Statistical inference problems in sequential parallel comparison design

The sequential parallel comparison designhas recently been considered to solve the problem with high placebo response and the required sample size in the psychiatric clinical trials. One feature with this design is that a difference between the placebo group and the drug group may also arise in the variance-covariance structure of the clinical outcome. Provided the heterogeneity of the second moment, the treatment effect estimation at the second stage can be biased for the entire randomized patient population that includes patient responders. Our work presented here aims at how the coverage probability of the interval estimation of treatment effect performs under the unstructured variance-covariance matrix. The interaction between the truncation after the first stage and the heterogeneity of the second moment causes a substantial coverage probability problem. The type I error probability may not be controlled under the weak null due to this bias. This bias can also cause spurious power evaluation under an alternative hypothesis. The coverage probability of the ordinary least square statistic is shown in different scenarios.