Using Interviewer Random Effects to Calculate Unbiased HIV Prevalence Estimates in the Presence of Non-Response: a Bayesian Approach

Consent rates for HIV testing in population surveys are often low, which may cause a bias in prevalence estimates if refusal to test is correlated with HIV status. Interviewer identity represents a plausible variable that affects testing, but not HIV status, and can be used in a Heckman-type selection model that provides consistent prevalence estimates. We innovate by adopting an interviewer random effects estimator which improves on the existing interviewer fixed effect approach in three respects. Firstly, using our model allows the effects of interviewer identity to be estimated even for those whose interviewers conducted a small number of interviews. Secondly, this methodology facilitates the use of bootstrapped standard errors which are necessary to correct for regression parameter uncertainty in the correlation between consent and HIV status. Thirdly, we propose a Bayesian model averaging approach that gives estimates that are consistent and unbiased. We report results for Zambia and Ghana. For Zambia we estimate a prevalence rate of 32% among males who refuse consent compared with 12 % among those who agree to test, substantially increasing the estimated population prevalence rate.