPnz57///vtyuTwuLm7KlCmtWrUCgAULFvTo0eOxUzp16tS/f38A6N2795kzZx77r4+Pz8SJE3Vfc3NFu4BJJJKlS5cuXLjw6NGjJ06cOHz4sOhe4eHh0bNnzxUrVowYMcLQz1zdu3f/6quv8vLy3N3dT548KX4HWg8agiNlt8t41UQnfwCgC/Lp/Fzzjb6Bb9E1MTV4GaglAi6nAADfoIRUih6lRm7m7bhRQ27egZycr3w7f+jqMqj2cR7DWxnS02X0d37KQY7mvcWNYHL8bLDfo5D0j/9wjhTRY1phPfeB8TxfMy2h0Wgee/LQ6mpQUx4hRFGUOCdfM4+KEHpylt623lUPOzstcUHNiPqmy1mWHT169OjRo41mTW1sbGwiIyPXrFnD87yfn9/IkSPrOmgIYuSpPaw9/KUuILpvWNuozdR9QwA+hgVXjOwxACgpgaM4QcOAAuFcBAiEEmQZG/0qKlOTUyLdW43o4PN27eMYYPFtyeFiZpuv6nlnol6E5sKQIUP++9//zp49WyqVjh8//sUXX+zTp09ycnJVVRXLsrt27RIHZwDA87yoTKdOnUpNTfX399+yZYufn5+zs/PgwYNnzZr19ttvu7q6bty4Uc8NTjUVmjvNK/zA3r17a7/t0aPHkyNirQeblntc+dnK++s8w6Em+kZobzDTDd0YkBUABagLT/XmH00h3i3VbJcAA6iDgJwsYfilVssTEqbLZJ5Ppkr5z23J7nxmQyfVGFfzjk1MsDBGjRp148aN7t27KxSK4cOHz549GyE0ZsyYoKCg9u3bjxw58tKlS2LJQYMGhYaGLl269JlnnlmwYMHNmze9vLx27doFAAMHDpw3b94zzzwjOnFs375dn6bFCsUazBpkkZHm5XK5/k5HT66BrSv4a3Ph1eQuMx1oKXv9quzkb1Wz5gmOTbx/2UhrYDzwG2T0PBW/U4J6amzDpTJWVhhViR9SaJgGlSNwEoyQM8Wga2AYC9cSppbKL/btfczW9p+BchGWDrjCFHHwkTf3VhvjrQyZcA2srKys5ayBVVZWNmgNrP6tUfqAMa5/E9HoRHplx/pCST1NOpXo6OhTp059//33jTvdImleI7DmAAa8V542yqGTAy0FMXlK+w5Nrl7GxgbT0zl+p4STYC6Pww8oqj9P9dEIJy0hhlLm7XWFRXGJ7j8su/VPkjYNRsUapOTBkcHf5jHf5v1zq//HSz2hFRmNEQhmDxGwx/mz8n4OV/6F52AAoPMe0vm5yhfHm9qopsAG09M5brtUqNCgQJ6KsJCAhwWFx7Oyv+jYYdEz3sMma1QAUCWgHblMTD5jx4ADg34LVD42zdBaYgmz/4RmSLAtdjXYM+G0adOmTZtmqNrNE90CVlpaevbs2czMzNdeey0/P79Dhw4m2eBiNGLkqV6sXT+btgDAXr+GrW3UHX1NbVTTINxHQgUgCaC2FtKDV1dn3Uie5+L8bKeOSxECO0bYW8CsuiMp5dFrHuo32lHTU5n2MsEi58kJzZDVnSzkl2Uu6BCwtLQ0MZdKUVHRmDFj1qxZc/78+RMnTvj4aElrawGU86pfy2+/49qDQuiR+0Z3s3Xf+Df4ISX8JKGcwGmBrGQrFhBQvc3bJY/nqxISpzOMfXDQVwjRCZXU8mzp5XJqqDP/iQ/nLROKMMndTiBYMjriEURGRvbr1+/evXvidoGNGzd27tx50aJFRrHNBBwoS1cK/ARHfwBgUpKQWq0ODNF5VvMHF1P8tyxIsfVbFO1M0dM5fIURLpm1MOMbyQuqqu+EBn9fhF3mZUifv24lV8Oerspd/kpvGXkQJhAsHx0jsLNnz546dapmztDJyWnp0qVjx441vGGmIUae9qytV3uJPQCwSQm8t/m7bwAABn67BDCmp3GUgxXAPz4dYIuReabazsrekpf/i2/Xbd+X9/gilWUQ+rgDN8ND/WS8AwKhqXj68G+mihtpqegQMCcnp8ccVTmOs7GxMaRJJuOmsvhadd72ts+DJblvIMAKAATIDYQ4tipeUFBKXiMBALDCOIdCHuY3WCku+TMj89P7rb9cnvfKQ46a4q55vx3nwpKFLoLB0T98MMEI6BCw0aNHr1ix4uDBg+LbtLS0JUuWDB8+3PCGmYAYeZo9LR1h3xEA2OtXsY2tBbhvCEk0AFA9eRTKA4BMJpNIJOXlfz+U8IDcTWhdY1Ao7v+S9MWPNn8mlwcPcOCjuyr8rbVrsD2LnnUx62lSQvMCY1xV9VQxQ59mHxjhSXQI2Lp166ZNm9a6dWtxm3dZWdmQIUOioqKMY5wx0WBhn/zmyw5+VhSDOI65mcKZv/sGvkcJhxkUwFMj1GJ4CtoaWBmFSsxv1CVSwnFLEpN+ZX/zkgg7fFSjXerbzmVH423BrEHj9hIIBBOiQ8BsbGwOHjyYlpaWnJzM87y/v39QUJBFDqJPVGQXaKonO/kDAJOahNRqjbm7b8gRv4cFT0yP1YD5f2NqAb7LZ9dkU2phxLxWd9/t7C5FZM6QQGjR6N4HVl5ejhAKDAwU3966dQsAxERqlkSMPK2LzCXUyh0A2KQEjblH31CBZjeLWKAnqYE2+47+Dzm9Ilt6qxr10hz4qH1lT++XnwwETiAQWho6BOzLL7+MjIx8Mm6xue8MdUv+sq7jvcr4P/MrFGbtviEAv18CZRQ9gwMb8/6mspTUJ3fYQ8VMkFXFf5UvP+vuGej9P1MbRSAQmgU6BGzVqlUzZsx4//33nZzM09u64cy8y2EbW405u2/wxxicQdGTOHA317UuAKji0f8eMJvus84sfNa+yCcrTGLtFNA1xtR2EQj/oEkC/iZC9tr+JwCuAOlE836CbOboEDCappcsWWKpcTeexE4DL+epuJ69zNd9AyfQ+BJDDdMgP3NVLwFDbCHz0R1JGY+me6jfa6dIS5hUKSi6hxyiKJmprSMQ/kHIAf4GMH0xcvv3P3jQ/AVCEZKacbpjM0DHrrrJkydHR0eb+4Sh/kx5qLLlQRMYampDGgm+QwlHWBTKU33NNdr61QpqxA2rtzOkoXbChe6KTztw9zM/KJX/FdRtu5VVO1NbRyD8C2QLdC/MJyPKGdjej/6YHsCnI6odalywdA8PDxcXFw8PD3d3dzc3tylTpoi++xqNJioqKjQ01N3dvWvXru+++26NTz/P82vXrg0JCXF1dfXz89u2bVsTXmNzRscHvHjxYl9f3wMHDnh7e9d2Pjxy5IiBDTMNr9/jTroyYY5mOV+Ki5DwkwTaCtRIs4w0/1CFPrkriS1gOlsLewOUzznyAJCbuz/n7jd+vitdXZ8ztYEEghYoe2BewdyPSPIypjsB5kEVjZAdSMdgTVIj3X/j4uJCQkIAoLy8vE+fPps3b162bNmrr75aWlq6b9++Dh06FBQULFu2bNCgQefPn6dpes6cObm5uceOHXN1db1y5crUqVPd3NzGjRvXpBfaHNEhYNOmTXNycgoPD28Ja2C95HxIOT8x1CbM1JY0AqwAfrcEZJiZqAZzm/5UCOibh8zn91kJhT7uwM30UNMIAKCiMjU5NdLd/QUf77dMbSOBUCe0J0hEDRuD1RceqZfOvSvR0dHx8fG5ubkpKSnt2rX75ptvnvTutre3f/755+/fv3/u3LkzZ87cvHnT1tYWANzd3Xfs2NGnT5/o6OiwsLD9+/dnZWU5OjoCQN++fb/66qu7d+8a5lqbFzoELCEh4dChQ2JAeotn1j1VvpT6rZUZ5njkQdgrQQpEzVKBtZnN9x4vod/LkuRy1BR3zfL2nDPzyH61Wp6QMF0maxsYsBksYCMbwVLg4kF94l83JHf80Qvld4+Oay4/elH13t8lpWCz8vHf5q5duy5evBgcHLxx48ZXXnnl8uXLtf+LMU5PTz9//vzq1asvXrwYEREhqpcIRVGjRo26cOECy7Ldu3cX1UskIiLiqa/SPNAhYKGhobTZujM0CAcNHpfLbfaWqs0w2KZwlMV3KXoqh1zMSb2SqqjlWZKL5fSzjvwu/2r/Wh7/GAvXb8zh1EV9+xxnGDsTGkkgPAbtB+jve5W/BYCA9gUQQP0XAgqgFOgemHIDAOAOI8moRyWRtn40IiJCnCqcP3/++++/L5fLRR0aPHgwy7KCIBQWFk6dOnXIkCEJCQkM83h3LZFIFAoFx3EtpJd+Eh0C9u67786ZMycyMrJ9+/a118AsT+EnPeSsePjOy/zClAnnGeEKTb2gRh3Mxu2wRA1R9yTf5rHtpcKOLloiQmVkri0q+j0k+FtbGzPez0CwSGhPoD3/flMFgIDpAapoRHuBdAzmc4H7ETEvY7oTcL8B27veqv4WHoQQRVE1O25r1sAePnwYHh5+9OjRXr16ffPNN0qlUiZ75IiLMT527Nj48eODg4OXLFlSUVEhJr0CgNjY2PXr11+6dKnJr725oUPAJkyYAAALFy587HhlZaWhLDIRr9/jTrqxOVZmNv7CmbRwiqH6aqhe5pGdUowI9dldiUbAi9pyC700kiciQhUUHMvK3tip4xIP95EmMZJA0B+M//HaAFRrPexl3dMhp06dSk1N9ff337Jli5+fn7Pz49F/PD09n3322aSkpGXLlgUEBEyaNGnjxo3t27cvLCxcuXJlcXHxrFmzpFLpwIEDp06dunXr1rZt22ZkZHz44Ydvv/22YS63eaFDwCxPqEQKu80HALv1q/59mBePmwu4EPH7WOTDU0PNw2n+Dzm9PFuSoaDGuWlWenNu2hKgVFXfTkqe5+oysGOHxca3kEBoEBgDn4AoL5AMw/jvHA+UE0gmYNUeBLrmRJ555pkFCxbcvHnTy8tr165dWst06tTpxIkT7733XmxsbFRU1KhRo3Jzc11cXEaMGHH27Fkxtv3u3btXrVo1ZMiQwsJCJyenOXPmvPVWi/B7Qlr3eG3fvj04ODgsLOz06dNaT2vmbh1yuVyj0dGnP6Fej6hY+qEBLNKCvb19eXl548+vRppvJIgBaqYK6b2719raWiaTlZSUNL7dRpGLbJek8idKqO52wic+qp522n/ZPF918a9hGk1VWN9TEsnTxqKUSqV2dnbFxcVG3sgok8kEQeA4zpiNMgzj6OhYVlamVht1EwXLsgzDKBQKYzYKAK6urpWVlY9lK9R5ylM2ijF+7JmeO4TUlwBJtJUWABBY//df917tdCrR0dGnTp36/vvvn9Kqloz2EdjcuXMXL14cFhY2bNgwrQUadN8YHysrq0afWzOPbGgYhml0W1gNFd9pkArbz2EoV62/njobRQgZ7RoBQK7GUdnw5R3sylI7gqgpnlTd2zvxxb/mVCtynguPd3Js//RNi9lv7ezsjCxgNE1jjI2c9klcora2tn4ycqlBoSgKIfSkf4ERkMlkLKuvz7CBnicko7FktCEqJuiF9hHYnTt37O3tn5yQNRd0jsDqGn6JGGcQ1vgRGAbhICuk0PQrHPJuWG9lzBGYGBFq5R1JJQ/z2qOFnioZ1PelZGVvSs/4OLDbljaeTRN+h4zAjEALH4E1FJLQsmnR7rPg7e0tqldERATP/8s7IC8vb8yYMcYwjVAHwhlGSKLpF9QNVS9jcq6MHnTd6u0MaXc74Xx35ce+yKberC7FxWcyMtd4t5/bVOpFIBAsnjoH/mvXrgWAuLi4tWvX1t5kkJGRcfbsWWOYRtAGTqOF0ww1gEfdm6nb4QMV+vSuZG8BE2gjHA5U9rXXbadCcT8xabaDQw/fzh8YwUICgWAZ1Clgx44dE1+cOHGi9g4wmqY///xzg9tlYCqWfmhyJ45GgHMp/gBLdRGoQc0x2qFCQJvvM1/eZ20Y9EmtiFD1IwiqxOuvUxQbGvwtRZlhGBQCgWAi6hQw0f+wZ8+ecXFxJlmhJTxOBRJiWOQiUGO55hZZCQMcLmb+my3JV6PXPNTL2nH2et8yKWn/qahM6d3zZ6nU3ZA2EghNgETSAJ+pJ2mxITMMhI5u5sqVK8axw/iII63a47DmPPYCDeL3sBgDPVkNzWyUcr2Sej9LcqmCHujIx3RVdWlIMMacuzsePNjdrevnjo71RiwgEJoBCCHigtGsaOlDq4qlH9rb2yOEysrKTG1L3WDgDzI4H9GvccihGUU7zOfQunuS6HzGRybs7qoc4tSwZblS+eVb6R+28ZzYtu0rBrKQQCBYMC1dwMwC4XcWp9L0WDVq21zUS4wItTaHpRBa3o6b46mWNDAIF8cVXk+aaWvjF+NBKUQAACAASURBVNA1yjA2EggEC4cIWHNHuE4Lf9LUIA0KbC5uh8dL6BXZkrsqapyb5iNvzlVbRKj6EQR1wvWZgqAKDd1JUXrHESEQCIRa6BYwhULx4MGDxw526tTJMPYQ/s09SjjEoK48NaBZRDvMUFAfZEviSulnHPjvuygCbBq5Ee1W+gdy+eVePfZZybya1kICgdBy0CFgsbGxr7zyikqleuy4kUMbtFDkSLOHRe6YHqMxuduhXAPr7kq+y2NbSfCWzqoJrTSNtuhh7r6cuzu6+K1ydu7XlCYSCIQWhu58YC+99NJHH33k4uJiHIMIj1CBZjeLWKCnqqHhc3RNiAbD7nzm07uSah4i23Lz22pkVOPtqahISUld1NpjjHf7uU1oJIFAaIHoELDS0tIPPvjAz8/PONYQHoGBPyABOUXP5MDGlOr1Zxm9PEtys5oa5aJZ6c15yZ7KGLW69FridCsr724BG5vKQgKB0GLR4Tr23HPPpaamGscUQg38MQanU/TLHLibLNrhHSU186Z0bLJMQsHhQOWOLqqnVC+Mhes35mo08u4hO2nauqnsJBAILRYdI7ClS5fOnTs3LS2tV69etXOUNPN8YGYNTqDxXwz1vAb5mUa9qgW05T7z5X3WkYUNHVVT3TX6RITSya30j4uL47uHRltb+zRBdQQCocWjQ8Cee+45APj0008fO97M84GZLziHEo6wKISnwgzidnirCsU/5F91rKN1gL0FzKo7klIeveahfq+92q7eEPL68+Dh4dtZmzp1XOrmOqRJKiQQCAQdAkaEyqiUIv4nFrURqFGGitV7V4kvlgpaBSyhklqeLb1cTg105D/14Xytm2z8V1WVeeXq7FathnbssLip6iQQCIQGhk8AuHr16qBBgwxhSgsHK4CPloAE6ElqZNyAn3kcWnxbOizJqlQNMV2V+wKUTahePF+VcP01qdQtJGg7Qg2+3wgEAqEudIzAEhIS3njjjezs7JojFRUVvXr1MrBVLQ8ehFgJrkT0TBU0JBjuU8IJ8H0+uyaHZRobEUoXOCn5HYXi3qDwMyzr8FhyVAKBQHgadHRX8+fPl8lkGzdupGl6/fr1q1atsre337lzp3GMazkIR1l8h6LHqVEr46nX8RI67JrVB9mSES78xe7V89s2uXpBVvam/PzDgQGbHBwCmrhqAoHQ4tE9Ajt06NCgQYPi4uI8PDyGDx9eWlq6bNmy2NhY49jXEhAuMMIVmhqhRp2NNEBJr6ZWZEvi5XR/B/7HroquTTdhWJui4j8yMtf6eM/z8HjJEPUTCIQWjo5HboSQIAgA0LNnz3PnzgFAeHh4fHy8MUwzFudL8elik20Wxpm0cJJBvTVU76ZXr2oByTUg10ChGtKr0V/l1KUydFmOn020ylSi//kqv+ui9JQIcg00+fUrFPeuJ73h5BTm23lFU9dNIBAIADpHYH369Fm9enX79u1DQkL+97//LVq06OLFixaWVPQvOVTzOLSVCZrGhYjfx1IdBGpYI53m1QKUaFCJGko1VIkGFamhREOVqKFUg4rV6K9ySikgAWOhVixFBNiBwQhg3V3JuruPDm715XrbNZmCCoIq4frrNG0VEvx/CJGMBwQCwSDo6Fw2b948derUAwcOLF682MXFxcPDQ61Wf/DBB8YxzrIRKjG/W4JsMRrHPTkS1uB/lKlYDSVqVFxLmUo1qFgNxWpUwT++x9iWxk4MdpOAE4OHO/POLHZmwYkWxCN3eWm8nP66Q4VBLy0ldWllRVqf3kckLAmhSSAQDIUOAfP397927ZogCBRFHT9+PD4+3sbGZuDAgcYxzlJRCihfiZx+0rAK9PvLmgelrFwN+Woqj0NyNZTxSK5BRWrE/3teT4qwIwuODHagsQuLA2ywOys4suBAY0cGOzLgIcGtpViC6p0OVABj4NTTOXe/efAwplvAFw4OoYZtiUAgtGy0C9j27duDg4PDwsJOnz5d+7iNjQ0A/PHHH8YJJXXy5Mn9+/crlUovL6+5c+d6enoCwLJly9LT0xFCADBs2LDZs2cbwRI9UQpIroF8DuVxSK5BZTySq0GuQeKRGmUSBPgyRXgxD0/uTp0rkEoL/1EmRxa62AiPKZMDI3hKsL05TMWVyi/fSl/p1XZ62zbTTG0LgUCwcLR3inPnzl28eHFYWNiwYcO0FjBChI4HDx5s375969atLi4uMTExX3zxxfr168Xj0dHR1tZGjQarjzIVq5Gm7jGTIwveVoKHBLtLcJ9EFJBL5b5Arw2obi3BDuagTPqg4goSr8+wtwv093889hiBQCA0Odr7zuzsbHt7ezBpKKmioqKhQ4e6u7sDQHh4+PHjxwFAoVAIgtC06oUB7inhWAldqqFK1FCkRsWiT0StBafHZuVkFHZmwYnBrixuI8VBLHZiBGcWnBnszGJXFjsx2JkFK215s4RUSrgkofrzAYMl5eWWkxdUENSJ12dizIcEf0shianNIRAIlo92AcvMzKz/tIiICAMY8y+Cg4ODg4MBgOO4mJiYAQMGAEBeXh5FUWvXrs3MzOzYsePMmTNbtXrkPrhz587NmzeLr6Ojo7t06fJknXI19o9Tqf6960kpYAWPvwMZACAAhAABUADhbrSfFJxY5ClDrWXIiQUnFjlJHh1p3EWp7wslPyukXSmnCbZAgaura+PqaTTSAh4h3hDtXrr8llx+JWLwKfdWQVoLyGSyJm9UH1pULlYHBweTtCsuLhgZW1tbW1tbPQsrFAqDGkMwCQhjLYOA2rdFdXW1WAYhhDG2sbHx9vZOTk42jn0XLlz47rvvevfu/frrr9M0fffu3fj4+JdeeomiqIMHD6akpHz22WdiyfT09BqrwsLC7Ozs9Gxi60NJdjV+p43aVYqsnyLXsE5wOSj+B8gGrOYASEAmkxl/gFsoSBIrqSH2Tdzuvft7rl6bHRiwtmPHeVoLSKVStVot7ik0GgzDyGSyqqoqrTe54WBZFmOs0Rgkn0BdUBRlbW2tUCiMHK+LpmmKotRqQ4WfrgtbW1uVSqV/uxqNxtGxjiwMBLNF+wissrJSfPHLL79ERkZu3bo1PDwcIfTnn3/OnTv3k08+MYJlGOPt27dnZ2d/8MEHXl5e4kEPD4+pU6cyDAMAL7744qFDhzDGokOHr6+vr6+vWEwul+uvDRizrSTQCimBAwPqiQbxOyWYB3oipxQwKEEikRhfwNytqRc9ZCUlTdluRUVy4vX5rT3Gtmkzs64rYhhGpVIZuW+VSqXiU4KRBQwABEHgOM6YLTIMY21tzXGckbWEZVmGYYx/J9va2qrVapIuo4WjIxLHihUrPv/882HDhslkMqlUGhERERUVZZx9YAkJCWlpaWvWrKlRLwA4c+bMf/7zn6qqKo7j4uPj/f39RfVq7mDgf2ZwPtATOeRgOeteAKBWl15LnG5t5dMt4AtT20IgEFoWOhzgcnJynJ2dax9xdHS8e/duXeWbkOTk5JycnAkTJohvra2tf/zxx0GDBuXk5MyZMwch5Ovru2DBAiNY8vQIvzM4habHqpGXRakXxsL1pDkaTXmvnvtp2qh+oQQCgaB9DayGiIgIiqL27dsnOiWWl5e//PLL4qZmY1nYGORyuf4rEDuK7ap5eKeVoYJT4BSa38dS4Rpq4L9Msre3Ly8vN1CjdWFtbS2TyUpKSpqktvSMVdl3/tc9dJebqw6nHltbW+Mvz0ilUjs7u+LiYiNPIcpkMpNMITo6OpaVlZlkCtH4LhKurq6VlZUNmkI0vs8UwdDoGIFt2bJl4MCB3t7eYg6wy5cvSySSM2fOGMU2i+AexR9kkD9PPWvUJX0jkF/wW1b2ls6dlulULwKBQDAEOgSsS5cumZmZu3btSktLYxhm/PjxkydPNonLrOEIdUCcYJAndCxH/B4WtcL0GA2Yw1Kd/lRVZd5IfruV29AOPgtNbQuBQGih6A4CodFo2rRpo1AoXnvttfz8fJZljWCWMQl3BoSosiaPEKgCPoYFCqhJamAtaulLo6lMuP6aROIWFLgVoaZOgkkgEAj6oUPA0tLSxLCHRUVFY8aMWbNmzfnz50+cOOHj42MM68wXDPwBCZRSzEwO7C1KvQDwjeR3FIr7ffscYxh7UxtDIBBaLjoenyMjI/v163fv3j1xX/DGjRs7d+68aNEio9hmxggnGJxO0WM5cDfq1l0jcDvr8/yCXwO7bbKz1RLrhEAgEIyGjhHY2bNnT506JZE8Cm3n5OS0dOnSsWPHGt4wMwYn0sIFhhqqQV0sTb2Kik9n3l7fwedtD/cXTW0LgUBo6egYgTk5OT3mqMpxnIU5cTQt+C4lHGZRCE89Y2luhwrFvetJbzo7PdO50/umtoVAIBB0Cdjo0aNXrFhRWFgovk1LS1uyZMnw4cMNb5h5Uor4PSy0EehRlqZegqBMuP4aw1gHB3+DkKUkgCEQCOaMDgFbt26dm5tb69aty8rKQkJCunbt2rp166ioKOMYZ2aogI+RgAToSWqgLcxxA1LSllZW3goJ+lbCtqDg7gQCoTmj41Haxsbm4MGDaWlpycnJPM/7+/sHBQWZR/hBIyMA/5MElyF6hgqsLU29cnK+evBgT7eAjQ4Ooaa2hUAgEB6hXcCezJbi7+8vvkhJSQGAbt26GdQss0M4yuI7FD2JQ+6Wpl7yssu3Mla185rRts1UU9tCIBAI/6BdwAIDA+s/zfj5KZoz+C9GuExTI9TI19LcDlVcQULiDHv7oC5dVpvaFgKBQPgX2gXM09MzNze3X79+48aNGzp0qJWVlZHNMiPwbZo/zqDuPNXbqJFqjYAgqBMTZ2DMhwR9SyGJqc0hEAiEf6E9Gr0gCBcvXty/f/+BAwcKCwtHjhw5bty44cOHm4sDfWVlpf5jRFGeGxdOWygA5TaE2mKr13U6xGhp1/gxvKVSKcuyNQlL6+d60sKcuz88E3bI1aX/07dr/IzMLMvKZLIG3QxN1a5JMjLb2NhUV1cbPyMzTdNGDr0PAHZ2dkqlUv/Q+zzPk4zMlof2TpeiqGeeeWbDhg1ZWVl//PFHhw4dli9f7ubm9vLLL8fExBg/CUjzBFeD8geE7EA2tcHq1fy5d3/PnZxvA7uteXr1IhAIBEOgIx9YDRjjlJSU/fv3f/3110VFRSqVytCWPQ0Nygdmb2+PECpraDRfHvgfJZBP0bNV4NyYB/zmnA+soiL5wl/D3d1fCA7c3iTtknxghobkA9PnFMPZQzAJ+g4cMjMzDx8+fOjQoby8vGeeecagNpkF/K8svkdRE7jGqVdzhuNKriVOt7Hu0K3rF6a2hUAgEOpEh4DdvHnz448/DgkJ8ff3//333994443c3Nz4+HjjGNdsEf6k8TWaGqFGPpbmdogxn5Q8R6MpDw3dSdPEeYdAIDRftHshpqam7tu3LzY29ubNm4MHD37nnXdefPFFMgAXEdIo4XeW6sdTPSzN7RAA0jNWFxf/0SN0t7WVt6ltIRAIhPrQLmABAQEA0K9fv08++cTZ2Rlj/PPPP9cuMGvWLGNY1/zAeZRwQII68tRgo640GIf8/F+z72z17fy+q+tgU9tCIBAIOtAuYO7u7gCQmZn5+eefay3QQgWsEgkxLHLC9Hi15bkdVlVl3Eh5p1Wr5zv4LDC1LQQCgaAb7QKWl5dnZDvMAA3i90gwD/RUDqSmNqap0WgqExJfk0paBXX7HwCJdUkgEMwAkhdDPzDwvzA4D+jpHHKwNLdDAJyc8o5C+aBvn2MMY29qYwgEAkEvLG4izDAIpxmcTFOjNcjL8tQLMm9H5eX/GtjtSzvbLqa2hUAgEPSFCJhucCotnGGogRoqyALdDouKT9/O2tCxwwIP99GmtoVAIBAaABEwHeCHFH+QQf48NdDSkiwDgEJ5L+nGm87O/Tp1XGZqWwgEAqFhkDWw+sDlSNjDIjdMj9FYhmfDgZ9tAGDY0EIAEARlQsJ0mrYOCfoGIdrUphEIBELDIAJWNxzwu1jAQE9SA2uBS18pqUsqq9L79D7Css6mtoVAIBAaDJlCrAMM/AEJFCN6khrZW4h6HTvhVvPiTs62Bw9/Cui63sE+xLRWEQgEQuNo7gLG8/wbb7xRO2r7tWvX5s2bN3PmzC+//NJwAb+Fkwy+RVHj1KiNpUU7FLl568P27Wa18ZxsakMIBAKhkTRrATt69OiyZctq76qurq7esGHD0qVLv/7668rKyiNHjhiiXZxIC+cZarCa6mI56lUz/KrBz/cjk1hCIBAITUKzFrB27dpNmDCBZdmaI1evXu3cubO3tzdN0yNGjDh37lyTN4rvUvxhhgrhqf4W6DRfmxOn2pjaBAKBQGg8zdqJQ4wpTNP/OMgVFRW5uT0aSbi5uRUVFdX8Kz09PTk5WXwdFhZmZ2enZysURSGEZDIZAOBSqP4J6LYgG0cjxrCOeRRFiY0agZ8Paf80jGYATdNSqVQQjDqiZRgGAGQymZETWrIsizGmKKM+HYrNSSSS2r8XI0DTtDHv5NrUfrTVif4ZbglmRLMWMJ3U7pguXLiwefNm8XV0dHTr1q3rOkudwxdvUFLSRzH/qkHMLo0AQFBiwGA3SCpzbMBvo9HY2toaoZXo3XXuAPj5kN20KUbq3BvU3TQhNjY2JmnXJFhZmSaFm1RqgvCgUqlU/3aNnzOaYATMTMBcXV2TkpLE10VFRbVTlE2fPn369Onia7lcXntw9hi4ggInFiOgp3Ngh+3t7RFCZaVl/C4WsmnkIFSgisoig48V7O3tazunmIro3UjcFmZQbG1tFQoFzxt1VlYqldrZ2RUXFxt5BCaTyQRBMJyHkVYYhnF0dCwrK1OrjZroh2VZhmGMLw+urq6VlZVKpVL/U0yl7gTD0azXwJ6ke/fuGRkZeXl5GOOTJ0/279+/cfUgO4zCNPxOCVQ8Gp3wR1icRVOBPLhZiNM8ACiVuU/6bhAIBIJlYGYjMBsbm8jIyDVr1vA87+fnN3LkyEZXRfXgBQB+pwS/DcorPL5GU34CNUbN7zLNTFfTIgjqe/e/S8/4VCpp5ev7YRvPCeIcqbW1tUwmKykpMbWBBAKB8LSYgYDt3bu39tsePXr06NGjSWoWNazsC0oow6itQE026pyP4SgtvZiatrSyKt2z9Tg/39USCQm0QSAQLBAzEDCDgrry+CxGEqAnGHXlwECo1aXpGR/fu/+jnV1An16/Ojr2NLVFBAKBYChatIBhBQg/SqzCaGSLqn/Aok+HqY1qNPjBw703b32Isca/y8ftvGaS+LwEAsGyabkCJqoX5S/IImiEkEKh4HdK6OlmOYtYUZGSmra0VH7ZzW1ogP96mczT1BYRCASCwWmpAiY8Ui804NH2xhqfDvMahPF89e2sDdl3tlpZefXssdfV5TlTW0QgEAhGokUKmBrwAwp14DHC+CytlPEAIChpAAAXAWfSmDOP5F8FhcdT097luOKOHSI7+CygKBNsJiUQCART0RIFDLkIKECDWmkZaSEvAVlhcGvuMXyrFXdS05YVFcW5OA/o1SPWxqazqS0iEAgEY9MSBQysgR77T2A0mT2NEOLKzCN0ryCo7+Rsy7y9jmUdA7ttaeM50dQWEQgEgmlokQJmtpSUnEtN+09VdVY7r9c7d3qPYfQNWEwgEAiWBxEw80DFFaSnf/Tg4V57++C+vX9zcAg1tUUEAoFgYixTwCQSif6xz8X0E8YP9EnTtD6NYizcyfk+OWUFQigocF0HnzkINT6CJcuyCCGTXKxUKjVyUF0xnYqVlZXx28UYGzmtiZhORSqVildtNMR0KsZssQaJRIKQvu5WJJ2KRWKZAsbzvP6ppwRBQAgZ//7GGOtstKzselLyIrn8mlfbif5dVkulbjwvADTex0Ts3Yx/sSzLNuhLaRLE3k2j0RhZwCiK0ufLbVpEveR53iQ9tUkabdDFGvneIxgHixUw/e9ssXczchIKABAEoZ5G1eqyzNuf3b33rbWVd88esa4uA6EpjBRzLRr/YqVSqUajMXI6FXFkoFarjSxgNE3X/+UaAvEaNRqN8b9cMMXPBwB4njdJu4Tmg2UKmLmTl38oNW0Zz1d27LCog89CipKY2iICgUBodhABa15UV2el3lxWVBTv5ja0q/9aK5mXqS0iEAiEZgoRsOaCICizsr/MytokkbqEBO/wcB9taosIBAKhWUMErFlQWHQyNW2ZSpXr5fWab+flNG1jaosIBAKhuUMEzMSoVHnpGasfPNzr5NS3e0i0nZ2/qS0iEAgE84AImMnAWJNz9+uMzDUIsQFdN3i1fQXMI4YwgUAgNAuIgJmGsvLES5eXlZRea+M5vovfapZ1NrVFBAKBYGYQATM2arU88/a6u/d2ODh069P7VyfHXqa2iEAgEMwSImDGBD94uPfW/7d350FRXOsCwE93z8oyrKOghkVEQRSNgjdxu64U7ktEo5ikEEjASoK7FljGuAQMUGqpuZZrqeQZEUudqmgU8wBRUZ+IGgQiKJskAwEFhmGGWbrfH13XUGh0gJnT0/D9/mp6zvT5ztDMR2/f+f0bI63xHZQwInCTStXKdUgAAMBX/EtgmzZtevLkCVslKDQ0NDo6muuITKJWlxUVb2h4kSuXhwz12yWVDiAI/n34AABgPfj3HVpTU5OWlmZjY8N1IKYyGjXlFfuele8Vi92DRv3k6jqV64gAAKAn4FkC02g0NE2/MXs1NDTU1dWxy3K53PSa3ARBEARhoRretXW/FD7e0Nam9PRY4TdkC0X9HbnlOn0LtjwgJ/1SFGV67XCzYOvbsrXhcfZLkiT+Xy47WIqi8Bd+JEkS/x7Fdm16v1DMt0ciMO/u3VReXr5ly5aAgICysjIfH5/IyMg+ffqwL504cWLfvn3sclpamp+fH3dhIoRQa+vze/mrqqrP9e3z7zFj/uMggwe8AOCMRqPBP4sQsDSeJbCqqqqsrKz58+eTJHn+/PnHjx/v2rWLfemPP/54/vw5u+zl5SUWi03cpo2NDUEQarXaXEHStL6y6mhxyXahwM7f/9sB/Ze88QEvW1tbM3ZqIolEIhKJmpubMfcrlUp1Oh3mavRCodDGxqa5uRnzTi4SifCX/Kcoys7OTq1WY57ZRCAQUBTV1taGs1OEkIODg0aj0el0JranadrJycmiIQH8eHYK0c3NLTw8nD1vMG/ePIVCwTAMe2KqX79+/fr1Y5s1Njaa/vVh3ulUXr7MKyre0KJ+0s99kd+QHUKhk17/5i8U/DNuIE6nU9Hr9TCdiuXAdCqgF+JmKtUuu379+oYNG9RqtU6ny8rK8vf3x3xZ5S30+pePi9be+b95BCH815hLw4cdEArhPz4AALAUnh2BTZkypbKyMiYmhiCIwYMHx8XFcR0Ri6n5I/33J1sYxujvt8PjvUiCwDqdPAAA9EI8S2AkSUZGRkZGRnIdyN9UqsLHxesbG+/J5SEB/skSST+uIwIAgF6BZwnMqhiNrU+fpZZXHJBKPYJGpbu6TuY6IgAA6EUggXVR3V9Xioo36nQNPgPXDBy4iiREXEcEAAC9CySwTmvVVBQVbaxv+F8X5wnBozNsbQdxHREAAPRGkMA6gab1FZX/KXv6vVDoNHzY/v79lnAdEQAA9F49M4Gx1aE6+5a3N3jx4kZh0frW1nJPjxW+g+IFArtuBGhqp2bH9sjJswdd+KV0v0fE0YeMf7Dtu8bfYy8ZLLA2PTOBSSQS0xuzj0Xb2f1jQtJqlY9+i6+s+h9np9Ef/CvH2Wm0GUJESCAQvKVTCxEIBARBcNIvSZL4axIihOzs7PA/yMwwjEiE9bIo+1UulUpNr0FjFmzhR7YSI2Zisdj0Woim1+wAPNIzE5hGozG9oI5MJiMIQqVSvf4Sw9DPa9J+f7KVICh/v50e70URBPnGll0gk8nMtSnT2djYSCQS/P3a2dlpNBrMlTjEYrFQKFSpVJgTmEQioWka8zemQCAQiUStra2Yi1MIhUKBQKDRaHB2ihASi8VarVar1Zr+Fnt7e8vFAzjRMxNYp6RniBFCoSF/dVjf3PzocfH6pqaC/v3ChgzZJhK6cBEdAACAN+NZKSmz++WqvMMCQkivbyouic+7E2IwNAePzhg+7ABkLwAAsDZwBNaRslZRVLzRaFT7DFwz0HsVScIDXgAAYI16dQJrf9TF/ujqMqm+IVsuDxnqlySVvsdVYAAAAN6pVyew17Wof39/xLG+fedwHQgAAIB34FkCYxgmLS3t2rVrCCFvb++4uLguT1LX4fCLpdX+CdkLAAB4gWc3cTx8+DA7O3vfvn1Hjx6VyWTp6elcRwQAAIAbPEtgcrl8/fr1MpnMYDA4ODjY2tp2bTtvPPx650sAAACsB4H5GU+zyM3N3bNnj4uLy+7du1/lsJycnMuXL7PLMTEx7u7u//T2s+feXacj7KNOPCDZNUKhEP+E6GxFDPxVCQQCgdFoxF+JQygU6nQ6Tipx0DSNs1OCIEQikV6vx9wvW4kD8yPqCCGxWGwwGEzvV6fTwYPMPQ/ProGxJkyYEBwcfPLkyb1798bHx7MrVSpVTU0Nu2w0GrtZ2wZDaRxOCvCw5eM46Zf9WsfcKfpvQSmc2KJZnBR+ZNMJ5n65KkjYqd8s/t0AYMCzI7DMzEyBQDB58mSE0LNnz3bs2HHs2LHXmzU2Nna2lFRTU5M5AzWt3+bmZsydsqWkXrx4gblfrkpJ2dvbNzQ09JJSUo6Ojk1NTb2klJSrq2tLS0unSkm5urpaLh7ACZ79VyKRSDIyMrRaLcMwN27c8PPz4zoiAAAA3ODZKcTx48eXlZWtXLmSJMlBgwbFxsZyHREAAABu8CyBEQQRERERERHBdSAAAAA4xrNTiAAAAAALEhgAAABeggQGAACAlyCBAQAA4CVIYAAAAHiJZ3chmkgsFovFYhMbUxRFEESXyyp2GUVR+DsVCoWcDFYgEEilUvwlnRBCtra2mPsVCAQMW23asAAADM9JREFUwwiFQpydspUmJBKJSIR1Clbyv3B2yhKLxabXlMFftg1g0DMTWKeKpAkEAoIg2traLBrSG/vF3ylBECRJ4u+XLcCIuUyfSCQSiURtbW34y83QNI35G5OiKLFYrNfrTa9BYxYCgYCTPVkqlRoMBtP7xbzvATx6ZgIzGo2m/xmz326Y/+zZfvF3yv4ZczJYo9GIuZQU+++5wWDAfwRG0zT+Dxl1cs83C7YWYi8ZLLA2cA0MAAAAL0ECQ1VVVRUVFfj7xT8DBUKorq6upKQEf7/451JBCDU3NxcWFuL/nBmGwT/Ytra2wsLC1tZWzP1yMliEUGFh4cuXL/H3C6wKz6rRW8LatWu1Wu2BAwe4DgSHH374QaFQ/PLLL1wHgsOVK1cSEhJ+/fVXBwcHrmOxuNLS0qVLlx46dGjUqFFcx2JxNE2PGTNm48aNYWFhXMcCuARHYAAAAHgJEhgAAABeorZu3cp1DBwTCoWDBw/28fHhOhAcKIry9PQMCAjgOhAcKIpyc3MbOXKkQNAz77ZtjyRJR0fHUaNG2dnZcR0LDhKJZPTo0TBHZS8H18AAAADwEpxCBAAAwEs99tSK0WiMjY1NSUmRyWSdfe/9+/ePHj2q1WpHjBgRExMjEokYhklLS7t27RpCyNvbOy4uzsnJyQJRd5F5B/vqpfz8/IMHDx4+fNiswXaX2Qe7adOmJ0+eEASBEAoNDY2OjjZ/0F1l9sFWVVXt37+/trZ2wIABa9ascXFxsUDUXWTewV68ePHkyZPtN37s2DFnZ2ezhgy4xvREly5dWrdu3Zw5c5qamjr7XrVavWzZsvLycoPBsHPnznPnzjEMU1BQsGLFiqamJr1en5qaevDgQQtE3UVmHyyrtrY2IiIiMjLSrMF2lyUGu3z5crVabe5IzcDsgzUYDJGRkQUFBUaj8ciRIykpKRaIuosstBuz7ty5s2fPHjNFCqxIzzyF6OHhsXjx4g7VVK9fvx4bGxsVFbVt27aGhoZ/em9+fr6vr6+XlxdFUTNnzrx58yZCSC6Xr1+/XiaTGQwGBwcH/MVw38Lsg0UI6fX6lJSUZcuWWTb0zjP7YDUaDU3TNjY2Fg+988w+2AcPHri6uo4cOZIkyU8//XTFihUWH4PJLLEbszQazcWLF7/44gtLhQ640zMTWEBAQHBwcPtK1ZWVlT/99FNiYuKhQ4fef//9lJSU9u3XrVv3arm+vl4ul7PLcrm8vr4eIdS/f38/P7/c3Nzw8PA7d+4sWLAAyzhMYvbBIoSOHDkyYcIEPz8/y4ffOWYfrFKpJEkyKSkpKioqMTGxrq4OyzhMYonB2tjYbN++PTIyMjExUavVYhmHSSyxG7NOnTo1a9YsiURiyfABN3rsNbAO7t+/r1ard+zYgRBiGEaj0TAMw172QG+tVM20u0tzwoQJwcHBJ0+e3Lt3b3x8vKVj7rJuDjY7O7u5uXn27Nk1NTV4Au6Obg6Woqhp06bNnz+fJMnz58+npqbu2rULT+Rd0M3BajSa0tLS+Ph4b29vhUKxe/fu77//Hk/kXWCWv9mampqioiKruq4JzKi3JDCapseOHcueRqBpWqVSEQRRU1PDVpB6/vw5m5C2bNni6ur66NEj9l319fXsgyaZmZkCgWDy5MkSiWTatGnsH5XV6uZgCwoKiouLo6