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.

翻译：动态治疗方案（DTR），亦称治疗算法或适应性干预，在健康领域发挥着日益重要的作用。DTR旨在通过按需提供所需治疗类型、同时减少非必要治疗，以满足个体独特且动态变化的需求。实践中，DTR是由一系列决策规则构成的序列，这些规则针对多个时间点，规定如何利用个体当前状态和进展的可获信息来决定实施何种治疗（例如类型或强度）。序贯多重分配随机试验（SMART）是一种广泛用于指导DTR开发的实验设计。现有SMART样本量规划资源主要涵盖连续、二分类及生存结局，但针对纵向计数结局的SMART样本量估计方法尚存在重要空白。此外，许多健康领域中计数数据存在过离散现象——即方差大于均值。本文提出一种基于蒙特卡洛的样本量估计方法，适用于多种纵向结局类型，并提供了纵向过离散计数结果的案例研究。本研究以一项旨在促进酒精与可卡因依赖患者参与治疗的SMART为切入点。