Optimal, two-stage, adaptive enrichment designs for randomized trials, using sparse linear programming

Isotonic design for single-arm biomarker stratified trials

In single-arm trials with a predefined subgroup based on baseline biomarkers, it is often assumed that a biomarker defined subgroup, the biomarker positive subgroup, has the same or higher response to treatment compared to its complement, the biomarker negative subgroup. The goal is to determine if the treatment is effective in each of the subgroups or in the biomarker positive subgroup only or not effective at all. We propose the isotonic stratified design for this problem. The design has a joint set of decision rules for biomarker positive and negative subjects and utilizes joint estimation of response probabilities using assumed monotonicity of response between the biomarker negative and positive subgroups. The new design reduces the sample size requirement when compared to running two Simon's designs in each biomarker positive and negative. For example, the new design requires 23%-35% fewer patients than running two Simon's designs for scenarios we considered. Alternatively, the new design allows evaluating the response probability in both biomarker negative and biomarker positive subgroups using only 40% more patients needed for running Simon's design in the biomarker positive subgroup only.

Optimal test procedures for multiple hypotheses controlling the familywise expected loss

We consider the problem of testing multiple null hypotheses, where a decision to reject or retain must be made for each one and embedding incorrect decisions into a real-life context may inflict different losses. We argue that traditional methods controlling the Type I error rate may be too restrictive in this situation and that the standard familywise error rate may not be appropriate. Using a decision-theoretic approach, we define suitable loss functions for a given decision rule, where incorrect decisions can be treated unequally by assigning different loss values. Taking expectation with respect to the sampling distribution of the data allows us to control the familywise expected loss instead of the conventional familywise error rate. Different loss functions can be adopted, and we search for decision rules that satisfy certain optimality criteria within a broad class of decision rules for which the expected loss is bounded by a fixed threshold under any parameter configuration. We illustrate the methods with the problem of establishing efficacy of a new medicinal treatment in non-overlapping subgroups of patients.

New insights into adaptive enrichment designs

The transition towards personalized medicine is happening and the new experimental framework is raising several challenges, from a clinical, ethical, logistical, regulatory, and statistical perspective. To face these challenges, innovative study designs with increasing complexity have been proposed. In particular, adaptive enrichment designs are becoming more attractive for their flexibility. However, these procedures rely on an increasing number of parameters that are unknown at the planning stage of the clinical trial, so the study design requires particular care. This review is dedicated to adaptive enrichment studies with a focus on design aspects. While many papers deal with methods for the analysis, the sample size determination and the optimal allocation problem have been overlooked. We discuss the multiple aspects involved in adaptive enrichment designs that contribute to their advantages and disadvantages. The decision-making process of whether or not it is worth enriching should be driven by clinical and ethical considerations as well as scientific and statistical concerns.

Adaptive enrichment designs with a continuous biomarker

A popular design for clinical trials assessing targeted therapies is the two-stage adaptive enrichment design with recruitment in stage 2 limited to a biomarker-defined subgroup chosen based on data from stage 1. The data-dependent selection leads to statistical challenges if data from both stages are used to draw inference on treatment effects in the selected subgroup. If subgroups considered are nested, as when defined by a continuous biomarker, treatment effect estimates in different subgroups follow the same distribution as estimates in a group-sequential trial. This result is used to obtain tests controlling the familywise type I error rate (FWER) for six simple subgroup selection rules, one of which also controls the FWER for any selection rule. Two approaches are proposed: one based on multivariate normal distributions suitable if the number of possible subgroups, k, is small, and one based on Brownian motion approximations suitable for large k. The methods, applicable in the wide range of settings with asymptotically normal test statistics, are illustrated using survival data from a breast cancer trial.