title: Adjusting HIV prevalence estimates for non-participation: an application to demographic surveillance.
abstract: BACKGROUND
  HIV testing is a cornerstone of efforts to combat the HIV epidemic, and testing conducted as part of surveillance provides invaluable data on the spread of infection and the effectiveness of campaigns to reduce the transmission of HIV. However, participation in HIV testing can be low, and if respondents systematically select not to be tested because they know or suspect they are HIV positive (and fear disclosure), standard approaches to deal with missing data will fail to remove selection bias. We implemented Heckman-type selection models, which can be used to adjust for missing data that are not missing at random, and established the extent of selection bias in a population-based HIV survey in an HIV hyperendemic community in rural South Africa.
  
  
  METHODS
  We used data from a population-based HIV survey carried out in 2009 in rural KwaZulu-Natal, South Africa. In this survey, 5565 women (35%) and 2567 men (27%) provided blood for an HIV test. We accounted for missing data using interviewer identity as a selection variable which predicted consent to HIV testing but was unlikely to be independently associated with HIV status. Our approach involved using this selection variable to examine the HIV status of residents who would ordinarily refuse to test, except that they were allocated a persuasive interviewer. Our copula model allows for flexibility when modelling the dependence structure between HIV survey participation and HIV status.
  
  
  RESULTS
  For women, our selection model generated an HIV prevalence estimate of 33% (95% CI 27-40) for all people eligible to consent to HIV testing in the survey. This estimate is higher than the estimate of 24% generated when only information from respondents who participated in testing is used in the analysis, and the estimate of 27% when imputation analysis is used to predict missing data on HIV status. For men, we found an HIV prevalence of 25% (95% CI 15-35) using the selection model, compared to 16% among those who participated in testing, and 18% estimated with imputation. We provide new confidence intervals that correct for the fact that the relationship between testing and HIV status is unknown and requires estimation.
  
  
  CONCLUSIONS
  We confirm the feasibility and value of adopting selection models to account for missing data in population-based HIV surveys and surveillance systems. Elements of survey design, such as interviewer identity, present the opportunity to adopt this approach in routine applications. Where non-participation is high, true confidence intervals are much wider than those generated by standard approaches to dealing with missing data suggest.
authors.affiliation: Queen's Management School, Queen's University Belfast, Belfast, Northern Ireland, UK.|UKCRC Centre of Excellence for Public Health (NI), Belfast, UK.|Wellcome Trust Africa Centre for Health and Population Studies, University of KwaZulu-Natal, KwaZulu-Natal, South Africa; m.mcgovern@qub.ac.uk.
authors.forename: Mark E
authors.initials: ME
authors.lastname: McGovern
authors.affiliation: Department of Statistical Science, University College London, London, UK.
authors.forename: Giampiero
authors.initials: G
authors.lastname: Marra
authors.affiliation: Department of Economics, Mathematics and Statistics, Birkbeck, University of London, London, UK.
authors.forename: Rosalba
authors.initials: R
authors.lastname: Radice
authors.affiliation: Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA, USA.
authors.forename: David
authors.initials: D
authors.lastname: Canning
authors.affiliation: Wellcome Trust Africa Centre for Health and Population Studies, University of KwaZulu-Natal, KwaZulu-Natal, South Africa.|Faculty of Medicine, University of Southampton, Southampton, UK.
authors.forename: Marie-Louise
authors.initials: ML
authors.lastname: Newell
authors.affiliation: Wellcome Trust Africa Centre for Health and Population Studies, University of KwaZulu-Natal, KwaZulu-Natal, South Africa.|Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA, USA.
authors.forename: Till
authors.initials: T
authors.lastname: Bärnighausen
mesh_terms: D005260:Female; D015658:HIV Infections / Q000175:diagnosis / Q000453:epidemiology*; D006801:Humans; D008297:Male; D015995:Prevalence; D015983:Selection Bias; D013019:South Africa / Q000453:epidemiology
keywords: HIV prevalence; Heckman-type selection models; demographic surveillance; missing data; non-participation; selection bias