Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA.
Department of Population Medicine, Harvard Pilgrim Health Care Institute and Harvard Medical School, Boston, Massachusetts, USA.
Stat Med. 2023 Nov 30;42(27):5054-5083. doi: 10.1002/sim.9901. Epub 2023 Sep 14.
Cluster randomized trials (CRTs) refer to a popular class of experiments in which randomization is carried out at the group level. While methods have been developed for planning CRTs to study the average treatment effect, and more recently, to study the heterogeneous treatment effect, the development for the latter objective has currently been limited to a continuous outcome. Despite the prevalence of binary outcomes in CRTs, determining the necessary sample size and statistical power for detecting differential treatment effects in CRTs with a binary outcome remain unclear. To address this methodological gap, we develop sample size procedures for testing treatment effect heterogeneity in two-level CRTs under a generalized linear mixed model. Closed-form sample size expressions are derived for a binary effect modifier, and in addition, a computationally efficient Monte Carlo approach is developed for a continuous effect modifier. Extensions to multiple effect modifiers are also discussed. We conduct simulations to examine the accuracy of the proposed sample size methods. We present several numerical illustrations to elucidate features of the proposed formulas and to compare our method to the approximate sample size calculation under a linear mixed model. Finally, we use data from the Strategies and Opportunities to Stop Colon Cancer in Priority Populations (STOP CRC) CRT to illustrate the proposed sample size procedure for testing treatment effect heterogeneity.
群组随机试验（CRTs）是一种流行的实验类型，其中随机化在群组水平上进行。虽然已经开发了用于规划 CRT 以研究平均治疗效果的方法，并且最近还开发了用于研究异质治疗效果的方法，但后者的目标开发目前仅限于连续结果。尽管 CRT 中存在二进制结果，但确定具有二进制结果的 CRT 中检测差异治疗效果所需的样本量和统计功效仍然不清楚。为了解决这一方法学差距，我们在广义线性混合模型下为两级 CRT 中的治疗效果异质性检验开发了样本量程序。为二进制效应修饰符推导出了闭式样本量表达式，此外，还为连续效应修饰符开发了一种计算效率高的蒙特卡罗方法。还讨论了对多个效应修饰符的扩展。我们进行模拟以检查拟议样本量方法的准确性。我们提出了几个数值说明，以阐明所提出公式的特征，并将我们的方法与线性混合模型下的近似样本量计算进行比较。最后，我们使用来自优先人群中的策略和机会停止结肠癌（STOP CRC）CRT 的数据来说明用于检验治疗效果异质性的建议样本量程序。
