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>2018-08-31</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>
<div id="installation" class="section level2">
<h2>Installation</h2>
<p>You can install <strong>cutpointr</strong> from CRAN using the menu in RStudio or simply:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">install.packages</span>(<span class="st">"cutpointr"</span>)</code></pre></div>
</div>
<div id="example" class="section level2">
<h2>Example</h2>
<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 1.75179 0.864662
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.888889 0.862903 0.923779 yes no 0.0676692 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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" 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>
<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>roc01</code>: Distance to the point (0,1) on ROC space</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 1.75179 0.864662
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.888889 0.862903 0.923779 yes no 0.0676692 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 1.75179 0.864662
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.888889 0.862903 0.923779 yes no 0.0676692 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 acc sensitivity
## <chr> <dbl> <chr> <dbl> <dbl> <dbl>
## 1 >= 2 maximize_metric 0.751792 0.864662 0.888889
## specificity AUC pos_class neg_class prevalence outcome predictor
## <dbl> <dbl> <chr> <chr> <dbl> <chr> <chr>
## 1 0.862903 0.923779 yes no 0.0676692 suicide dsi
## data roc_curve boot
## <list> <list> <lgl>
## 1 <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 acc sensitivity specificity AUC n_pos n_neg
## 2 0.7518 0.8647 0.8889 0.8629 0.9238 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>(opt_cut)</code></pre></div>
<p><img 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" 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 1.75179 0.864662
## sensitivity specificity AUC pos_class neg_class prevalence outcome
## <dbl> <dbl> <dbl> <fct> <fct> <dbl> <chr>
## 1 0.888889 0.862903 0.923779 yes no 0.0676692 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_o… 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
## <chr> <chr> <dbl> <chr> <dbl>
## 1 female >= 2 maximize_metric 1.80812
## 2 male >= 3 maximize_metric 1.62511
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <chr> <fct> <dbl>
## 1 0.885204 0.925926 0.882192 0.944647 yes no 0.0688776
## 2 0.842857 0.777778 0.847328 0.861747 yes no 0.0642857
## 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 [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
## <chr> <chr> <dbl> <chr> <dbl>
## 1 female >= 5.59375 maximize_boot_metric 0.956633
## 2 male >= 7.93333 maximize_boot_metric 0.957143
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <fct> <fct> <dbl>
## 1 0.956633 0.444444 0.994521 0.944647 yes no 0.0688776
## 2 0.957143 0.333333 1 0.861747 yes no 0.0642857
## outcome predictor grouping data roc_curve boot
## <chr> <chr> <chr> <list> <list> <lgl>
## 1 suicide dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 suicide 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
## <chr> <chr> <dbl> <chr> <dbl>
## 1 female >= 2.47775 oc_youden_normal 1.71618
## 2 male >= 3.17226 oc_youden_normal 1.54453
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <fct> <fct> <dbl>
## 1 0.895408 0.814815 0.901370 0.944647 yes no 0.0688776
## 2 0.864286 0.666667 0.877863 0.861747 yes no 0.0642857
## outcome predictor grouping data roc_curve boot
## <chr> <chr> <chr> <list> <list> <lgl>
## 1 suicide dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 suicide 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
## <chr> <chr> <dbl> <chr> <dbl>
## 1 female >= 1.18128 oc_youden_kernel 1.80812
## 2 male >= 1.31636 oc_youden_kernel 1.58694
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <fct> <fct> <dbl>
## 1 0.885204 0.925926 0.882192 0.944647 yes no 0.0688776
## 2 0.807143 0.777778 0.809160 0.861747 yes no 0.0642857
## outcome predictor grouping data roc_curve boot
## <chr> <chr> <chr> <list> <list> <lgl>
## 1 suicide dsi gender <tibble [392 × 2]> <data.frame [11 × 9]> NA
## 2 suicide 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 src="data:image/png;base64,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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
## <chr> <chr> <dbl> <chr> <dbl>
## 1 FALSE >= 1.79176 maximize_metric 1.61486
## 2 TRUE >= 1.09861 maximize_metric 1.80766
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <lgl> <lgl> <dbl>
## 1 0.848837 0.75 0.864865 0.851351 TRUE FALSE 0.139535
## 2 0.892377 0.916667 0.890995 0.922887 TRUE FALSE 0.0538117
## 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 <= 3.2 1
## 4 Petal.Width <= 1 1</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 0.9846
## 2 Sepal.Width >= 3.3500 0.834400
## 3 Petal.Length <= 3.2 1
## 4 Petal.Width <= 1 1</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="calculating-additional-metrics" class="section level2">
<h2>Calculating additional metrics</h2>
<p>By default, the output of cutpointr includes the optimized metric and several other metrics. The <code>add_metric</code> function adds further metrics. Suitable metric functions are all metric functions that are included in the package or that comply with those standards. Here, we’re adding the negative predictive value (NPV) and the positive predictive value (PPV) at the optimal cutpoint per subgroup:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">cutpointr</span>(suicide, dsi, suicide, gender, <span class="dt">metric =</span> youden, <span class="dt">silent =</span> <span class="ot">TRUE</span>) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">add_metric</span>(<span class="kw">list</span>(ppv, npv)) <span class="op">%>%</span><span class="st"> </span>
<span class="st"> </span><span class="kw">select</span>(subgroup, optimal_cutpoint, youden, ppv, npv)</code></pre></div>
<pre><code>## # A tibble: 2 x 5
## subgroup optimal_cutpoint youden ppv npv
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 female 2 0.808118 0.367647 0.993827
## 2 male 3 0.625106 0.259259 0.982301</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 0.0437341
## 2 male >= 2 minimize_metric 0.0313825
## acc sensitivity specificity AUC pos_class neg_class prevalence
## <dbl> <dbl> <dbl> <dbl> <fct> <fct> <dbl>
## 1 0.885204 0.925926 0.882192 0.944647 yes no 0.0688776
## 2 0.807143 0.777778 0.809160 0.861747 yes no 0.0642857
## 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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" 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">56.21193</td>
<td align="right">3.017892</td>
<td align="right">78.88322</td>
<td align="right">8.334464</td>
<td align="right">9.131493</td>
</tr>
<tr class="even">
<td align="right">1e+04</td>
<td align="right">5383.76537</td>
<td align="right">11.284935</td>
<td align="right">7930.97356</td>
<td align="right">13.057035</td>
<td align="right">94.403445</td>
</tr>
<tr class="odd">
<td align="right">1e+05</td>
<td align="right">NA</td>
<td align="right">108.988626</td>
<td align="right">NA</td>
<td align="right">68.155645</td>
<td align="right">1021.098187</td>
</tr>
<tr class="even">
<td align="right">1e+06</td>
<td align="right">NA</td>
<td align="right">1250.425970</td>
<td align="right">NA</td>
<td align="right">708.193360</td>
<td align="right">NA</td>
</tr>
<tr class="odd">
<td align="right">1e+07</td>
<td align="right">NA</td>
<td align="right">13247.381417</td>
<td align="right">NA</td>
<td align="right">5893.323971</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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