Estimation of the relative difference (or relative risk reduction) under the sequential parallel comparison design

To increase power or reduce the number of patients needed in trials studying treatments for psychiatric or mental disorders with a high placebo response rate, we may consider use of the sequential parallel comparison design proposed elsewhere. Because statistical significance does not necessarily imply that the difference between treatment and placebo is of clinical importance, it is always of importance to quantify the treatment effect in clinical trials. When the patient responses are dichotomous, the treatment and other covariates effects are not likely additive. Thus, using a weighted average of the risk differences over two phases may not be a meaningful summary index to measure the treatment effect. To alleviate this concern, we consider use of the relative difference or relative risk reduction to measure the treatment effect. We derive both point and interval estimators for the relative difference by use of the weighted-least-squares estimator and Mantel-Haenszel type estimator. We employ Monte Carlo simulation to evaluate the finite-sample performance of these estimators in a variety of situations. We also include a procedure for testing the homogeneity of the relative difference between phases under the sequential parallel comparison design. We use the placebo-controlled study to assess the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy in the treatment of patients with major depressive disorder to illustrate the use of estimators developed here.