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 non-participation in testing is correlated with HIV status. Longitudinal data suggests that individuals who know or suspect they are HIV positive are less likely to participate in testing in HIV surveys, in which case methods to correct for missing data which are based on imputation and observed characteristics will produce biased results. Interviewer identity is associated with testing participation, but is plausibly uncorrelated with HIV status, allowing a Heckman-type correction that produces asymptotically unbiased HIV prevalence estimates, even when non-response is correlated with unobserved characteristics, such as knowledge of HIV status. We introduce a new random effects method which overcomes non-convergence caused by collinearity, small sample bias, and incorrect inference in existing approaches. It is easy to implement in standard statistical software, and allows the construction of bootstrapped standard errors which adjust for the fact that the relationship between testing and HIV status is uncertain and needs to be estimated. Using nationally representative data from the Demographic and Health Surveys, we illustrate our approach with new point estimates and confidence intervals (CI) for HIV prevalence among men in Ghana and Zambia. In Ghana, we find little evidence of selection bias as our selection model gives a HIV prevalence estimate of 1.4% (95% CI 1.2% ? 1.6%), compared to 1.6% among those with a valid HIV test. In Zambia, our selection model gives a HIV prevalence estimate of 16.3% (95% CI 11% - 18.4%), compared to 12.1% among those with a valid HIV test. Therefore, those who decline to test in Zambia are found to be more likely to be HIV positive, however our new bootstrap confidence intervals are wide. Our approach corrects for selection bias in HIV prevalence estimates, is possible to implement even when HIV prevalence or non-response is very high or low, and provides a practical solution to account for both sampling and parameter uncertainty in the estimation of confidence intervals. These wide confidence intervals reflect that it is difficult to correct statistically for the bias that may occur when many people refuse to test.