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

Adaptive enrichment designs in clinical trials have been developed to enhance drug developments. They permit, at interim analyses during the trial, to select the sub‐populations that benefits the most from the treatment. Because of this selection, the naive maximum likelihood estimation of the treatment effect, commonly used in classical randomized controlled trials, is biased. In the literature, several methods have been proposed to obtain a better estimation of the treatments' effects in such contexts. To date, most of the works have focused on normally distributed endpoints, and some estimators have been proposed for time‐to‐event endpoints but they have not all been compared side‐by‐side. In this work, we conduct an extensive simulation study, inspired by a real case‐study in heart failure, to compare the maximum‐likelihood estimator (MLE) with an unbiased estimator, shrinkage estimators, and bias‐adjusted estimators for the estimation of the treatment effect with time‐to‐event data. The performances of the estimators are evaluated in terms of bias, variance, and mean squared error. Based on the results, along with the MLE, we recommend to provide the unbiased estimator and the single‐iteration bias‐adjusted estimator: the former completely eradicates the selection bias, but is highly variable with respect to a naive estimator; the latter is less biased than the MLE estimator and only slightly more variable.

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See 3 more Smart Citations

A comparison of estimation methods adjusting for selection bias in adaptive enrichment designs with time‐to‐event endpoints

Stefano

Pannaux

Correges

et al. 2022

Bias correction based on weighted likelihood for conditional estimation of subgroup effects in randomized clinical trials

Toyoizumi

Matsui

2022

Currently, many confirmatory randomized clinical trials (RCTs) with predictive markers have taken the all‐comers approach because of the difficulty in developing predictive markers that are biologically compelling enough to apply the enrichment approach to restrict the patient population to a marker‐defined subgroup. However, such a RCT with weak marker credentials can conclude that the new treatment is efficacious only in the subgroup, especially when the primary analysis demonstrates some treatment efficacy in the subgroup, but the overall treatment efficacy is not significant under a control of study‐wise alpha rate. In this article, we consider conditional estimation of subgroup treatment effects, given the negative result in testing the overall treatment efficacy in the trial. To address the problem of unstable estimation due to the truncation in the distribution of the test statistic on overall treatment efficacy, we propose a new approach based on a weighted likelihood for the truncated distribution. The weighted likelihood can be derived by invoking a randomized test with a smooth critical function for the overall test. Our approach allows for point and interval estimations of the conditional effects consistently based on the standard maximum likelihood inference. Numerical evaluations, including simulations and application to real clinical trials, and guidelines for implementing our methods with R‐codes, are provided.

Point estimation for adaptive trial designs I: A methodological review

Robertson

Choodari‐Oskooei

Dimairo

et al. 2022

In adaptive clinical trials, the conventional end-of-trial point estimate of a treatment effect is prone to bias, that is, a systematic tendency to deviate from its true value. As stated in recent FDA guidance on adaptive designs, it is desirable to report estimates of treatment effects that reduce or remove this bias. However, it may be unclear which of the available estimators are preferable, and their use remains rare in practice. This paper is the second in a two-part series that studies the issue of bias in point estimation for adaptive trials. Part I provided a methodological review of approaches to remove or reduce the potential bias in point estimation for adaptive designs. In part II, we discuss how bias can affect standard estimators and assess the negative impact this can have. We review current practice for reporting point estimates and illustrate the computation of different estimators using a real adaptive trial example (including code), which we use as a basis for a simulation study. We show that while on average the values of these estimators can be similar, for a particular trial realisation they can give noticeably different values for the estimated treatment effect. Finally, we propose guidelines for researchers around the choice of estimators and the reporting of estimates following an adaptive design. The issue of bias should be considered throughout the whole lifecycle of an adaptive design, with the estimation strategy pre-specified in the statistical analysis plan. When available, unbiased or bias-reduced estimates are to be preferred.