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.

翻译：动态治疗疗法(DTRs)也称为治疗算法或适应性干预,在许多卫生领域发挥着日益重要的作用。DTRs具有满足个人独特和不断变化的需要的动机,必要时提供所需的治疗类型,同时尽量减少不必要的治疗。实际上,DTR是决策规则的顺序,它规定,对于每个时间点,如何实际使用关于个人的现有信息来决定提供何种治疗(例如,类型或强度),顺序的多重派任随机试验(SMART)是一种实验性设计,广泛用于实证性地为DTRs的发展提供参考。SMART研究的现有样本规模规划资源适合连续、二进制或生存结果。然而,在SMARTs规划具有纵向计数结果的样本规模估计方法方面存在着重大差距。此外,在许多卫生领域,计数数据过于分散,其差异大于其平均值。为了缩小这一差距,这份手稿描述了基于蒙特卡洛的样本规模估计方法的发展。在研究中采用模拟性研究方法来调查各种酒精治疗的动机。