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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. [ABSTRACT FROM AUTHOR]

While 2-in-1 designs give a flexibility to make a clinical trial either an information generation Phase 2 trial or a full scale confirmatory Phase 3 trial, flexible sample size designs can naturally fit into the 2-in-1 design framework. This study is to show that the CHW design can be blended into a 2-in-1 design to improve the adaptive performance of the design. Commenting on the usual 2-in-1 design, we demonstrated that the CHW design can achieve the goal of a 2-in-1 design with satisfactory statistical power and efficient average sample size for a targeted range of the treatment effect. [ABSTRACT FROM AUTHOR]

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 Statistical Inference Problems in Sequential Parallel Comparison Design (2019) 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. [ABSTRACT FROM AUTHOR]

Often one of the primary objectives of an active-controlled noninferiority trial without a placebo arm is to assert that an experimental treatment would have been more effective than a putative placebo had the placebo been included in the trial. This may be an important consideration for regulatory applications. To achieve this objective, such a noninferiority analysis entails cross-trial statistical inference. Because of the uncertainty and difficulty surrounding cross-trial inference, the noninferiority analysis often aims to demonstrate that the experimental treatment preserves a specified fraction of the effect of the active control. The rationale is that by demonstrating the percent effect retention, the efficacy of the experimental treatment can be established with a great level of confidence. The confidence interval approach and synthesized test approach have been used for inferring the percent effect preservation. In this work we evaluate the type I error rates of these approaches to the cross-trial statistical inference for establishing treatment efficacy. The evaluation provides guidance as to what percentage of the control effect needs to be preserved so that through noninferiority testing of effect retention one can assert the treatment efficacy within a desired level of the error rate. [Copyright &y& Elsevier]

Increasingly often, the study objective in an active controlled clinical trial without a placebo arm is to show that a new treatment is no less effective than the active control treatment within some noninferiority range. Two issues behind this objective are that of whether the new treatment is efficacious relative to a putative placebo and that of whether the new treatment preserves a certain fraction of effect of the active control. To address these issues, two types of statistical analysis methods are employed in recent pharmaceutical applications. In one type of method, a noninferiority margin is determined, and then the relative effect of the new treatment versus the control is compared against the margin to test noninferiority and the efficacy of the new treatment. In the other type of method, a synthetic statistic is constructed to directly estimate or test the effect of the new treatment relative to the putative placebo without resorting to noninferiority argument. Preservation of control effect can also be estimated and tested. These methods carry some crucial assumptions. The effect of active control is often estimated from a collection of historical placebo controlled trials using the random effects modeling of DerSimonian and Laird. In this work we find that statistical validity of the latter method rests highly on the assumptions that control effect is not reduced in the current active controlled trial population compared to the historical trials and that a normal approximation is appropriate in the random effects modeling. This type of method is very sensitive to departure from these assumptions. In contrast, the former method is ultraconservative in terms of type I error when the assumptions are met and can be anticonservative when control effect is substantially less in the active controlled trial than estimated from the historical placebo controlled trials. [Copyright &y& Elsevier]

The article reports that the sample size during the course of a conventional fixed design clinical trial covers relevant points for the context of adjusting. By use of a nonconstant critical value perceived as an additional flexibility to control its conditional Type I error, the conventional Z test controls the unconditional Type I error.