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

Till Bärnighausen, Harvard University 
David Canning, Harvard University 
*Mark E. McGovern, Harvard University 
Joshua Salomon, Harvard University 

Keywords: HIV, H eckman Selection Models, Missing Data, Bayesian Estimation

Estimates of HIV prevalence in developing countries from nationally representative household surveys are considered the “gold standard”. However, consent to test rates are often low. If individuals who are more likely to be HIV positive tend to decline to be tested, ignoring non-response will bias population prevalence estimates. Conventional imputation does not account for this problem, which is particularly relevant in an era of treatment as prevention which will require an increase in the coverage and frequency of HIV testing. Interviewer identity is plausibly correlated with consenting to test, but not HIV status, allowing a Heckman-type correction. We show that a random effects Bayesian estimator is unbiased and consistent. We construct bootstrapped standard errors to correct for uncertainty in the estimation of the relationship between consent to test and HIV status. We produce new estimates and confidence intervals for HIV prevalence among men in Zambia and Ghana. For Zambia we obtain point estimates for HIV prevalence among the group who refused consent of 29%, compared to 12% as estimated by imputation. Previous approaches overstate the precision of point estimates by up to 10 times. For Ghana, we find that conventional methods slightly overstate prevalence. We provide the first practical solution to account for both sampling and parameter uncertainty in the estimation of HIV prevalence confidence intervals. The wide confidence intervals we find point towards a need to improve survey design and execution so as to increase consent rates and reduce the uncertainty induced by selection bias.