Sample size considerations for paired experimental design with incomplete observations of continuous outcomes

Paired experimental design is widely used in clinical and health behavioral studies, where each study unit contributes a pair of observations. Investigators often encounter incomplete observations of paired outcomes in the data collected. Some study units contribute complete pairs of observations, while the others contribute either pre- or post-intervention observations. Statistical inference for paired experimental design with incomplete observations of continuous outcomes has been extensively studied in literature. However, sample size method for such study design is sparsely available. We derive a closed-form sample size formula based on the generalized estimating equation approach by treating the incomplete observations as missing data in a linear model. The proposed method properly accounts for the impact of mixed structure of observed data: a combination of paired and unpaired outcomes. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness, and correlation parameter values. We demonstrate that under complete observations, the proposed generalized estimating equation sample size estimate is the same as that based on the paired t-test. In the presence of missing data, the proposed method would lead to a more accurate sample size estimate comparing with the crude adjustment. Simulation studies are conducted to evaluate the finite-sample performance of the generalized estimating equation sample size formula. A real application example is presented for illustration.