Misspecifying the covariance structure in a linear mixed model under MAR drop-out

Abstract

Misspecification of the covariance structure in a linear mixed model (LMM) can lead to biased population parameters' estimates under MAR drop-out. In our motivating example of modeling CD4 cell counts during untreated HIV infection, random intercept and slope LMMs are frequently used. In this article, we evaluate the performance of LMMs with specific covariance structures, in terms of bias in the fixed effects estimates, under specific MAR drop-out mechanisms, and adopt a Bayesian model comparison criterion to discriminate between the examined approaches in real-data applications. We analytically show that using a random intercept and slope structure when the true one is more complex can lead to seriously biased estimates, with the degree of bias depending on the magnitude of the MAR drop-out. Under misspecified covariance structure, we compare in terms of induced bias the approach of adding a fractional Brownian motion (BM) process on top of random intercepts and slopes with the approach of using splines for the random effects. In general, the performance of both approaches was satisfactory, with the BM model leading to smaller bias in most cases. A simulation study is carried out to evaluate the performance of the proposed Bayesian criterion in identifying the model with the correct covariance structure. Overall, the proposed method performs better than the AIC and BIC criteria under our specific simulation setting. The models under consideration are applied to real data from the CASCADE study; the most plausible model is identified by all examined criteria.