Generalized treatment effects for clinical trials

Practice in the analysis of clinical trials with continuously measured endpoints is to focus on the difference or percentage change in mean or median response. However, treatments may have effects on the distribution of responses other than on the average response. We sought an approach to such generalized treatment effects that: (i) targets a parameter that is easily understood by our clinical colleagues; and (ii) employs confidence intervals as the basis for inference. We consider one such approach based on work in reliability theory, namely setting Pr[Y>X] as the target parameter, and compare this approach to an earlier one due to O'Brien. The two approaches have similar properties when they both seek to reject the null hypothesis of no effect due to different variances but differ when the larger variance corresponds to the larger mean. In that case, our approach views that the larger variance attenuates the effect of the larger mean. Out suggested approach applies easily to positive control (clinical) equivalence trials.