Multilevel modelling of child mortality : Gibbs sampling versus other approaches

Prevost, Andrew Toby (1996) Multilevel modelling of child mortality : Gibbs sampling versus other approaches. University of Southampton, Doctoral Thesis.

Abstract

An association between birth intervals and child mortality is widely observed. Plausible mechanisms are maternal depletion and sibling competition. Causality is important in determining the effectiveness of future birth spacing programmes. An objective of this thesis is the estimation of birth interval effects net of potential confounders. Clustering of details in families is also widely observed. This has implications for inference based on correlated sibling data, such as that collected in the hierarchically structured Tunisian Demographic and Health Survey. An objective of this thesis is to use multilevel models to account for and quantify sibling correlation and the related maternal heterogeneity in child mortality.

Multilevel models for binary responses require approximation to circumvent intractable integrations. The accuracy of Taylor series expansions is seen to affect consistency of estimates and convergence in a quasilikelihood implementation. This arises from the presence of many small clusters with a rare underlying response. The efficiency of the Gibbs sampling method is also affected by the weak identifiability of variance components. Different parameterisations result in more than a one order of magnitude reduction in the time required for obtaining equally accurate estimates. Gaussian quadrature implementations are adopted to show that covariate effects are robust to departures from symmetry in the random effects distribution. Gaussian quadrature and Gibbs sampling methods are used to include information relevant to maternal heterogeneity from the traditionally excluded first order births. Gibbs sampling is then used to link regressions from the three periods of childhood in order to obtain a more reliable quantification of maternal heterogeneity. Such simultaneous estimation is then extended to include a third hierarchical level.

There is considerable heterogeneity in Tunisian child mortality at the maternal and regional level. There is large unexplained child mortality in Kairouan. The Gibbs sampling approach is effective in making model based predictions. The spacing of births by an extra three months is associated with a 15% reduction in early child mortality. Birth interval effects are strong during infancy but not in toddlers, and this suggests the presence of maternal depletion. Socio-economic and seasonal effects are also important in the postneonatal period of childhood.

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