A Note on the Bias of Standard Errors when Orthogonality of Mean and Variance Parameters is Not Satisfied in the Mixed Model for Repeated Measures Analysis

The mixed effect models for repeated measures (MMRM) analysis is sometimes used as a primary analysis in longitudinal randomized clinical trials. The SE for the treatment effect in the MMRM analysis is usually estimated by assuming the orthogonality of the fixed effect and variance-covariance parameters, which is the orthogonality property of a multivariate normal distribution, because of default settings of most standard statistical software. However, this property might be lost when analysis models are misspecified and/or data include missing values with the mechanism of being missing at random. In this study, we investigated the effect of the assumption of the orthogonality property on the estimation of the SE for the MMRM analysis. From simulation and case studies, it was shown that the SE with the assumption of orthogonality property had nonnegligible bias, especially when the analysis models assuming heteroscedasticity between treatment groups were applied. We also introduce the SAS code for the MMRM analysis without assuming the orthogonality property. Assuming the orthogonality property in the MMRM analysis would lead to invalid statistical inference, and it is necessary to be careful when applying the MMRM analysis with most standard software.