Sequential multiple assignment randomized trials (SMARTs) are a useful and increasingly popular approach for gathering information to inform the construction of adaptive interventions to treat psychological and behavioral health conditions. Until recently, analysis methods for data from SMART designs considered only a single measurement of the outcome of interest when comparing the efficacy of adaptive interventions. Lu et al. proposed a method for considering repeated outcome measurements to incorporate information about the longitudinal trajectory of change. While their proposed method can be applied to many kinds of outcome variables, they focused mainly on linear models for normally distributed outcomes. Practical guidelines and extensions are required to implement this methodology with other types of repeated outcome measures common in behavioral research. In this article, we discuss implementation of this method with repeated binary outcomes. We explain how to compare adaptive interventions in terms of various summaries of repeated binary outcome measures, including average outcome (area under the curve) and delayed effects. The method is illustrated using an empirical example from a SMART study to develop an adaptive intervention for engaging alcohol- and cocaine-dependent patients in treatment. Monte Carlo simulations are provided to demonstrate the good performance of the proposed technique.
Keywords: Sequential multiple randomization trial (SMART); binary outcome; logistic regression; longitudinal data.