Sample size calculation for the sequential multiple assignment randomized trial (SMART) design with a skewed outcome: Application to the SMART+ study

With the rapid emergence of personalized healthcare, adaptive interventions have gained significant traction and relevance. Contemporary research has introduced a sophisticated trial design known as the sequential multiple assignment randomized trial (SMART) to advance the development of effective adaptive interventions. A critical element of the SMART design is the determination of the sample size. The existing literature provides sample size calculation formulas for SMART designs, which encompass a variety of approaches and types of outcome data. However, these formulas have primarily been developed under the assumption of normality for the outcome data. In practice, the fields where SMART is employed exhibit a significant prevalence of non-normality in the outcomes of interest. This paper delves into a specific scenario where the outcome demonstrates skewed behavior. We develop precision-based and power-based formulas for skewed outcomes, considering the requirements of both pilot and full-scale SMARTs. We present the operating characteristics of the formulas and perform extensive simulations under various design specifications to validate their usefulness. To demonstrate practical utility, we apply our formulas to the SMART+ study, a digital intervention trial that includes a skewed outcome among its outcomes of interest, highlighting relevance in real-world planning.