Inferring Zambia's HIV prevalence from a selected sample. Issue 39 (20th August 2020) - Chan, Jessica Ying; Cook, Jonathan A.
ABSTRACT: This paper estimates HIV prevalence in Zambia from survey data that are subject to sample selection: some surveyed individuals do not consent to take an HIV test. We introduce semiparametric estimators that incorporate recent developments in machine learning. The semiparametric estimators perform well in Monte Carlo experiments and obtain narrower confidence intervals than a fully parametric estimator when the model is misspecified. Our semiparametric estimates of the HIV rate are roughly equal to the rate in the selected sample. In contrast, recent parametric estimates find a higher rate – implying that some form of sample-selection correction is warranted. Further, parametric estimates find a 14% decline in Zambia's HIV prevalence from 2007 to 2014, whereas semiparametric estimates find that the HIV rate was relatively stable over this time period.