Confidence Intervals for the Treatment Effects in Adaptive Enrichment Designs

Zhu, Jinyu and Wan, Fang and Titman, Andrew (2023) Confidence Intervals for the Treatment Effects in Adaptive Enrichment Designs. PhD thesis, Lancaster University.

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Abstract

While safety is the primary objective in Phase I designs of pharmacological or novel treatment development clinical trials, the focus shifts to detecting the effectiveness of the experimental treatment in confirmatory seamless Phase II/III designs. The presence of patient heterogeneity in modern medication development is widely acknowledged. The response of patients to the same treatment might vary depending on factors such as their gender, age, lifestyle, or genetic diversity. Therefore, it is necessary to determine which group of the population is more likely to benefit from the experimental treatment in the Phase II/III designs. In order to save time and cost, the adaptive enrichment design was proposed. The adaptive enrichment design concentrates resources on promising subgroups by allowing modifications based on the interim analysis results. However, the adaptive nature of the procedure complicates the estimation of the treatment effects and makes the quantification of uncertainty in treatment effects challenging. In particular, confidence intervals based on the naive maximum likelihood estimate and corresponding Fisher information will tend to have incorrect coverage. Focusing on a two-stage design with two disjoint subgroups, we develop a general method based on devising an appropriate p-value function. We derive the conditional confidence intervals for selected subgroups by inverting their corresponding conditional p-value functions, which are obtained using stage-wise, score, and MLE sample space orderings methods. Comparing the confidence intervals produced from the aforementioned space ordering methods reveals that score ordering treats each stage more evenly. Additionally, we construct the unconditional p-value function for each subgroup and utilize the classic Bonferroni, Bonferroni-Holm, and parameter-dependent weighted Bonferroni multiple testing procedures to create simultaneous confidence intervals at the end of the trial. We demonstrate that BonferroniHolm is most effective at detecting actual treatment effects, but its confidence interval for rejected hypotheses is uninformative when not all hypotheses are rejected. In contrast, the traditional Bonferroni simultaneous confidence intervals provide information regarding the magnitude of the real treatment effect but are less effective at rejecting false null hypotheses. The weighted parameter-dependent Bonferroni method compromises between informativeness and power. The confidence interval construction approach is illustrated through the application of two adaptive enrichment designs. Simulation studies show that our approach constructs confidence intervals with exact asymptotic coverage probabilities. Our method may be extended to k-stage msubgroup adaptive enrichment design with k ≥ 3 and m ≥ 3; although, the computation cost will also increase.