A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses

Giampierro Marra, Rosalba Radice, Till Bärnighausen , Simon Wood, Mark E. McGovern

Research output: Contribution to journalArticle (Academic Journal)peer-review

40 Citations (Scopus)
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Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach which accounts for non-ignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogeneous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parametrization of the smoothing criterion which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe and Zambia.
Original languageEnglish
Pages (from-to)484-496
Number of pages13
JournalJournal of the American Statistical Association
Issue number518
Early online date26 Aug 2016
Publication statusPublished - 3 Apr 2017


  • Heckman-Type Selection Model
  • HIV
  • Penalized Regression Spline
  • Selection Bias
  • Simultaneous Equation Model
  • Spatial Dependence


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  • Transfer from Bath

    Wood, S.


    Project: Research

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