The effectiveness of risk scores: the logit rank plot

A risk score s for event E is a function of covariates with the property th at P(E\s) is an increasing function of s. Motivated by applications in medi cine and in criminology, we suggest the legit rank plot as a good way of su mmarizing the effectiveness of such a score. Explicitly, plot togit {P(E\s) } against logit(r), where r is the proportional rank of s in a sample or po pulation. The slope of this plot gives an overall measure of effectiveness, and the logit rank transformation provides a common basis on which differe nt risk scores can be compared. Some practical and theoretical aspects are discussed.