Accelerated Failure Time Model with Spatial Dependency and Covariates Interaction Structures: Application to Under-Five Mortality in Nigeria

Abstract

Under-five mortality (U5M) remains a pressing public health concern in Nigeria, 
characterized by persistent regional disparities and influenced by a complex interplay of 
socioeconomic, demographic, and healthcare-related factors. This study extends the Bayesian 
Weibull Accelerated Failure Time (AFT) modeling framework by incorporating spatial 
dependency and covariate interaction structures to better elucidate the determinants of 
U5M across Nigeria. Utilizing nationally representative data from the 2018 Nigeria 
Demographic and Health Survey (NDHS), the study evaluates multiple model specifications, 
including the AFT model with standard covariate interaction structures (SCIS) and logistic
type covariate interaction structures (LTCIS). Spatial clustering at the state level is 
accounted for using Intrinsic Conditional Autoregressive (ICAR) priors. Model comparison 
based on Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion 
(WAIC) indicates that the Weibull AFT model with spatial effects and SCIS structure 
provides the best fit (DIC = 152,058.77; WAIC = 152,049.57), outperforming models without 
spatial or interaction terms. Key findings highlight breastfeeding as the most protective 
factor against U5M (time ratio [TR] = 52.405), with its effect further enhanced among 
children from the richest households (TR up to 3.438). Other significant protective factors 
include longer birth intervals (24–33 months: TR = 1.346; >33 months: TR = 2.435), maternal 
education, and higher household wealth. The spatial analysis uncovers distinct geographic 
disparities, with elevated U5M risks concentrated in several southern states, underscoring 
the role of regional context. This study advances the methodological and substantive 
understanding of child mortality by quantifying both spatial heterogeneity and synergistic 
interactions among key predictors. The findings provide actionable insights for policymakers 
aiming to design geographically and socioeconomically targeted interventions. Moreover, the 
research underscores the value of integrating interaction structures within spatial survival 
models to enhance the precision and relevance of public health analytics.