Lorenz Curves and Treatment-Covariate Interactions in Clinical Trials

A common objective in comparative two-treatment randomized clinical trials is the study of the possible heterogeneity of the treatment effect across subgroups of patients, with the objective of identifying patients who benefit the most (or the least) from a new treatment. Here we describe the connection that exists between an exploratory approach to such problem (STEPP, or the Subpopulation Treatment Effect Pattern Plot approach) and the Lorenz curve, and in particular the generalized Lorenz curve. We exploit such connection to construct a test for the absence of interaction between a continuous covariate and the difference in the mean of a continuous outcome between the two treatment groups. We also review some recent developments in the study of concentration for right censored survival data, which are also closed related to the Lorenz curve.