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

Selection bias in HIV prevalence estimates occurs if refusal to test is correlated with HIV status. Interviewer identity is plausibly correlated with consenting to test, but not with HIV status, allowing a Heckman-type correction that produces consistent HIV prevalence estimates. We innovate on existing approaches by showing that an interviewer random effects Bayesian estimator produces prevalence estimates that are unbiased as well as consistent. An additional advantage of this new estimator is that it allows the construction of bootstrapped standard errors. It is also easily implemented in standard statistical software. The model is used to produce new estimates and confidence intervals for HIV prevalence among men in Zambia and Ghana.