Bayesian analysis of zero inflated spatiotemporal HIV/TB child mortality data through the INLA and SPDE approaches: Applied to data observed between 1992 and 2010 in rural North East South Africa

Eustasius Musenge; Tobias Freeman Chirwa; Kathleen Kahn; Penelope Vounatsou

doi:10.1016/j.jag.2012.04.001

Bayesian analysis of zero inflated spatiotemporal HIV/TB child mortality data through the INLA and SPDE approaches: Applied to data observed between 1992 and 2010 in rural North East South Africa

Int J Appl Earth Obs Geoinf. 2013 Jun;22(100):86-98. doi: 10.1016/j.jag.2012.04.001.

Authors

Eustasius Musenge¹, Tobias Freeman Chirwa², Kathleen Kahn³, Penelope Vounatsou⁴

Affiliations

¹ MRC/Wits Rural Public Health & Health Transitions Research Unit, School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa ; Biostatistics and Epidemiology Division, School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa.
² Biostatistics and Epidemiology Division, School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa.
³ MRC/Wits Rural Public Health & Health Transitions Research Unit, School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa ; Centre for Global Health Research, Umeå University, Umeå, Sweden ; INDEPTH Network, Accra, Ghana.
⁴ Swiss Tropical and Public Health Institute, Basel, Switzerland.

Abstract

Longitudinal mortality data with few deaths usually have problems of zero-inflation. This paper presents and applies two Bayesian models which cater for zero-inflation, spatial and temporal random effects. To reduce the computational burden experienced when a large number of geo-locations are treated as a Gaussian field (GF) we transformed the field to a Gaussian Markov Random Fields (GMRF) by triangulation. We then modelled the spatial random effects using the Stochastic Partial Differential Equations (SPDEs). Inference was done using a computationally efficient alternative to Markov chain Monte Carlo (MCMC) called Integrated Nested Laplace Approximation (INLA) suited for GMRF. The models were applied to data from 71,057 children aged 0 to under 10 years from rural north-east South Africa living in 15,703 households over the years 1992-2010. We found protective effects on HIV/TB mortality due to greater birth weight, older age and more antenatal clinic visits during pregnancy (adjusted RR (95% CI)): 0.73(0.53;0.99), 0.18(0.14;0.22) and 0.96(0.94;0.97) respectively. Therefore childhood HIV/TB mortality could be reduced if mothers are better catered for during pregnancy as this can reduce mother-to-child transmissions and contribute to improved birth weights. The INLA and SPDE approaches are computationally good alternatives in modelling large multilevel spatiotemporal GMRF data structures.

Keywords: Agincourt South Africa; Big “N”; GMRF; HIV/TB mortality; INLA SPDE; Spatiotemporal; Zero inflated.