A BAYESIAN APPROACH TO EPIDEMIOLOGIC ESTIMATION FOR POLICY MODELS IN THE PRESENCE OF SPARSE DATA: THE EXAMPLE OF HEPATITIS C PREVALENCE AMONG INJECTION DRUG USERS

Purpose: Planning for increased hepatitis C virus (HCV) screening and treatment requires a detailed understanding of HCV prevalence among specific risk-groups defined in terms of injection drug use, heavy alcohol use, and membership in high-risk birth cohorts. To address the problem of sparse data on prevalence in particular subgroups—usually represented by small samples in national surveys—we used a Bayesian approach to model HCV prevalence in the US.

Methods: We used data from the National Health and Nutrition Examination Survey (NHANES) from 2001-2010 to estimate odds ratios (OR) for HCV infection among injection drug users (IDUs) and non-IDUs. First, we fit standard regression models. Next, we used a hierarchical Bayesian analytic approach based on the following steps: (1) meta-analysis of published HCV prevalence estimates in IDUs; (2) generating prior distributions for model parameters based on these meta-analytic results; (3) running Bayesian regression using Markov Chain Monte Carlo techniques. We determine convergence by visual inspection and the Gelman-Rubin statistic. We compared findings from the standard and Bayesian regressions and assessed the sensitivity of the Bayesian estimates to key assumptions in the priors. We conducted analyses using SAS, R, and OpenBUGS.

 

Results: Among all NHANES respondents in the analytic sample (N~16000), 1.7% were HCV-infected, and <0.3% self-reported as IDUs. In the standard regression model, the estimated OR of HCV for IDU was 79 (95% CI:  53-118). The meta-analysis estimate of HCV prevalence in IDUs was 56% (95% CI: 42%-69%), implying an OR of 43 (95% CI: 32-53). The hierarchical Bayesian model yielded drug use estimates consistent with the meta-analysis (OR=47, 95% CI: 43-52). Coefficient and standard error (SE) estimates of model parameters without priors were consistent with the standard regression results, and SEs in the Bayesian model were always lower than in the standard regression.

 

Conclusions: We present a Bayesian method to estimate risk of HCV in the presence of sparse data on sub-group outcomes in a large national survey. While survey design methods cannot be exactly replicated in the Bayesian setting, hierarchical methods yield similar results. In cases where coefficient and SE estimates are implausible or unreliable, a Bayesian approach may allow more precise estimates by incorporating information from other sources.