Longitudinal data tend to be correlated and hence posing a challenge in the analysis since the correlation has to be accounted for to obtain valid inference. We study various statistical methods for such correlated longitudinal binary responses. These models can be grouped into five model families, namely, marginal, subject-specific, transition, joint and semi-parametric models. Each one of the models has its own strengths and weaknesses. Application of these models is carried out by analyzing data on patient’s adherence status to highly active antiretroviral therapy (HAART). One other complicating issue with the HAART adherence data is missingness. Although some of the models are flexible in handling missing data, they make certain assumptions about missing data mechanisms, the most restrictive being missing completely at random (MCAR). The test for MCAR revealed that dropout did not depend on the previous outcome. A logistic regression model was used to identify predictors for the patients’ first month’s adherence status. A marginal model was then fitted using generalized estimating equations (GEE) to identify predictors of long-term HAART adherence. This provided marginal population-based estimates, which are important for public health perspective. We further explored the subject’s specific effects that are unique to a particular individual by fitting a generalized linear mixed model (GLMM). The GLMM was also used to assess the association structure of the data. To assess whether the current optimal adherence status of a patient depended on the previous adherence measurements (history) in addition to the explanatory variables, a transition model was fitted. Moreover, a joint modeling approach was used to investigate the joint effect of the predictor variables on both HAART adherence status of patients and duration between successive visits. Assessing the association between the two outcomes was also of interest. Furthermore, longitudinal trajectories of observed data may be very complex especially when dealing with practical applications and as such, parametric statistical models may not be flexible enough to capture the main features of the longitudinal profiles, and so a semiparametric approach was adopted. Specifically, generalized additive mixed models were used to model the effect of time as well as interactions associated with time non-parametrically.

Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.