Bayesian INGARCHX Modeling for Forecasting Necrotizing Fasciitis in Thailand With Cellulitis and Seasonal Effects

ABSTRACT This study investigates the temporal relationship between necrotizing fasciitis (NF) and cellulitis using a Bayesian time series forecasting framework. Weekly NF case counts from Mahasarakham Hospital, Thailand, were modeled via integer‐valued generalized autoregressive conditional heteroskedasticity models with exogenous covariates (INGARCHX) to capture serial dependence and improve predictive accuracy. To accommodate overdispersion and serial dependence in the count data, both Poisson and negative binomial specifications were considered. The models included lagged counts of cellulitis cases and seasonal indicators as external covariates, with parameters estimated using Markov chain Monte Carlo methods to enable comprehensive probabilistic inference. Results reveal a significant lagged association between cellulitis incidence and NF risk. The negative binomial INGARCHX model consistently outperformed alternative specifications, especially during periods of increased variability. Posterior predictive assessments and diagnostic checks confirm the model's adequacy in capturing key temporal dynamics and dispersion patterns. These findings underscore the utility of cellulitis incidence as a leading indicator for NF outbreaks and demonstrate the broader applicability of the NB‐INGARCHX framework for epidemiological forecasting.