An account is given of the analysis of data from 2 × 2 cross-over trials which include baseline measurements. We show that most of the previously proposed methods can be incorporated into a general framework of least-squares estimation with a simple linear model. A simple analysis based on ordinary least-squares estimators is described which can be used with either two-sample t-tests and confidence intervals or with the corresponding non-parametric procedures. It is shown how the use of generalized least-squares estimators is equivalent to the use of covariance adjustment. These methods require no assumptions about the covariance structure of the measurements from each subject. The results of assessing the covariance structure present in examples of data from a number of trials are summarized. These results suggest that previously proposed simple covariance structures are unlikely to be appropriate in general.
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