Improved power in crossover designs through linear combinations of baselines.

In a crossover design in the absence of any carryover effect, including period-specific baselines as covariates in an analysis of covariance, is known to increase the precision of the estimated treatment effect. The extent of the efficiency gain is a function of the joint covariance structure of the baselines and post-treatment responses, as well as the metric used to incorporate the baselines into the analysis. Here, we show how the underlying covariance structure can be leveraged to find an optimal linear combination of baselines so as to minimize the theoretical variance of the analysis of covariance-based estimated treatment effect. Our work is relevant to complete designs with up to four periods, specifically the 2 × 2, 3 × 3, and 4 × 4. Given that the optimal linear combination of baselines is a function of the covariance structure, which in practice is unknown, we propose an adaptive method. Here, the covariance structure is chosen using information criterion to guide the choice of the linear combination of baselines. Evaluation of the proposed approach suggests that the type I error rate is maintained. Moreover, relative to previously published methods, sizeable gains in power are possible with this method. Results from a 2 × 2 trial exploring renal function, and a 3 × 3 trial with heart rate as the outcome, are used to illustrate the methods. Copyright © 2016 John Wiley & Sons, Ltd.