Rejoinder to "Statistical inference problems in sequential parallel comparison designs".

In this rejoinder the authors stipulate further for two challenging issues. First, if placebo non-responders are selected simply by their response meeting a threshold, this selection may have misclassification error and consequently the treatment effect estimate may be biased, regardless of whether the estimand at the second stage is the treatment effect in the entire population or placebo non-responders. Secondly, the weak null hypothesis considered in our article is that the expected treatment effects in placebo non-responders and in the entire set of patients entering the trial are both zero, in contrast to the strong null hypothesis that the statistical distribution of the response variable is equal in the compared treatments. The impact of violating the assumption of equal moments other than the mean parameter on statistical operating characteristics in estimation and testing of treatment effect can be substantial. As an example, the ordinary least squares based test detects a treatment difference even if the expected treatment effects in placebo non-responders and the entire population are both zero.