title: On the assumption of bivariate normality in selection models: a Copula approach applied to estimating HIV prevalence.
abstract: BACKGROUND
  Heckman-type selection models have been used to control HIV prevalence estimates for selection bias when participation in HIV testing and HIV status are associated after controlling for observed variables. These models typically rely on the strong assumption that the error terms in the participation and the outcome equations that comprise the model are distributed as bivariate normal.
  
  
  METHODS
  We introduce a novel approach for relaxing the bivariate normality assumption in selection models using copula functions. We apply this method to estimating HIV prevalence and new confidence intervals (CI) in the 2007 Zambia Demographic and Health Survey (DHS) by using interviewer identity as the selection variable that predicts participation (consent to test) but not the outcome (HIV status).
  
  
  RESULTS
  We show in a simulation study that selection models can generate biased results when the bivariate normality assumption is violated. In the 2007 Zambia DHS, HIV prevalence estimates are similar irrespective of the structure of the association assumed between participation and outcome. For men, we estimate a population HIV prevalence of 21% (95% CI = 16%-25%) compared with 12% (11%-13%) among those who consented to be tested; for women, the corresponding figures are 19% (13%-24%) and 16% (15%-17%).
  
  
  CONCLUSIONS
  Copula approaches to Heckman-type selection models are a useful addition to the methodological toolkit of HIV epidemiology and of epidemiology in general. We develop the use of this approach to systematically evaluate the robustness of HIV prevalence estimates based on selection models, both empirically and in a simulation study.
authors: From the aHarvard Center for Population and Development Studies, Cambridge, MA; bDepartment of Global Health and Population, Harvard School of Public Health, Boston, MA; cWellcome Trust Africa Centre for Health and Population Studies, University of KwaZulu-Natal, Mtubatuba, South Africa; dDepartment of Statistical Science, University College London, London, UK; and eDepartment of Economics, Mathematics and Statistics, Birkbeck, University of London, London, UK.
authors: Mark E
authors: ME
authors: McGovern
authors: Till
authors: T
authors: Bärnighausen
authors: Giampiero
authors: G
authors: Marra
authors: Rosalba
authors: R
authors: Radice
mesh_terms: D000328:Adult; D003198:Computer Simulation; D005260:Female; D015658:HIV Infections / Q000175:diagnosis / Q000453:epidemiology*; D006801:Humans; D008297:Male; D015233:Models, Statistical; D016011:Normal Distribution; D015995:Prevalence; D015983:Selection Bias; D015024:Zambia / Q000453:epidemiology
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