Bayesian negative binomial modelling of spatial and temporal patterns of road traffic deaths in Ghana

Abstract Road traffic fatalities constitute a critical and preventable public health burden in Ghana, yet granular subnational analyses of monthly mortality patterns across the country’s sixteen administrative regions remain sparse. This study uses a Bayesian spatio-temporal negative binomial (NB) model to analyse monthly road traffic death counts across sixteen Ghanaian regions from January 2019 to December 2022, disaggregated by vehicle type (commercial, private, and cycle). The model decomposes the expected death count into a global intercept, fixed effects for vehicle type, accident counts entered as a log-transformed covariate rather than an offset, and temporal trend, together with region-specific spatial random effects (u i ) and year-level temporal random effects (v t ). Overdispersion (variance-to-mean ratio = 18.6) is explicitly accommodated by the NB distribution. Posterior inference was conducted using the no-U-turn sampler (NUTS) implemented in brms (version 2.21) under R 4.5, with four chains of 2000 iterations each (1000 warm-up), target acceptance rate δ = 0.90, and random seed 2024. Spatial random effects were specified as independent hierarchical Normal priors, not CAR/BYM priors, with a HalfNormal(0, 1.5) hyperprior on the regional standard deviation. The Bayesian NB model achieved superior fit (LOO-CV ELPD = − 2381.4; AIC = 4646; BIC = 4739 reported for comparison) relative to the competing count-data specifications. The posterior mean for the global intercept was β 0 = 2.070 (SD = 0.339; 94% HDI: 1.458, 2.677), corresponding to a baseline expected monthly death count of approximately 7.9. Substantial spatial heterogeneity was confirmed (σ_region = 1.139; 94% HDI: 0.786, 1.574), with Greater Accra and Ashanti exhibiting the largest positive spatial random effects (both u i = 1.699). A statistically significant negative monthly trend (β m = − 0.084; 94% HDI: − 0.160, − 0.013) was identified, while the annual temporal trend remained uncertain (β t = 0.043; 94% HDI: − 0.325, 0.361; HDI includes zero). Year-level random effects were small, and their credible intervals broadly included zero, indicating modest inter-annual variation beyond the linear trend. No divergent transitions were detected; all $${\hat{\text{R}}}$$ values were ≤ 1.01, and bulk ESS was > 350. Marked regional heterogeneity and vehicle-type-specific mortality patterns underscore the need for spatially differentiated road safety interventions.