Adherence to medication is critical to achieving effectiveness of any treatment. Poor adherence often results in lack of treatment effects, worsening of diseases and increased health care costs. Therefore, it has significant public health importance. However, determining factors that influence adherence behavior is complicated because adherence is often measured on multiple drugs over a long period of time, resulting in multivariate ordinal longitudinal outcome. In the first part of this dissertation, we present a joint model which assumes ordered outcomes arose from a partitioned latent multivariate normal process. This joint model provides a framework for analyzing multivariate ordered longitudinal data with a general multilevel association structure, covering both between and within outcome correlation within each individual. Simulation studies show that the estimators of regression parameters are more efficient than those obtained through fitting separate standard GEE for each outcome, though estimators from each method are unbiased. The proposed method also yields unbiased estimators for correlation parameters given the correct correlation structure. However, standard GEE estimators are biased when missing data are present and data are not missing completely at random (MCAR). In the second part of this dissertation, we apply inverse probability weighted (IPW) estimating equations to the proposed joint model to obtain consistent estimators when data are missing at random (MAR). Simulation studies show that IPW estimators are consistent when the missing model is correctly specified. Furthermore, we observe that fitting with correct correlation structures can also help reduce bias for standard GEE estimators. This demonstrates both a better correlation structure and a better missing model will reduce bias in the analysis of missing at random longitudinal data using IPW GEE. We illustrate application of the proposed joint model to the Virahep-C data.
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