A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses

ABSTRACT

Estimates of HIV prevalence are important for policy 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 that accounts for nonignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogenous 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 parameterization 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. Supplementary materials for this article are available online.

KEYWORDS:

• Heckman-type selection model
• HIV
• Penalized regression spline
• Selection bias
• Simultaneous equation model
• Spatial dependence

Supplementary Materials

The supplementary materials contain the justification for using a new parametrization of the smoothing approach, some software details, an example of three dependence scenarios, details on the settings used for the simulation study, additional empirical results drawn from the application study, and a table of letters and symbols used in the paper.

Acknowledgments

The authors are indebted to the editor, associate editor, and two anonymous reviewers for many detailed and well thought out suggestions that helped to clarify the contribution and the presentation of the article.

Funding

Mark E. McGovern and Till Bärnighausen acknowledge funding from the Program on the Global Demography of Aging, which receives funding from the National Institute on Aging, Grant No. 1 P30 AG024409-09. Till Bärnighausen also acknowledges funding from the Wellcome Trust, and Eunice Kennedy Shriver National Institute of Child Health and Human Development and National Institute of Allergy and Infectious Diseases of NIH (R01-HD084233, R01-AI124389, and R01-AI112339). Simon N. Wood acknowledges funding from EPSRC (EP/K005251/1).