Asymptotic and exact interval estimators of the common odds ratio under the sequential parallel comparison design

When studying treatments for psychiatric or mental diseases in a placebo-controlled trial, we may consider use of the sequential parallel comparison design to reduce the number of patients needed through the reduction of the high placebo response rate. Under the assumption that the odds ratio of responses is constant between phases in the sequential parallel comparison design, we derive the conditional maximum likelihood estimator for the odds ratio. On the basis of the conditional likelihood, we further derive three asymptotic interval and an exact interval estimators for the odds ratio of responses. We employ Monte Carlo simulation to evaluate the performance of these interval estimators in a variety of situations. We find that the asymptotic interval and exact interval estimators developed here can all perform well. We use the double-blind, placebo-controlled study assessing the efficacy of a low dose of aripiprazole adjunctive to antidepressant therapy for treating patients with major depressive disorder to illustrate the use of these estimators.