DEVELOPMENT OF BAYESIAN SPATIAL MIXTURE MODELS FOR ANALYSIS OF CORRELATED OUTCOMES OF MATERNAL AND CHILD HEALTH

Abstract

Joint modeling instead of seperate modeling of correlated health outcomes have become popular in recent times with the view to improving parameter estimates and investigating spill-over effects. However, there has not been intensive work in this regard especially when the outcomes are conditionally independent but are correlated by some latent factor, hence the need for more indepth and extensive work in this area. Many researchers have either considered such health outcomes separately or jointly but not considering the misalignment that arises from combining such health outcomes either due to having different distributions, scale of measurement or emanating from different locations. Literatures have shown that ignoring the misalignment in such health outcomes will result in bias in both the point estimates and uncertainty. This will ultimately lead to inaccurate predictions of mother and child health outcomes. This research therefore is aimed at developing joint spatial mixture model with correlated error terms to analyse multiple health outcomes and specifically addressing the issue of misalignment. The key objectives include developing joint spatial models for pairs of mother and child health outcomes with different distributions, evaluate the performance of the joint models with respect to the seperate models, estimate the spatial variabilities of the models, and determine the driving factors and spatial patterns of the health outcomes. Predictions about the responses of respondents were also attempted. Using data from the Nigeria Demographic and Health Survey 2013 and 2018, we modelled the spatial distributions of the correlation between antenatal care utilization and sufficient knowledge of mother to child transmission (MTCT) of HIV and its prevention as well as ANC4+ attendance and under-five child stunting (ST5-) among pregnant women in Nigeria. Gaussian Markov Random Field (GMRF) and the Stochastic Partial Differential Equation (SPDE) methods were used to fit single and joint health outcome models on the areal and pointreferenced data respectively. The various variables, fixed, non-linear and random, were jointly analysed using the instrumentality of the structured additive regression modeling technique. Bayesian methods were utilized with appropriate prior distributions introduced. In all, a total of twelve spatial models were finally fitted and discussed, comprising eight separate and four joint full models. The predictability of the spatial models were validated using different validation techniques. The Integrated Nested Laplace Approximation (INLA), one of the most recent and computationally efficient Bayesian estimation methods developed over the last three decades, was used to estimate the parameters of the models. This was made possible with the availability of an R package (R-INLA). The INLA serves as a welcome alternative to the common use Markov Chain Monte Carlo (MCMC) methods. The results revealed that the joint models performed better than the separate models in this study and should be preferred. The risk factors that determine the separate and joint health outcomes were identified. The results also revealed significant spill-over in the fixed, nonlinear and spatial effects when the pairs of responses were jointly modeled. For example, by jointly modeling the correlation between ANC utilization and MTCT of HIV knowledge, the importance of television, radio, being a Yoruba woman, wealth index and urban residence in ANC utilization when considered separately were significantly reduced. The knowledge of MTCT had a spillover effect on ANC utilization through the fixed variables. That is, what seemed to be impacted by the variables when ANC was considered alone can be partially contributed to a respondent’s exposure to the knowledge of MTCT and its prevention. In the same vein, by jointly modeling the correlation between under-five child stunting and ANC4+, the importance of television, newspaper, birth order 23 and 4, mother’s education, economic advantage, female gender, exclusive breastfeeding, and women employment in preventing ST5- when considered separately were significantly reduced, showing that what seemed to be impacted by these variables can be partially contributed to one’s attendance at ANC at least four times. Furthermore, ANC4+ and knowledge of MTCT were found to share the same spatial patterns which implied that they were significantly spatially dependent. Different spatial patterns and indirect relationship were however followed by ANC4+ and under-five child stunting across Nigeria. The spatial variabilities of the joint models were also found to be lower than those of the separate models. It is therefore recommended that policy decisions and intervention strategies by stakeholders in the area of mother and child health care should be based on or tailored towards estimates that emanate from joint consideration of at least pairs of health outcomes for better understanding and consequent optimum allocation of available scarce resources.