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

Area of Science:

• Biostatistics
• Statistical Modeling
• Longitudinal Data Analysis

Background:

• Covariance structure misspecification in linear mixed models (LMMs) can bias population parameter estimates, particularly under missing at random (MAR) drop-out.
• LMMs with random intercept and slope structures are common for longitudinal data, such as CD4 cell counts in HIV infection.

Purpose of the Study:

• To evaluate LMM performance with different covariance structures under MAR drop-out mechanisms.
• To compare bias in fixed effects estimates between fractional Brownian motion (BM) and spline approaches for random effects.
• To assess a Bayesian model comparison criterion for selecting the correct covariance structure.

Main Methods:

• Analytical derivation of bias under misspecified covariance structures.
• Comparison of fractional Brownian motion (BM) and spline methods for random effects under misspecification.
• Simulation study to evaluate a Bayesian criterion against AIC and BIC.
• Application to real-world data from the CASCADE study.

Main Results:

• Analytical results show that misspecified random intercept and slope structures can lead to significant bias, dependent on MAR drop-out magnitude.
• Both BM and spline approaches demonstrated satisfactory performance, with the BM model generally exhibiting less bias.
• The proposed Bayesian criterion outperformed AIC and BIC in identifying the correct covariance structure in simulations.

Conclusions:

• Misspecification of covariance structure in LMMs is a critical issue impacting parameter estimates.
• Fractional Brownian motion and spline approaches offer viable solutions, with BM often yielding lower bias.
• The proposed Bayesian model comparison criterion is effective for selecting appropriate covariance structures in LMMs.