HIV ESTIMATION USING POPULATION-BASED SURVEYS WITH NON-RESPONSE: A PARTIAL IDENTIFICATION APPROACH*

Background HIV estimation using data from the Demographic and Health Surveys (DHS) is limited by the presence of non-response and test refusals. Conventional adjustments such as imputation require the data to be missing at random. Methods that use instrumental variables allow the possibility that prevalence is different between the respondents and non-respondents, but their performance depends critically on the validity of the instrument. Methods Using Manski’s partial identification approach, we form instrumental variable bounds for HIV prevalence from a pool of candidate instruments. Our method does not require all candidate instruments to be valid. We use a simulation study to evaluate our method and compare it against its competitors. We illustrate the proposed method using DHS data from Zambia. Results Our simulations show that imputation leads to seriously biased results even under mild violations of non-random missingness. Using worst case identification bounds that do not make assumptions about the non-response mechanism is robust but not informative. By taking the union of instrumental variable bounds balances informativeness of the bounds and robustness to inclusion of some invalid instruments. Conclusions Non-response and refusals are ubiquitous in population based HIV data such as those collected under the DHS. Partial identification bounds provide a robust solution to HIV prevalence estimation without strong assumptions. Union bounds are significantly more informative than the worst case bounds, without sacrificing credibility. Key messages Partial identification bounds are useful for HIV estimation when data are subject to non-response bias Instrumental variables can narrow the width of the bounds but validity of an instrument variable is an untestable hypothesis This paper proposes pooling candidate instruments and creating union bounds from the pool Our approach significantly reduces the width of the worst case bounds without sacrificing robustness