A Bayesian spline-augmented piecewise exponential model with spatial frailty for under-five mortality in Nigeria

Area of Science:

• Biostatistics
• Spatial epidemiology
• Demography

Background:

• The Cox proportional hazards (PH) model's assumption of constant hazards over time is often violated in child mortality studies.
• Existing piecewise exponential models (PEMs) typically ignore spatial heterogeneity and smooth baseline hazards, limiting their public health application.
• There is a need for a unified Bayesian framework that combines smooth baseline hazards, temporal heterogeneity across intervals, and spatial frailty.

Purpose of the Study:

• To propose and apply a Bayesian spline-augmented piecewise exponential model (PEM) to analyze under-five mortality (U5M) in Nigeria.
• To simultaneously account for smooth baseline hazards, interval-specific temporal heterogeneity, and spatial frailty.
• To compare the performance of nested model specifications using various model selection criteria.

Main Methods:

• A Bayesian spline-augmented PEM was formulated using integrated nested Laplace approximation (INLA) and a Poisson likelihood.
• The model incorporated a cubic-spline-smoothed baseline hazard, interval-specific Gaussian random effects, and an intrinsic conditional autoregressive (ICAR) spatial frailty prior.
• The model was applied to U5M data from the 2024 Nigeria Demographic and Health Survey (NDHS), comparing five nested specifications.

Main Results:

• The global test for the PH assumption was significant (χ² = 898.66, p < 2 x 10⁻¹⁶), confirming the need for flexible models.
• The full spline-interval-spatial model demonstrated the best fit and calibration across different sample sizes.
• Key determinants of U5M included twin birth, breastfeeding status, and term delivery, with elevated risks in North West and North East regions; residual spatial clustering was noted in these zones.

Conclusions:

• Jointly modeling temporal and spatial heterogeneity provides the best-fitting and calibrated model for U5M analysis.
• The Poisson-INLA formulation offers a computationally efficient alternative to MCMC for large demographic datasets.
• Findings underscore the need for integrated interventions addressing identified determinants and structural vulnerabilities in Nigeria's northern regions.