A powerful test for Balaam's design

The crossover trial design (AB/BA design) is often used to compare the effects of two treatments in medical science because it performs within-subject comparisons, which increase the precision of a treatment effect (i.e., a between-treatment difference). However, the AB/BA design cannot be applied in the presence of carryover effects and/or treatments-by-period interaction. In such cases, Balaam's design is a more suitable choice. Unlike the AB/BA design, Balaam's design inflates the variance of an estimate of the treatment effect, thereby reducing the statistical power of tests. This is a serious drawback of the design. Although the variance of parameter estimators in Balaam's design has been extensively studied, the estimators of the treatment effect to improve the inference have received little attention. If the estimate of the treatment effect is obtained by solving the mixed model equations, the AA and BB sequences are excluded from the estimation process. In this study, we develop a new estimator of the treatment effect and a new test statistic using the estimator. The aim is to improve the statistical inference in Balaam's design. Simulation studies indicate that the type I error of the proposed test is well controlled, and that the test is more powerful and has more suitable characteristics than other existing tests when interactions are substantial. The proposed test is also applied to analyze a real dataset.