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

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.

Self-refraction, ready-made glasses and quality of life among rural myopic Chinese children: a non-inferiority randomized trial.

PURPOSE: To study, for the first time, the effect of wearing ready-made glasses and glasses with power determined by self-refraction on children's quality of life. METHODS: This is a randomized, double-masked non-inferiority trial. Children in grades 7 and 8 (age 12-15 years) in nine Chinese secondary schools, with presenting visual acuity (VA) ≤6/12 improved with refraction to ≥6/7.5 bilaterally, refractive error ≤-1.0 D and <2.0 D of anisometropia and astigmatism bilaterally, were randomized to receive ready-made spectacles (RM) or identical-appearing spectacles with power determined by: subjective cycloplegic retinoscopy by a university optometrist (U), a rural refractionist (R) or non-cycloplegic self-refraction (SR). Main study outcome was global score on the National Eye Institute Refractive Error Quality of Life-42 (NEI-RQL-42) after 2 months of wearing study glasses, comparing other groups with the U group, adjusting for baseline score. RESULTS: Only one child (0.18%) was excluded for anisometropia or astigmatism. A total of 426 eligible subjects (mean age 14.2 years, 84.5% without glasses at baseline) were allocated to U [103 (24.2%)], RM [113 (26.5%)], R [108 (25.4%)] and SR [102 (23.9%)] groups, respectively. Baseline and endline score data were available for 398 (93.4%) of subjects. In multiple regression models adjusting for baseline score, older age (p = 0.003) and baseline spectacle wear (p = 0.016), but not study group assignment, were significantly associated with lower final score. CONCLUSION: Quality of life wearing ready-mades or glasses based on self-refraction did not differ from that with cycloplegic refraction by an experienced optometrist in this non-inferiority trial.