A key issue when designing clinical trials is the estimation of the number of subjects required. Assuming for multicenter trials or biomarker-stratified designs that the effect size between treatment arms is the same among the whole study population might be inappropriate. Limited work is available for properly determining the sample size for such trials. However, we need to account for both, the heterogeneity of the baseline hazards over clusters or strata but also the heterogeneity of the treatment effects, otherwise sample size estimates might be biased. Most existing methods account for either heterogeneous baseline hazards or treatment effects but they dot not allow to simultaneously account for both sources of variations. This article proposes an approach to calculate sample size formula for clustered or stratified survival data relying on frailty models. Both theoretical derivations and simulation results show the proposed approach can guarantee the desired power in worst case scenarios and is often much more efficient than existing approaches. Application to a real clinical trial designs is also illustrated.

中文翻译：

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存在异质人群时癌症随机试验的样本量估计

设计临床试验时的一个关键问题是估计所需受试者的数量。对于多中心试验或生物标志物分层设计，假设治疗组之间的效应量在整个研究人群中相同可能是不合适的。有限的工作可用于正确确定此类试验的样本量。然而，我们需要同时考虑集群或层级的基线危害的异质性以及治疗效果的异质性，否则样本量估计可能会有偏差。大多数现有方法都考虑了异质性基线危害或治疗效果，但它们不允许同时考虑这两种变化来源。本文提出了一种方法来计算依赖脆弱模型的聚类或分层生存数据的样本量公式。理论推导和仿真结果都表明，所提出的方法可以在最坏情况下保证所需的功率，并且通常比现有方法更有效。还说明了在实际临床试验设计中的应用。