Abstract: In clinical trials, treatment comparisons are often cast in a regression framework that evaluates the dependence of the relevant clinical outcomes on treatment assignment and possibly other baseline characteristics. This article introduces a reverse regression approach to randomized clinical trials, with focus on the dependence of treatment assignment on the clinical outcomes of interest. A reverse regression model is essentially a semiparametric density ratio model for the outcome distributions in the two treatment groups. The resulting inferences can be expected to be more robust than those based on fully parametric models for the outcome distributions and more efficient than nonparametric inferences. In the presence of multiple endpoints, the reverse regression approach leads to a novel procedure for multiplicity adjustment that is readily available in standard logistic regression routines. The proposed approach is evaluated in simulation experiments and illustrated with an example.

Key words and phrases: Density ratio, discriminant analysis, efficiency, logistic regression, multiplicity, semiparametric likelihood.