Borrowing strength across space in distributed lag non-linear models: a geographically weighted approach

Abstract Distributed lag non-linear models (DLNMs) are widely used to estimate exposure-response associations across geographic areas. Because units with few events can give unstable estimates in independent models, spatial methods are designed to borrow strength from nearby units. We propose a geographically weighted DLNM (GW-DLNM), in which each unit’s first-stage estimates are shrunk toward a local mean formed from its neighbors, weighted by distance and precision. We compared GW-DLNM with Pooled, Two-stage, Tensor, and spatial Bayesian (SB-DLNM) approaches in 1,600 simulated scenarios with 48,000 replicates. The design varied region shape, number and size inequality of units, spatial pattern and magnitude of heterogeneity, exposure-response and lag-response shapes, effect size, and event rate. Accuracy depended mainly on effect heterogeneity and event rate. Pooled was most accurate when all units shared one effect. When the effect varied, SB-DLNM had the lowest median error, and GW-DLNM was most often the most accurate method under high heterogeneity. The first-stage heterogeneity statistic I², together with event rate, indicated which method was likely to be most accurate. An application to temperature and mortality in the 853 municipalities of Minas Gerais, Brazil, illustrates the methods. These results provide practical guidance for choosing among methods when exposure-response associations vary geographically.