  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's status and progress 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 widely used to empirically inform the development of DTRs. Sample size
planning resources for SMARTs have been developed for continuous, binary, and
survival outcomes. However, an important gap exists in sample size estimation
methodology for SMARTs with longitudinal count outcomes. Further, in many
health domains, count data are overdispersed - having variance greater than
their mean. We propose a Monte Carlo-based approach to sample size estimation
applicable to many types of longitudinal outcomes and provide a case study with
longitudinal overdispersed count outcomes. A SMART for engaging alcohol and
cocaine-dependent patients in treatment is used as motivation.
