The Effectiveness of Risk Scores: the Logit Rank Plot

A risk score s for event E is a function of covariates with the property that P ( E | s ) is an increasing function of s . Motivated by applications in medicine and in criminology, we suggest the logit rank plot as a good way of summarizing the effectiveness of such a score. Explicitly, plot logit{ P ( E | s )} against logit( r ), where r is the proportional rank of s in a sample or population. The slope of this plot gives an overall measure of effectiveness, and the logit rank transformation provides a common basis on which different risk scores can be compared. Some practical and theoretical aspects are discussed.