Point estimation following two‐stage adaptive threshold enrichment clinical trials

Abstract

Recently, several study designs incorporating treatment effect assessment in biomarker‐based subpopulations have been proposed. Most statistical methodologies for such designs focus on the control of type I error rate and power. In this paper, we have developed point estimators for clinical trials that use the two‐stage adaptive enrichment threshold design. The design consists of two stages, where in stage 1, patients are recruited in the full population. Stage 1 outcome data are then used to perform interim analysis to decide whether the trial continues to stage 2 with the full population or a subpopulation. The subpopulation is defined based on one of the candidate threshold values of a numerical predictive biomarker. To estimate treatment effect in the selected subpopulation, we have derived unbiased estimators, shrinkage estimators, and estimators that estimate bias and subtract it from the naive estimate. We have recommended one of the unbiased estimators. However, since none of the estimators dominated in all simulation scenarios based on both bias and mean squared error, an alternative strategy would be to use a hybrid estimator where the estimator used depends on the subpopulation selected. This would require a simulation study of plausible scenarios before the trial.

Point and interval estimation in two‐stage adaptive designs with time to event data and biomarker‐driven subpopulation selection

“…Several efficient two-stage adaptive designs with an interim analysis to determine the part of the population (subpopulation) to benefit most from a new treatment have been proposed. 2 – 6 The general framework of such designs is that patients are recruited from the full population in stage 1, with an interim analysis performed to determine the subpopulation where the new treatment is apparently beneficial. In stage 2, patients are recruited from this group.…”

“… 2 , 3 , 7 However, existing point estimators and confidence intervals that adjust for subpopulation selection do not consider time to event data. 4 – 6 , 11 Li et al 12 quantify the bias of the naive estimator for time to event data but do not derive unbiased estimators. Thus, there is a need to develop point and interval estimators for time to event data in two-stage adaptive trials with subpopulation selection.…”

“…The first involves estimating and subtracting the bias of the naive estimator. 6 , 13 – 15 The second utilizes the empirical Bayes technique to obtain shrinkage estimators. 6 , 15 – 17 The third is based on the Rao-Blackwell theorem that the expected value of the unbiased stage 2 estimator conditional on the selected subpopulation and a sufficient statistic is the uniformly minimum variance conditional unbiased estimator (UMVCUE).…”

“… 6 , 13 – 15 The second utilizes the empirical Bayes technique to obtain shrinkage estimators. 6 , 15 – 17 The third is based on the Rao-Blackwell theorem that the expected value of the unbiased stage 2 estimator conditional on the selected subpopulation and a sufficient statistic is the uniformly minimum variance conditional unbiased estimator (UMVCUE). 4 , 6 , 18 – 22 Kimani et al 6 compared the estimation approaches in the context of subpopulation selection, concluding that the UMVCUE was superior.…”

“… 6 , 15 – 17 The third is based on the Rao-Blackwell theorem that the expected value of the unbiased stage 2 estimator conditional on the selected subpopulation and a sufficient statistic is the uniformly minimum variance conditional unbiased estimator (UMVCUE). 4 , 6 , 18 – 22 Kimani et al 6 compared the estimation approaches in the context of subpopulation selection, concluding that the UMVCUE was superior. As we expect the same conclusion if the three estimators are extended to time to event data, in this article, we have only extended the UMVCUE.…”