Exact and asymptotic tests under the sequential parallel comparison design

When one studies treatments for psychological or mental diseases in a double-blind placebo-controlled trial with a high placebo response rate, the sequential parallel comparison design (SPCD) has been proposed elsewhere to improve power. All procedures for testing equality of treatments under the SPCD have been so far derived from large sample theory. If the trial size is small, asymptotic test procedures can be theoretically invalid. Thus, the development of an exact test procedure assuring type I error rate to be less than or equal to the nominal α-level is of use and interest. Using the conditional arguments to remove nuisance parameters, we derive two exact and one asymptotic procedures for testing equality of treatments for the SPCD. On the basis of Monte Carlo simulation, we find that all three test procedures can control type I error rate well in a variety of situations. We use the data taken from a double-blind placebo-controlled SPCD trial to assess the efficacy of a low dose (2 mg/day) of aripiprazole adjunctive to antidepressant therapy in the treatment of patients with major depressive disorder with a history of inadequate response to prior antidepressant therapy to illustrate the use of these test procedures.