OjDQZDY2NjVFRUcnKyVd200l43B+vm5hYeHs4+KDZv3jyFQtH+W9LadHOwzs7OAQEB/v7+CKHQ0ND09PQePFjW9evXp0+fbrVjBN2F/aobPmFhYa8uCJeWli5fvry2tpam6R9//HHXrl3tW65evfrVcktLS3h4+J9//knTdHJyMntB+Pr16ytXrmSvl5w4caLD262BGQf7SnV1tbXdxMEy42AzMzNXr17d0tLS1tZ2/vz5zZs34xyIKcw42BcvXkRERDx9+lSv1587dy4+Ph7nQExh3t2YpumYmJgXL15gix9g1luOwAYNGvTJJ59s2bJFp9N5e3t//fXX/9TS1tZ29erViYmJRqNxyJAhs2fPRgiNHz++rKxs5cqVJEkOGjQoNjYWY+yd1s3B8ks3BztlypTKysqYmBiCIAYPHhwXF4cx9k7r5mCdnJyio6OTk5NbWlp8fHx69mARQk+fPkUIWe3JA9B9UIkDAAAAL/XMuxABAAD0eJDAAAAA8BIkMAAAALwECQwAAAAvQQIDAADAS5DAAAAA8BIkMAAAALwECQxYHb1eHxwc/NdffyGECIK4ffs21xG9I4y8vLxFixbhjAcAgCCBASu0d+/ewMDAV/XFrd8HH3xQVVV15coVrgMBoHeBBAasi16v3717t5VXOeqAIIi4uDhrruwOQI8ECQzgI5FI8vLyFi5c6OTk5OPjk5GR8Xqby5cvu7u7BwYGdlhfV1e3dOnSvn37urm5LV26tLa2ll1fXV09Z84cJyenoKCg3NxcOzu7wsLCDu+9cOHCyJEjpVKpp6dnamoqu1KpVC5evNjV1dXNze3LL79kJ8cqKSkJCQlxcHCwt7efOHFiQUFBh02p1eqvvvrK09PT3t5+5syZJSUl7PqwsLC7d+8+e/ase58QAKATIIEBrGJiYpYsWZKbmxscHLx8+XKNRtOhwdWrVwMCAjqspGl61qxZ5eXlZ86cOXPmTEVFxYwZM2ia1uv1U6ZMYRjm0qVL8fHxERERr2+woqIiLCxs6tSpOTk5K1euXLdu3a1bt4xG47Rp05qamhQKRXJycnp6+rZt2xBC4eHhbW1t586du3DhAsMwn3/+eYetLV++/P79+8ePH7969apYLJ40adLLly8RQiKRyNfX99q1a+b8sAAAb8dxNXzQm4jF4m+//ZZdZo9dSktLO7QZM2bM9u3bX/2IEMrLy8vOzqYoqrKykl1ZWVlJkmRWVtbZs2ft7e1fTcBx/PhxhNBvv/3WfoOZmZkIoadPnzIMQ9N0RkZGWVmZQqGQSqUNDQ1sm0OHDn322WdGozEpKenJkyfsylOnTrm4uLQPo7i4mKKouro6dmVbW5tcLmenEGMYZvHixVFRUWb4mAAApukt06kAKxEcHMwuuLi4vLGBUqn09fXtsLKkpMTLy8vDw4P90cPDw9PTs6SkRKlUBgYGymQydv24ceNe3+CHH344bty4wMDA+fPnT58+PSwszMbG5uzZs0OHDnV2dmbbREdHs5P2rl279u7du5mZmffu3fv55587bKqwsNBoNLYPT6VSlZWVscu+vr4PHz40+ZMAAHQXJDCAlVQqfWcbU+bPJUnSYDAYDIb2jUnyDafEbW1tb9y4cffu3dOnTyclJa1du/bkyZN6vZ6iqA4tW1tbQ0ND6+vrFy5cuGjRovHjx2/YsKF9A4PB4Ojo2OHCmIODw6uw3zLPPQDA7OAaGLAubm5upaWlHVYOGTKkoqLi+fPn7I/V1dUVFRVDhw4dOnToo0ePVCoVu/6Nj2rl5OTs3LlzzJgxu3fvLioqGj9+/OHDh/39/YuKipqamtg2aWlpU6ZMycrKunfvXkFBwY4dO2bOnMne1tGev79/Y2OjRqPx8vLy8vJydHT85ptvlEol+2ppaam7u7u5PgcAwDtBAgPWJSgo6PUENnHixBEjRoSFheXk5OTk5CxevDgwMHDSpEkLFy50dHQMDw+/ffu2QqFITEykKKrDoZXRaNy8eXNqamp+fn5GRsaDBw8CAwPnzp3r5ua2bNmyvLy8jIyMhISEYcOG2draajSa/fv337p167vvvtu6datKpcrPz3+1qcDAwGnTpi1ZsiQzMzM7Ozs8PPzmzZsDBw5kXy0tLQ0KCrL05wMA+BvXF+FALyIWi7OysthlttDG6zdxXLhwISgo6NWPCKG8vDyGYZRK5ZIlS/r06dOnT5+PP/5YqVSyDUpLS6dOnSqTycaOHXv//n2SJOvr6ztsMyUlxcvLSyQSDRgwYM2aNVqtlmGYysrKuXPnOjo6srfRq9VqmqYTEhJcXV2dnZ0/+uijsrKycePGTZ48uX0YL1++XLFihbu7u4ODw9y5c9l7QxiG0el09vb2rw8HAGA5BMMwHKdQANrR6XReXl5XrlwZPnz4Oxsrlcpbt24tWLCAvRL28OHDsWPHqlSqN14Ms6jTp08fOnQoKysLc78A9GbU1q1buY4BgL9RFGU0Gi9dujR37tx3Nm5paZk4caJIJPL09Kyuro6NjQ0JCZkzZw6GONtjGCYqKiohIeH1+ycBAJYD18CA1Vm1atWDBw/Yc4xv5+bmplAo0tPTBw8eHBIS4ufnl5SUhCHCDm7fvv3ee+/NmDEDf9cA9GZwChEAAAAvwREYAAAAXoIEBgAAgJcggQEAAOAlSGAAAAB4CRIYAAAAXoIEBgAAgJcggQEAAOCl/wdLY+jTQiGAPwAAAABJRU5ErkJggg==" style="display: block; margin: auto;" /></p>
<table>
<thead>
<tr class="header">
<th align="right">n</th>
<th align="right">OptimalCutpoints</th>
<th align="right">ROCR</th>
<th align="right">ThresholdROC</th>
<th align="right">cutpointr</th>
<th align="right">pROC</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">1e+03</td>
<td align="right">47.84453</td>
<td align="right">3.209919</td>
