Sample size calculation for count outcomes in cluster randomization trials with varying cluster sizes

Abstract

In many cluster randomization studies, cluster sizes are not fixed and may be highly variable. For those studies, sample size estimation assuming a constant cluster size may lead to under-powered studies. Sample size formulas have been developed to incorporate the variability in cluster size for clinical trials with continuous and binary outcomes. Count outcomes frequently occur in cluster randomized studies. In this paper, we derive a closed-form sample size formula for count outcomes accounting for the variability in cluster size. We compare the performance of the proposed method with the average cluster size method through simulation. The simulation study shows that the proposed method has a better performance with empirical powers and type I errors closer to the nominal levels.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

“…There are several existing sample size formulas developed for analyzing clustered count outcomes, all of which assume the absence of truncation (Amatya et al., 2013; Hayes & Moulton, 2009; Wang et al., 2020). Ogungbenro and Aarons (2010) obtained a closed‐form power formula for longitudinal pharmacodynamic studies with repeated count measurements based on the Poisson random‐effects model.…”

Incorporating pragmatic features into power analysis for cluster randomized trials with a count outcome

“…In this article, we propose a sample size calculation method for count data in CRTs. Compared with existing methods, 8,12 it is advantageous in directly incorporating pragmatic features including overdispersion, varying cluster sizes, varying lengths of patient's follow‐up, and arbitrary randomization ratios. Furthermore, the sample size formula retains a closed form, facilitating its wide implementation by practitioners.…”

“…Many researchers have shown that ignoring cluster size variability in sample size calculation can lead to underpowered studies 9‐11 . Wang et al 12 proposed to incorporate cluster size variability into sample size calculation for CRTs with count outcomes, where a correction term defined based on the coefficient of variation in cluster size is included 13 . The relative efficiency of unequal vs equal cluster sizes when testing the treatment effect in two‐arm CRTs was investigated continuous, binary and count outcomes.…”

“…The relative efficiency of unequal vs equal cluster sizes when testing the treatment effect in two‐arm CRTs was investigated continuous, binary and count outcomes. It is noteworthy that the aforementioned works on count outcomes 8,12,14 all employed the Poisson model, which by definition imposes the restriction that the mean and variance of the count outcome are equal 15 . In practice, however, the phenomenon of a count variable having a variance larger than its mean (referred to as overdispersion) has been widely reported in biomedical research 16,17 .…”

“…Finally, most of existing methods 8,12,14 assume patients to contribute an equal length of follow‐up, during which the counts of certain events are measured. In pragmatic CRT trials, patients may experience early treatment discontinuation or early dropouts, hence lead to varying lengths of follow‐up to measure the count outcome.…”