Comparing the effectiveness of k$$ k $$‐different treatments through the area under the ROC curve

Abstract

The area under the receiver‐operating characteristic curve (AUC) has become a popular index not only for measuring the overall prediction capacity of a marker but also the strength of the association between continuous and binary variables. In the current considered study, the AUC was used for comparing the association size of four different interventions involving impulsive decision making, studied through an animal model, in which each animal provides several negative (pretreatment) and positive (posttreatment) measures. The problem of the full comparison of the average AUCs arises therefore in a natural way. We construct an analysis of variance (ANOVA) type test for testing the equality of the impact of these treatments measured through the respective AUCs and considering the random‐effect represented by the animal. The use (and development) of a post hoc Tukey's HSD‐type test is also considered. We explore the finite‐sample behaviour of our proposal via Monte Carlo simulations, and analyse the data generated from the original problem. An R package implementing the procedures is provided in the supporting information.