A mixed effects model for the analysis of repeated measures cross-over studies

A mixed effects model is developed for cross-over trials in which the response is measured repeatedly within each time period. Relative to previous work on repeated measures cross-overs, the methodology synthesizes two important features. First, our procedure eliminates preliminary testing for carry-over, defined loosely as the component of a response that is due to treatment in the preceding period. This is achieved by generalizing the methodology to cross-over designs in which preliminary testing for carry-over is unnecessary. We focus largely on 'simple' carry-over, that is, carry-over that lasts for exactly one period and is independent of the treatment administered in the period in which the carry-over occurs. However, we also illustrate a modification of the procedure for a repeated measures cross-over design which uses a more complicated model of carry-over. Second, the model allows both the between- and within-subject variance to differ among treatments. Conditions are described wherein closed-form (CF) solutions to the variance components as well as closed-form hypothesis tests of the treatment differences exist. Flexibility in the model is illustrated with an example in which inference based on the CF likelihood-based estimates of the variance, and estimates formed using an iterative routine (PROC MIXED) are compared.