Impact of subject attrition on sample size determinations for longitudinal cluster randomized clinical trials

Subject attrition is a ubiquitous problem in any type of clinical trial and, thus, needs to be taken into consideration at the design stage particularly to secure adequate statistical power. Here, we focus on longitudinal cluster randomized clinical trials (cluster-RCT) that aim to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time. In this setting, the cluster-RCT assumes a three-level hierarchical data structure in which subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. Furthermore, the subject-specific slopes can be modeled in terms of fixed or random coefficients in a mixed-effects linear model. Closed-form sample size formulas for testing the preceding hypothesis have been developed under an assumption of no attrition. In this article, we propose closed-form approximate samples size determinations with anticipated attrition rates by modifying those existing sample size formulas. With extensive simulations, we examine performances of the modified formulas under three attrition mechanisms: attrition completely at random, attrition at random, and attrition not at random. In conclusion, the proposed modification is very effective under fixed-slope models but yields biased, perhaps substantially so, statistical power under random slope models.