A GEE approach to determine sample size for pre- and post-intervention experiments with dropout

Pre- and post-intervention experiments are widely used in medical and social behavioral studies, where each subject is supposed to contribute a pair of observations. In this paper we investigate sample size requirement for a scenario frequently encountered by practitioners: all enrolled subjects participate in the pre-intervention phase of study, but some of them will drop out due to various reasons, thus resulting in missing values in the post-intervention measurements. Traditional sample size calculation based on McNemar's test could not accommodate missing data. Through the GEE approach, we derive a closed-form sample size formula that properly accounts for the impact of partial observations. We demonstrate that when there are no missing data, the proposed sample size estimate under the GEE approach is very close to that under McNemar's test. When there are missing data, the proposed method can lead to substantial saving in sample size. Simulation studies and an example are presented.