Sample size considerations for matched-pair cluster randomization design with incomplete observations of continuous outcomes

Matched-pair cluster randomization design is becoming increasingly used in clinical and health behavioral studies. Investigators often encounter incomplete observations in the data collected. Statistical inference for matched-pair cluster randomization design with incomplete observations has been extensively studied in literature. However, sample size method for such study design is sparsely available. We propose a closed-form sample size formula for matched-pair cluster randomization design with continuous outcomes, based on the generalized estimating equation approach by treating incomplete observations as missing data in a marginal linear model. The sample size formula is flexible to accommodate different correlation structures, missing patterns, and magnitude of missingness. In the presence of missing data, the proposed method would lead to a more accurate sample size estimation than the crude adjustment method. Simulation studies are conducted to evaluate the finite-sample performance of the proposed sample size method under various design configurations. We use bias-corrected variance estimators to address the issue of inflated type I error when the number of clusters per group is small. A real application example of physical fitness study in Ecuadorian adolescents is presented for illustration.