Analysis of cross-over designs with serial correlation within periods using semi-parametric mixed models

The use of semi-parametric mixed models has proven useful in a wide variety of settings. Here, we focus on the application of the methodology in the particular case of a cross-over design with relatively long sequences of repeated measurements within each treatment period and for each subject. Other than an overall measure of the difference between each one of the experimental groups and the control group, specific time point comparisons may also be of interest. To that effect, we propose the use of flexible semi-parametric mixed models, enabling the construction of simulation-based simultaneous confidence bands. The bands take into account both between- and within-subject variabilities, while simultaneously correcting for multiple time point comparisons. Owing to the relatively long sequences of measurements per subject, the presence of serially correlated errors is anticipated and investigated. We illustrate how several formulations of semi-parametric mixed models can be fitted and the construction of simulation-based simultaneous confidence bands using SAS PROC MIXED.