Small sample adjustment for inference without assuming orthogonality in a mixed model for repeated measures analysis

The mixed model for repeated measures (MMRM) analysis is sometimes used as a primary statistical analysis for a longitudinal randomized clinical trial. When the MMRM analysis is implemented in ordinary statistical software, the standard error of the treatment effect is estimated by assuming orthogonality between the fixed effects and covariance parameters, based on the characteristics of the normal distribution. However, orthogonality does not hold unless the normality assumption of the error distribution holds, and/or the missing data are derived from the missing completely at random structure. Therefore, assuming orthogonality in the MMRM analysis is not preferable. However, without the assumption of orthogonality, the small-sample bias in the standard error of the treatment effect is significant. Nonetheless, there is no method to improve small-sample performance. Furthermore, there is no software that can easily implement inferences on treatment effects without assuming orthogonality. Hence, we propose two small-sample adjustment methods inflating standard errors that are reasonable in ideal situations and achieve empirical conservatism even in general situations. We also provide an R package to implement these inference processes. The simulation results show that one of the proposed small-sample adjustment methods performs particularly well in terms of underestimation bias of standard errors; consequently, the proposed method is recommended. When using the MMRM analysis, our proposed method is recommended if the sample size is not large and between-group heteroscedasticity is expected.