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

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.

Highlights

Public Health data on mortality have been growing increasingly rich as more accurate information on “who”, “where” and “when” becomes available
We modelled the spatial random effects using the Stochastic Partial Differential Equations (SPDEs)
Banerjee et al (2004) give brief summaries of these: subsampling, spectral, lattice, dimension reduction and course fine coupling methods (Banerjee et al, 2004, 2008; Banerjee and Carlin, 2003; Kamman and Wand, 2001; Johnson et al, 1990; French et al, 2002). These techniques attempt to reduce the dimension of the Gaussian fields (GF) by selecting a “representative” sub-sample or fixing some parameters or changing the scale from continuous to discrete with the aim of reducing the computational burden in running Markov chain Monte Carlo (MCMC) simulations. We addressed this problem using techniques proposed by Rue and Held (2005) who changed the continuous scale GF to a discrete scale Gaussian Markov Random Field (GMRF), for the Matérn family of covariance structures (Rue and Held, 2005)

Summary

Introduction

Public Health data on mortality have been growing increasingly rich as more accurate information on “who”, “where” and “when” becomes available. These form hierarchical (multilevel) data structures which are correlated such that person-level (“who”) information can be repeated, geo-statistical (“where”) data often has spatial correlation and temporal (“when”) data can be autocorrelated. As a result of this the statistical significance is overestimated leading to erroneous results and subsequent inferences (Cressie, 1993) This defeats the main goal in epidemiological analysis, which is to identify and quantify correctly any exposures, behaviours and characteristics that may modify a population’s or individuals risk and use these to implement more appropriate interventions (Rose, 2001). In modelling hierarchical data we can take into account spatial and temporal correlations by introducing in the model spatiotemporal random effects. As the number of geo-locations increases, MCMC computations of a dense GF m × m spatial correlation matrix become

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