\name{ROC}
\alias{lroc}
\alias{roc.from.table}
\title{ROC curve}
\description{Receiver Operating Characteristic curve of a logistic regression model and a diagnostic table}
\usage{
lroc(logistic.model, graph = TRUE, add = FALSE, title = FALSE, 
    line.col = "red", auc.coords = NULL, grid = TRUE, grid.col = "blue", ...)
roc.from.table(table, graph = TRUE, add = FALSE, title = FALSE, 
	line.col = "red", auc.coords = NULL, grid = TRUE, grid.col = "blue", ...) 
}
\arguments{
	\item{logistic.model}{A model from logistic regression}
	\item{table}{A cross tabulation of the levels of a test (rows) vs a gold standard positive and negative (columns)}
	\item{graph}{Draw ROC curve}
	\item{add}{Whether the line is drawn on the existing ROC curve}
	\item{title}{If true, the model will be displayed as main title}
	\item{line.col}{Color of the line}
	\item{auc.coords}{Coordinates for label of 'auc' (area under curve)}
	\item{grid}{Whether the grid should be drawn}
	\item{grid.col}{Grid colour, if drawn}
	\item{...}{Additional graphic parameters}
}
\details{
'lroc' graphs the ROC curve of a logistic regression model. If `table=TRUE', the diagnostic table based on the regression will be printed out.

'roc.from.table' computes the change of sensitivity and specificity of each cut point and uses these for drawing the ROC curve.

In both cases, the area under the curve is computed.
}
\author{Virasakdi Chongsuvivatwong
	\email{ <cvirasak@medicine.psu.ac.th>}
}
\seealso{'glm'}
\examples{
# Single ROC curve from logistic regression
# Note that 'induced' and 'spontaneous' are both originally continuous variables
model1 <- glm(case ~ induced + spontaneous, data=infert, family=binomial)
logistic.display(model1)
# Having two spontaneous abortions is quite close to being infertile!
# This is actually not a causal relationship

lroc(model1, title=TRUE, auc.coords=c(.5,.1))
# For PowerPoint presentation, the graphic elements should be enhanced as followed 
lroc(model1, title=TRUE, cex.main=2, cex.lab=1.5, col.lab="blue", cex.axis=1.3, lwd=3)
lroc1 <- lroc(model1) # The main title and auc text have disappeared
model2 <- glm(case ~ spontaneous, data=infert, family=binomial)
logistic.display(model2)
lroc2 <- lroc(model2, add=TRUE, line.col="brown", lty=2)
legend("bottomright",legend=c(lroc1$model.description, lroc2$model.description),
        lty=1:2, col=c("red","brown"), bg="white")
title(main="Comparison of two logistic regression models")
lrtest(model1, model2) 
# Number of induced abortions is associated with increased risk for infertility

# Various form of logistic regression
# Case by case data
data(ANCdata)
use(ANCdata)
glm1 <- glm(death ~ anc + clinic, binomial, data=.data)
lroc(glm1)

# Frequency format
data(ANCtable)
ANCtable
use(ANCtable)
death <- factor (death)
levels (death) <- c("no","yes")
anc <- factor (anc)
levels (anc) <- c("old","new")
clinic <- factor (clinic)
levels (clinic) <- c("A","B")
pack()
glm2 <- glm(death ~ anc + clinic, binomial, weights=Freq, data=.data)
lroc(glm2)

# yes/no format
.data$condition <- c(1,1,2,2,3,3,4,4)
data2 <- reshape (.data, timevar="death", v.name="Freq", idvar="condition", direction="wide")
data2
glm3 <- glm(cbind(Freq.yes, Freq.no) ~ anc + clinic, family=binomial, data=data2)
lroc(glm3)


# ROC from a diagnostic table
table1 <- as.table(cbind(c(1,27,56,15,1),c(0,0,10,69,21)))
colnames(table1) <- c("Non-diseased", "Diseased")
rownames(table1) <- c("15-29","30-44","45-59","60-89","90+")
table1
roc.from.table(table1)
roc.from.table(table1, title=TRUE, auc.coords=c(.4,.1), cex=1.2)

# Application of the returned list
roc1 <- roc.from.table(table1, graph=FALSE)
cut.points <- rownames(roc1$diagnostic.table)
text(x=roc1$diagnostic.table[,1], y=roc1$diagnostic.table[,2], 
	labels=cut.points, cex=1.2, col="brown")
}
\keyword{array}