Differences in Mortality among Heroin, Cocaine, and Methamphetamine Users: A Hierarchical Bayesian Approach

Abstract

Studies examining differences in mortality among long-term drug users have been limited. In this paper, we introduce a Bayesian framework that jointly models survival data using a Weibull proportional hazard model with frailty, and substance and alcohol data using mixed-effects models, to examine differences in mortality among heroin, cocaine, and methamphetamine users from five long-term follow-up studies. The traditional approach to analyzing combined survival data from numerous studies assumes that the studies are homogeneous, thus the estimates may be biased due to unobserved heterogeneity among studies. Our approach allows us to structurally combine the data from different studies while accounting for correlation among subjects within each study. Markov chain Monte Carlo facilitates the implementation of Bayesian analyses. Despite the complexity of the model, our approach is relatively straightforward to implement using WinBUGS. We demonstrate our joint modeling approach to the combined data and discuss the results from both approaches.

Figure 1

Kaplan-Meier Curves for (a) within 20 years and (b) 30 years of first use of substance, and (c) from first use of substance to October, 2006. The curves with circle (black), triangular (red), and plus (blue) are for Heroin, Cocaine, and Methamphetamine, respectively. The horizontal dotted lines are 80% and 50% survival.

Figure 2

Posterior Kernel Density Estimates (KDEs) of Kendall's τ for all addicts (solid), male addicts (dash), and females addicts (dot).