In the management of most chronic conditions characterized by the lack of universally effective treatments, adaptive treatment strategies (ATSs) have been growing in popularity as they offer a more individualized approach, and sequential multiple assignment randomized trials (SMARTs) have gained attention as the most suitable clinical trial design to formalize the study of these strategies. While the number of SMARTs has increased in recent years, their design has remained limited to the frequentist setting, which may not fully or appropriately account for uncertainty in design parameters and hence not yield appropriate sample size recommendations. Specifically, standard frequentist formulae rely on several assumptions that can be easily misspecified. The Bayesian framework offers a straightforward path to alleviate some of these concerns. In this paper, we provide calculations in a Bayesian setting to allow more realistic and robust estimates that account for uncertainty in inputs through the `two priors approach. Additionally, compared to the standard formulae, this methodology allows us to rely on fewer assumptions, integrate pre-trial knowledge, and switch the focus from the standardized effect size to the minimal detectable difference. The proposed methodology is evaluated in a thorough simulation study and is implemented to estimate the sample size for a full-scale SMART of an Internet-Based Adaptive Stress Management intervention based on a pilot SMART conducted on cardiovascular disease patients from two Canadian provinces.
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