Power and sample size for GEE analysis of incomplete paired outcomes in 2 x 2 crossover trials

The 2 x 2 crossover trial uses subjects as their own control to reduce the intersubject variability in the treatment comparison, and typically requires fewer subjects than a parallel design. The generalized estimating equations (GEE) methodology has been commonly used to analyze incomplete discrete outcomes from crossover trials. We propose a unified approach to the power and sample size determination for the Wald Z-test and t-test from GEE analysis of paired binary, ordinal and count outcomes in crossover trials. The proposed method allows misspecification of the variance and correlation of the outcomes, missing outcomes, and adjustment for the period effect. We demonstrate that misspecification of the working variance and correlation functions leads to no or minimal efficiency loss in GEE analysis of paired outcomes. In general, GEE requires the assumption of missing completely at random. For bivariate binary outcomes, we show by simulation that the GEE estimate is asymptotically unbiased or only minimally biased, and the proposed sample size method is suitable under missing at random (MAR) if the working correlation is correctly specified. The performance of the proposed method is illustrated with several numerical examples. Adaption of the method to other paired outcomes is discussed.

Automated summary

The 2 x 2 crossover trial reduces intersubject variability in treatment comparison by using subjects as their own control and typically requires fewer subjects than a parallel design. The generalized estimating equations (GEE) methodology is commonly used for analyzing incomplete discrete outcomes from crossover trials, and a unified approach to power and sample size determination for Wald Z-test and t-test in GEE analysis of paired outcomes is proposed. The method allows for misspecification of variance and correlation functions, missing outcomes, and adjustment for period effect, with minimal efficiency loss demonstrated in GEE analysis.