Spatially varying coefficient generalized distributed lag models for binary response with MCEM estimation

The adverse health effects of environmental exposures often manifest after a time delay. Distributed lag models (DLMs) are well-suited for modeling these delayed effects and play a central role in identifying critical exposure windows in environmental epidemiology. However, traditional DLMs frequently fail to account for potential spatial dependence and spatial non-stationarity, limiting their accuracy and generalizability across diverse geographical contexts. To address this gap, we propose a spatially varying coefficient generalized distributed lag model (SVCGDLM) that integrates spatial heterogeneity directly into the DLM framework. To estimate model parameters, we develop an efficient Monte Carlo Expectation–Maximization (MCEM) algorithm employing Pólya-Gamma data augmentation and Gibbs sampling to approximate the conditional expectations in the E-step. Through a comprehensive simulation study, we show that the proposed model significantly outperforms standard generalized linear models (GLMs), generalized geographically weighted regression (GGWR), and Generalized Linear Mixed Model using the INLA Approximation (GLMM-INLA) in terms of parameter estimation accuracy and predictive power. Finally, we apply our model to a real-world dataset from Mashhad, Iran, to estimate the spatially varying association between short-term exposure to PM 2.5 and cardiovascular mortality.