Sequential Multiple-Assignment Randomized Trials (SMARTs) play an increasingly important role in psychological and behavioral health research. This experimental approach enables researchers to answer scientific questions about how to sequence and match interventions to the unique, changing needs of individuals. A variety of sample size planning resources for SMART studies have been developed in recent years; these enable researchers to plan SMARTs for addressing different types of scientific questions. However, relatively limited attention has been given to planning SMARTs with binary (dichotomous) outcomes, which often require higher sample sizes relative to continuous outcomes. Existing resources for estimating sample size requirements for SMARTs with binary outcomes do not consider the potential to improve power by including a baseline measurement and/or multiple repeated outcome measurements. The current paper addresses this issue by providing sample size simulation code and approximate formulas for two-wave repeated measures binary outcomes (i.e., two measurement times for the outcome variable, before and after receiving the intervention). The simulation results agree well with the formulas. We also discuss how to use simulations to calculate power for studies with more than two outcome measurement occasions. The results show that having at least one repeated measurement of the outcome can substantially improve power under certain conditions.

翻译：序贯多分配随机试验（SMARTs）在心理与行为健康研究中的作用日益重要。这种实验方法使研究者能够回答关于如何根据个体独特且动态变化的需求，对干预措施进行排序与匹配的科学问题。近年来已开发出多种针对SMART研究的样本量规划工具，帮助研究者设计能解决不同类型科学问题的SMART试验。然而，针对二元（二分类）结局变量的SMART研究规划受到的关注相对有限，这类研究通常比连续结局需要更大的样本量。现有估算二元结局SMART研究样本量需求的方法未考虑通过纳入基线测量和/或多次重复结局测量来提高统计功效的潜力。本文通过提供两波重复测量二元结局（即在干预前后对结局变量进行两次测量）的样本量模拟代码与近似计算公式来解决该问题。模拟结果与公式高度吻合。我们还讨论了如何利用模拟计算包含两次以上结局测量场合的研究功效。结果表明，在特定条件下，至少对结局进行一次重复测量可显著提升统计功效。