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. Copyright © 1999 John Wiley & Sons, Ltd.