Area Under Receiver Operating Curve
Compute exact area under the ROC for empirical data.
auROC(truth, stat=NULL)
truth |
logical vector, or numeric vector of 0s and 1s, indicating whether each case is a true positive. |
stat |
numeric vector containing test statistics used to rank cases, from largest to smallest.
If |
A receiver operating curve (ROC) is a plot of sensitivity (true positive rate) versus 1-specificity (false positive rate) for a statistical test or binary classifier. The area under the ROC is a well accepted measure of test performance. It is equivalent to the probability that a randomly chosen pair of cases is corrected ranked.
Here we consider a test statistic stat, with larger values being more significant, and a vector truth indicating whether the alternative hypothesis is in fact true.
truth==TRUE or truth==1 indicates a true discovery and truth=FALSE or truth=0 indicates a false discovery.
Correct ranking here means that truth[i] is greater than or equal to truth[j] when stat[i] is greater than stat[j].
The function computes the exact area under the empirical ROC curve defined by truth when ordered by stat.
If stat contains ties, then auROC returns the average area under the ROC for all possible orderings of truth for tied stat values.
The area under the curve is undefined if truth is all TRUE or all FALSE or if truth or stat contain missing values.
Numeric value between 0 and 1 giving area under the curve, 1 being perfect and 0 being the minimum.
Gordon Smyth
auROC(c(1,1,0,0,0)) truth <- rbinom(30,size=1,prob=0.2) stat <- rchisq(30,df=2) auROC(truth,stat)
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