<td align="right">59.86058</td>
<td align="right">25.09471</td>
<td align="right">8.891217</td>
</tr>
<tr class="even">
<td align="right">1e+04</td>
<td align="right">5194.47377</td>
<td align="right">10.158945</td>
<td align="right">8252.99037</td>
<td align="right">29.01353</td>
<td align="right">83.237628</td>
</tr>
<tr class="odd">
<td align="right">1e+05</td>
<td align="right">NA</td>
<td align="right">109.492256</td>
<td align="right">NA</td>
<td align="right">85.94157</td>
<td align="right">939.500229</td>
</tr>
<tr class="even">
<td align="right">1e+06</td>
<td align="right">NA</td>
<td align="right">1117.249976</td>
<td align="right">NA</td>
<td align="right">617.25418</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1e+07</td>
<td align="right">NA</td>
<td align="right">13565.716659</td>
<td align="right">NA</td>
<td align="right">5906.54936</td>
<td align="right">NA</td>
</tr>
</tbody>
</table>
<div id="roc-curve-only" class="section level3">
<h3>ROC curve only</h3>
<p>As we can see, the ROC curve calculation that is implemented in <strong>cutpointr</strong> is considerably faster in samples > 1000 than the ones offered by <strong>ROCR</strong> and <strong>pROC</strong>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># ROCR package</span>
rocr_roc <-<span class="st"> </span><span class="cf">function</span>(x, class) {
pred <-<span class="st"> </span>ROCR<span class="op">::</span><span class="kw">prediction</span>(x, class)
<span class="kw">return</span>(<span class="ot">NULL</span>)
}
<span class="co"># pROC package</span>
proc_roc <-<span class="st"> </span><span class="cf">function</span>(x, class, <span class="dt">levels =</span> <span class="kw">c</span>(<span class="st">"no"</span>, <span class="st">"yes"</span>), <span class="dt">algo =</span> <span class="dv">2</span>) {
r <-<span class="st"> </span>pROC<span class="op">::</span><span class="kw">roc</span>(class, x, <span class="dt">algorithm =</span> algo)
<span class="kw">return</span>(<span class="ot">NULL</span>)
}</code></pre></div>
<p><img 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" style="display: block; margin: auto;" /></p>
<table>
<thead>
<tr class="header">
<th align="right">n</th>
<th align="right">ROCR</th>
<th align="right">cutpointr</th>
<th align="right">pROC</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">1e+03</td>
<td align="right">1.223025</td>
<td align="right">1.302793</td>
<td align="right">8.905319</td>
</tr>
<tr class="even">
<td align="right">1e+04</td>
<td align="right">5.190217</td>
<td align="right">2.889493</td>
<td align="right">81.582236</td>
</tr>
<tr class="odd">
<td align="right">1e+05</td>
<td align="right">59.418236</td>
<td align="right">28.598465</td>
<td align="right">968.227087</td>
</tr>
<tr class="even">
<td align="right">1e+06</td>
<td align="right">559.158593</td>
<td align="right">265.087399</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1e+07</td>
<td align="right">6227.157674</td>
<td align="right">3218.965990</td>
<td align="right">NA</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
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