Robust procedures for analysing a two-period cross-over design with baseline measurements

Patel analysed a two-period cross-over design with baseline measurements assuming bivariate normality for the joint distribution of the period responses. In this paper, we propose non-parametric methods for analysing this design, including the use of the Wilcoxon rank sum test to derive the preliminary tests from the baseline measurements. We fit a robust regression line of the treatment response on baseline for each period and compute residuals. We also fit a robust locally weighted regression as an alternative method for computing residuals. Then, following Koch's procedure, we analyse the residuals for testing the significance of the treatment x period interaction and the treatment difference. We provide a numerical example to illustrate the methods.