A recommended analysis for 2 × 2 crossover trials with baseline measurements

In many two-period, two-treatment (2 × 2) crossover trials, for each subject, a continuous response of interest is measured before and after administration of the assigned treatment within each period. The resulting data are typically used to test a null hypothesis involving the true difference in treatment response means. We show that the power achieved by different statistical approaches is greatly influenced by (i) the 'structure' of the variance-covariance matrix of the vector of within-subject responses and (ii) how the baseline (i.e., pre-treatment) responses are accounted for in the analysis. For (ii), we compare different approaches including ignoring one or both period baselines, using a common change from baseline analysis (which we advise against), using functions of one or both baselines as period-specific or period-invariant covariates, and doing joint modeling of the post-baseline and baseline responses with corresponding mean constraints for the latter. Based on theoretical arguments and simulation-based type I error rate and power properties, we recommend an analysis of covariance approach that uses the within-subject difference in treatment responses as the dependent variable and the corresponding difference in baseline responses as a covariate. Data from three clinical trials are used to illustrate the main points.