  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.
