Estimation of treatment effect in two-stage confirmatory oncology trials of personalized medicines.

A personalized medicine may benefit a subpopulation with certain predictive biomarker signatures or certain disease types. However, there is great uncertainty about drug activity in a subpopulation when designing a confirmatory trial in practice, and it is logical to take a two-stage approach with the study unless credible external information is available for decision-making purpose. The first stage deselects (or prunes) non-performing subpopulations at an interim analysis, and the second stage pools the remaining subpopulations in the final analysis. The endpoints used at the two stages can be different in general. A key issue of interest is the statistical property of the test statistics and point estimate at the final analysis. Previous research has focused on type I error control and power calculation for such two-stage designs. This manuscript will investigate estimation bias of the treatment effect, which is implicit in the adjustment of nominal type I error for multiplicity control in such two-stage designs. Previous work handles the treatment effect of an intermediate endpoint as a nuisance parameter to provide the most conservative type I error control. This manuscript takes the same approach to explore the bias. The methodology is applied to the two previously studied designs. In the first design, patients with different biomarker levels are enrolled in a study, and the treatment effect is assumed to be in an order. The goal of the interim analysis is to identify a biomarker cut-off point for the subpopulations. In the second design, patients with different tumour types but the same biomarker signature are included in a trial applying a basket design. The goal of the interim analysis is to identify a subset of tumour types in the absence of treatment effect ordering. Closed-form equations are provided for the estimation bias as well as the variance under the two designs. Simulations are conducted under various scenarios to validate the analytic results that demonstrated that the bias can be properly estimated in practice. Worked examples are presented. Extensions to general adaptive designs and operational considerations are discussed.