Bayesian inference in time-varying additive hazards models with applications to disease mapping

Area of Science:

• Environmental Health
• Biostatistics
• Spatial Epidemiology

Background:

• Disease mapping and environmental health studies often analyze time-to-event data influenced by socio-demographic, behavioral, and environmental factors.
• Spatial variations in hazard functions are common, where proximity influences risk, often addressed by Cox's Proportional Hazards (PH) models with spatial frailties.
• The PH assumption of constant covariate effects over time is frequently unrealistic in long-term studies, limiting its applicability.

Purpose of the Study:

• To propose a flexible semiparametric additive hazards (AH) model incorporating spatial frailties.
• To develop a model that accommodates time-varying regression coefficients and spatial frailties, overcoming the limitations of the PH assumption.
• To provide a Bayesian estimation framework using Markov chain Monte Carlo (MCMC) techniques for the proposed model.

Main Methods:

• Development of a semiparametric additive hazards model with time-varying spatial frailties and regression coefficients.
• Bayesian estimation framework utilizing advanced posterior sampling strategies through MCMC techniques.
• Application of the model to prostate cancer survival data from Louisiana to demonstrate its utility.

Main Results:

• The proposed additive hazards model with spatial frailties effectively relaxes the proportionality assumption of the Cox model.
• The model allows for dynamic estimation of covariate effects and spatial risk variations over time.
• Demonstrated the model's practical advantages using a real-world prostate cancer survival dataset.

Conclusions:

• The flexible additive hazards model with spatial frailties offers a powerful alternative to the Cox PH model for analyzing complex time-to-event data in environmental health and disease mapping.
• The Bayesian MCMC approach provides a robust estimation strategy for this advanced statistical model.
• This methodology enhances the understanding of disease etiology by accounting for time-dependent and spatially correlated risk factors.