FLEXIBLE ACCELERATED FAILURE TIME MODEL WITH SPATIAL DEPENDENCY: APPLICATION TO UNDER-FIVE MORTALITY RATE

Abstract

Under-five mortality (U5M) data often exhibit complex spatial dependencies and nonlinear
temporal patterns that conventional survival models may fail to capture adequately. This study
provides an extension to Bayesian Accelerated Failure Time (AFT) model that simultaneously
accounts for nonlinear (NL) effects of continuous covariate, time-varying acceleration factors,
and spatial heterogeneity in child survival analysis. Using data from the 2018 Nigeria
Demographic and Health Survey (NDHS), the study extended the Weibull AFT model by
incorporating B-splines for nonlinear effects of continuous covariate, random-walk time-varying
coefficients, and intrinsic conditional autoregressive (ICAR) spatial random effects. Model
performance was evaluated using Deviance Information Criterion (DIC) and Watanabe-Akaike
Information Criterion (WAIC). Results demonstrate that the extended model (flexible spatial AFT
model) significantly outperforms traditional parametric specifications. The findings revealed
breastfeeding as the strongest protective factor (time ratio [TR]=5.95, 95% CI: 5.65-6.25),
followed by complete antenatal care utilization (TR=2.14, 95% CI: 1.86-2.46) and longer birth
intervals (TR=1.17, 95% CI: 1.12-1.23). Spatial analysis identified significant geographic
clustering, with northern Nigerian states showing higher survival times than southern regions.
The time-varying effects revealed that urban residence advantages diminish as children age
while breastfeeding protection remains stable. This study provides a methodological
advancement in survival analysis by simultaneously integrating NL effect of continuous
covariates, non-constant acceleration factor and spatial effects within the AFT framework,
offering policymakers a refined tool for targeted U5M interventions. The approach is broadly
applicable to clustered survival data in global health and demographic research.