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

In many health domains such as substance-use, outcomes are often counts with an excessive number of zeros (EZ) - count data having zero counts at a rate significantly higher than that expected of a standard count distribution (e.g., Poisson). However, an important gap exists in sample size estimation methodology for planning sequential multiple assignment randomized trials (SMARTs) for comparing dynamic treatment regimens (DTRs) using longitudinal count data. DTRs, also known as treatment algorithms or adaptive interventions, mimic the individualized and evolving nature of patient care through the specification of decision rules guiding the type, timing and modality of delivery, and dosage of treatments to address the unique and changing needs of individuals. To close this gap, we develop a Monte Carlo-based approach to sample size estimation. A SMART for engaging alcohol and cocaine-dependent patients in treatment is used as motivation.