Sample size estimation for pre- and post-intervention design with incomplete observations of count outcomes

The pre- and post-intervention design is frequently utilized in medical and behavioral research, with each subject typically providing a pair of observations collected before and after the intervention. However, not all subjects furnish complete pairs of data. Some subjects may contribute either pre- or post-intervention information only. In this study, we proposed a sample size formula based on the generalized estimating equation (GEE) method for clinical trials where subjects are supposed to provide pre- and post-intervention measurements of a count outcome. The sample size formula is flexible to accommodate different missing patterns, magnitude of missingness and correlation. We compared it with the crude sample size adjustment approach for missing data, which is commonly used in practice and involves dividing the required sample size under complete observations by the proportion of subjects with complete data. Through simulation studies, we evaluated the empirical performance of the proposed sample size formula in preserving desired power and type I error. Furthermore, we presented a clinical trial example to demonstrate its application.