The P-P Plot as a Method for Comparing Treatment Effects

Abstract

Abstract This article examines the use of the probability-probability plot (p-p plot) as a method for comparing treatment effects. To begin in the context of three examples the p-p plot is contrasted with the quantile-quantile plot (q-q plot), which is an alternative means of describing treatment effects. In these examples it is shown that p-p plots representing different experimental conditions or patient populations allow scale-invariant comparisons of treatment effects but q-q plots do not; that the presentation of the treatment effect by the p-p plot is not obscured by outliers, whereas it may be in the q-q plot; and that the p-p plot encompasses information in the control distributions that is important for the assessment of treatment effects but that is not incorporated in the q-q plot. Theoretical considerations are presented that show that under appropriate assumptions, the p-p plot is a maximal invariant and contains all the information necessary to make scale-invariant comparisons of treatment effects. Further, statistical methods for assessing patterns observed in the p-p plots are presented and illustrated in two examples.