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Refusal Bias in the Estimation of HIV Prevalence


In 2007, UNAIDS corrected estimates of global HIV prevalence downward from 40 million to 33 million based on a methodological shift from sentinel surveillance to population-based surveys. Since then, population-based surveys are considered the gold standard for estimating HIV prevalence. However, prevalence rates based on representative surveys may be biased because of nonresponse. This article investigates one potential source of nonresponse bias: refusal to participate in the HIV test. We use the identity of randomly assigned interviewers to identify the participation effect and estimate HIV prevalence rates corrected for unobservable characteristics with a Heckman selection model. The analysis is based on a survey of 1,992 individuals in urban Namibia, which included an HIV test. We find that the bias resulting from refusal is not significant for the overall sample. However, a detailed analysis using kernel density estimates shows that the bias is substantial for the younger and the poorer population. Nonparticipants in these subsamples are estimated to be three times more likely to be HIV-positive than participants. The difference is particularly pronounced for women. Prevalence rates that ignore this selection effect may be seriously biased for specific target groups, leading to misallocation of resources for prevention and treatment.

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Fig. 1
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  1. Information about DHS+ surveys is available online (

  2. In repeat population-based surveys, a fourth source of bias may arise: attrition (Obare 2010). A fifth bias inherent to household surveys is the sampling frame when only people residing in households are included.

  3. Estimates are from authors’ own calculations.

  4. The test results of 384 individuals were dropped from the sample because of fraudulent practices by one of the interviewers (Janssens et al. 2010). Because the interviewers were randomly assigned to households, this should not affect the results.

  5. The wealth index is calculated based on the first factor loadings of a principal component analysis of 28 assets and 7 dwelling characteristics, with missing values imputed.

  6. This can be calculated with the margins command in STATA version 11.0.

  7. The Staiger and Stock (1997) rule of thumb to assess the strength of instrumental variables is not applicable in the case of a Heckman model. Instead, we calculate the likelihood ratio for the first stage with and without instruments. This shows that including the instrumental variables substantially increases the ratio from 187 to 298.

  8. See Online Resource 1, sections 3 and 4, for the detailed regression results of the probit and Heckman model, respectively.

  9. Another way of correctly calculating standard errors is by bootstrapping. The bootstrapped confidence intervals are not reported in the table because in about 10 % of the bootstrap iterations, the probit and Heckman models do not converge and it cannot be ruled out that nonconvergence is selective. The other 90 % yield intervals that are very similar to the intervals calculated with the delta method.

  10. Online Resource 1, section 5, compares observed with predicted prevalence rates by stratum of probit predicted HIV prevalence, which is presumably less sensitive to probit misspecification. The results show that the probit predictions are very similar to the observed rates in all strata. The Heckman predictions are increasingly higher than the probit estimates for each consecutive stratum, suggesting that the bias in the population prevalence increases with the propensity of HIV-infection. However, refusal is most common in the first stratum with the lowest HIV infection rate. The section A Detailed Look at Nonparticipants explores the characteristics of nonparticipants in more detail.

  11. Although the estimates are large and negative at –.329, –.198, and –.622, respectively, for all individuals and males and females, they are not significant at the 5 % level. For females, the p value is .061. A negative sign of indicates that individuals less likely to participate are more likely to be HIV-positive.

  12. Attrition rates, which may be selective with respect to HIV status (Obare 2010), were very similar for HIV-negative versus HIV-positive participants: 36 % versus 35 %.

  13. Section 6 of Online Resource 1 discusses how increases in sample size affect confidence intervals.

  14. The subgroups overlap because the Heckman model does not converge for our data when taking a strict boundary between subgroups.

  15. For comparison, Online Resource 1, section 7, shows the same plots including the densities from the probit model. The Heckman model shifts the kernel to the right compared with the probit model for the young and poor, but not the old and nonpoor subsamples.


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This work was supported by the Dutch Ministry of Development Cooperation (Grant No. 13298) and the Dutch Organization of Scientific Research (NWO) (Rubicon Grant No. 446-08-004 to W.J.). The survey data used in this article were collected by the University of Namibia (UNAM) and the National Institute of Population (NIP), with technical assistance from PharmAccess International and the Amsterdam Institute of International Development. Special thanks are due to Ingrid De Beer, Gert van Rooy, and Christa Schier for organizing the fieldwork and providing detailed insights into the data collection process. We are also grateful to Chris Elbers, Angus Deaton, and Aico van Vuren for helpful discussions on technical aspects of the estimation. We would like to thank participants at the 2007 AIID workshop on “The Economic Consequences of HIV/AIDS,” the 2008 Tinbergen Annual Conference in Amsterdam, the 2009 CSAE Conference in Oxford, and the 2012 Scientific EUDN Conference in Paris for useful comments and suggestions. Finally, we thank the editors of this journal and three anonymous reviewers for the positive and constructive feedback on earlier versions of this article.

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Correspondence to Wendy Janssens.

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Janssens, W., van der Gaag, J., Rinke de Wit, T.F. et al. Refusal Bias in the Estimation of HIV Prevalence. Demography 51, 1131–1157 (2014).

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  • HIV prevalence
  • Population-based survey
  • Refusal bias
  • Heckman selection model
  • Namibia