Comparison of Test Statistics for the Sequential Parallel Design

AbstractThe sequential parallel design has been proposed to improve the efficiency of clinical trials in psychiatry. The design randomizes patients into three treatment groups. Each group has two phases. The three groups are (1) placebo in the first phase followed by placebo in the second phase, (2) placebo in the first phase followed by drug in the second phase, and (3) drug in the first phase followed by drug in the second phase. We consider the case of binary response data. The analysis of data in the second phase of the trial is restricted to placebo patients who failed to respond in the first phase of the trial. A crucial element in the choice of test statistics is the underlying assumptions of treatment effect in the two phases of the trial. We develop various likelihood-based statistics when the treatment effect is different in the two phases and for the special case in which the treatment effect is equal in the two phases. These statistics are compared in simulation studies to determine their underlying null and nonnull behavior. The score test under the assumption of equal treatment effects is seen to have advantages in terms of Type I error and robustness to assumptions.