Longitudinal cohorts are valuable resources for HIV researchers investigating drug and alcohol use (DAU) and its association with HIV clinical outcomes. Dropout due to loss to follow-up or death is common in these studies, and HIV-infected individuals with poor outcomes, such as those who use drugs and alcohol, may be more likely to drop out. Therefore, when estimating the relationship between DAU and longitudinal outcomes, analyses must consider subject loss or the impact of DAU will be underestimated. Natural cubic B-spline varying coefficient models (NSV) can flexibly account for dropout, but in order to implement this method, the number and location of knots for the B-splines must be specified. These parameters can influence model fit and the bias of estimates, but it is unclear how they should be chosen. To address this problem, we propose a Bayesian framework for the NSV, utilizing a reversible jump Markov Chain Monte Carlo approach that formally models these parameters and does not require the choice of a single set of spline knots in order to make statistical inference. Our approach will accommodate continuous and binary categorical outcomes, as well as the joint modeling of 2 or more outcomes. These methods will make statistical inference less dependent on "nuisance parameters," reduce bias, and more accurately characterize model uncertainty than the current NSV method. We will utilize these methods to estimate the impact of DAU on longitudinal clinical outcomes in HIV infection using data from the Women's Interagency HIV Study.
Longitudinal studies are often plagued by dropout, particularly in subjects that use illicit drugs and/or have poor outcomes, such that dropout may mask associations. To control for dropout, we propose Bayesian semi- parametric varying-coefficient methods to more accurately determine clinical outcome trajectories and associations with drug use. Methods will be applied to data from the Women's Interagency HIV Study.