A note on misspecification in general linear models with correlated errors for the analysis of crossover clinical trials

Among various approaches to the repeated measures analysis in crossover clinical trials, the general linear models (GLMs) with correlated errors attract substantial attention due to their simplicity in model specification, implementation, and interpretation. The goal of this research note is to conduct simulation studies to numerically investigate the impact of model misspecification in the GLMs with correlated errors in the analysis of crossover trials. A series of synthetic two-treatment and three-treatment crossover trials were designed, and simulation studies were conducted to assess how treatment effect estimation, type I error rates, and power can be affected by misspecified period effects, carryover effects, and variance-covariance structures in the GLMs. Numerical studies confirm that (i) the GLMs with terms for both carryover and period effects and with an unstructured variance-covariance matrix can provide unbiased treatment effect estimates and control of Type I error rates and that (ii) misspecification in either period effects, carryover effects, or covariance structures in the GLMs can induce inflated type I error, declined power, or biased treatment effect estimates. Although methodologic contribution of this research note is minimal, we provide practical recommendations and advice to pharmaceutical sponsors and other investigational drugs and device applicants in designing and analyzing crossover trials using the GLMs with correlated errors.