Planning SMARTs: Sample size estimation for comparing dynamic treatment regimens using longitudinal count outcomes with overdispersion

Dynamic treatment regimens (DTRs), also known as treatment algorithms or adaptive interventions, play an increasingly important role in many health domains. DTRs are motivated to address the unique and changing needs of individuals by delivering the type of treatment needed, when needed, while minimizing unnecessary treatment. Practically, a DTR is a sequence of decision rules that specify, for each of several points in time, how available information about the individual should be used in practice to decide which treatment (e.g., type or intensity) to deliver. The sequential multiple assignment randomized trial (SMART) is an experimental design that is widely used to empirically inform the development of DTRs. Existing sample size planning resources for SMART studies are suitable for continuous, binary, or survival outcomes. However, an important gap exists in sample size estimation methodology for planning SMARTs with longitudinal count outcomes. Further, in many health domains, count data are overdispersed - that is, having variance greater than their mean. To close this gap, this manuscript describes the development of a Monte Carlo-based approach for sample size estimation. Simulation studies were employed to investigate various properties of this approach. Throughout, a SMART for engaging alcohol and cocaine-dependent patients in treatment is used as motivation.