SMART Binary: Sample Size Calculation for Comparing Adaptive Interventions in SMART studies with Longitudinal Binary Outcomes

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.