Modeling Mortality of Children Under Five in Ethiopia Using Bayesian Approach

This study utilizes a Bayesian Semi-Parametric Discrete-Time Survival Model to analyze the determinants of under-five child mortality in Ethiopia, with a particular emphasis on the time-varying effects of key covariates. Employing data from the 2005 Ethiopia Demographic and Health Survey, encompassing 9,861 children, the research investigates the influence of socio-economic, demographic, and environmental factors on child survival. Given that traditional parametric approaches to modeling child mortality often impose restrictive assumptions and assume constant effects throughout a child's life, this study reveals that several critical factors exhibit distinct age dependencies that conventional methods may overlook. The Bayesian framework facilitates flexible modeling that captures complex non-linear relationships and time-varying effects while providing robust uncertainty quantification. The methodology combines parametric components for fixed effects with non-parametric components for time-varying effects. Diffuse priors are specified for fixed effects parameters, while smoothness priors using cubic P-splines with second-order random walk priors are employed for time-varying covariates. Posterior inference is conducted via Markov Chain Monte Carlo (MCMC) simulation techniques implemented in BayesX software. The results indicate significant socio-economic determinants, including the mother's education level, household economic status, and the partner's education. Demographic factors such as birth order, preceding birth interval, and type of birth emerged as significant predictors. Environmental factors, including residence type and access to protected water sources, substantially influence child survival outcomes. The study identifies three key variables with distinct age-dependent effects: the baseline hazard function, which shows mortality risk is highest immediately after birth, decreases sharply during the first few months, then declines gradually; breastfeeding's protective effect, which varies with the child's age, being strongest in early months and changing as the child develops; and the effect of the mother's age at birth, which exhibits time-varying patterns, with both very young and older mothers associated with higher mortality risks that vary across the child's life. Model comparison using Bayesian criteria confirms that incorporating these time-varying effects significantly improves the model's explanatory power compared to simpler alternatives. This research demonstrates the utility of Bayesian semi-parametric methods for analyzing child mortality and provides insights into how risk factors operate throughout early childhood. The findings have important implications for designing targeted interventions that account for how risk factors change in importance at different developmental stages, potentially leading to more effective strategies for reducing child mortality in Ethiopia and similar contexts.