Sample size calculation for before–after experiments with partially overlapping cohorts

We investigate sample size calculation for before–after experiments where the outcome of interest is binary and the enrolled subjects contribute a mixed type of data: some subjects contribute complete pairs of before- and after-intervention outcomes, while some subjects contribute incomplete data (before-intervention only or after-intervention only). We use the GEE approach to derive a closed-form sample size formula by treating the incomplete observations as missing data in a generalized linear model. The impacts of various designing factors are appropriately accounted for in the sample size formula, including intervention effect, baseline response rate, within-subject correlation, and distribution of missing values in the before- and after-intervention periods. We illustrate sample size estimation using a real application example. We conduct simulation studies to demonstrate that the proposed sample size maintains the nominal power and type I error under a wide spectrum of trial configurations.