Power comparison of robust approximate and non-parametric tests for the analysis of cross-over trials

The main advantage of cross-over designs in practice is the use of a smaller number of subjects to produce treatment comparisons with sufficient precision. Bellavance and Tardif proposed a non-parametric approach to test the hypotheses of direct treatment and carry-over effects for the three-treatment three-period and six sequences cross-over design and showed the high asymptotic efficiency of their approach relative to the classical F-test based on ordinary least squares (OLS). In a more recent paper, Ohrvik suggested another non-parametric method for the analysis of cross-over trials. The power of these two non-parametric approaches is evaluated for small sample sizes via simulations, and compared to the power of the usual analysis of variance model based on OLS and a modified F-test approximation that take into account the correlation structure of the repeated measurements within subjects. Different covariance structures, sample sizes, and probability distributions for the responses, namely normal and gamma, are used in the simulations to evaluate the power and robustness of these different methods of analysis.