A penalized distributed-lag non-linear model for modeling the joint delayed effect of two predictors: impact of minimum and maximum temperature on mortality

Distributed lag non-linear models (DLNMs) offer a flexible approach towards modelling time-delayed exposures. They are popular to study the effect of environmental exposure on health outcomes, such as the effect of temperature on mortality. Conventional distributed lag non-linear models typically focus on a single exposure variable, potentially overlooking complex interactions between multiple predictors. In this paper, we propose a distributed lag non-linear model that captures the joint delayed impact of two exposure variables by incorporating their interaction through a tensor basis constructed from univariate P-splines. This model is compared to a model assuming an additive effect of delayed exposures. Our model is used to examine the joint impacts of maximum and minimum temperatures on all-cause mortality in Flanders during summer. The results show that our model provides a flexible strategy towards the analysis of two predictors with interacting time-delayed effects on an outcome of interest. The importance of both maximum and minimum temperatures in explaining variability in mortality is illustrated, and we show that the interaction effect varies across age and gender groups. A spatial risk analysis at the municipality level reveals that mortality is attributed differently to temperature exposure across different areas, due to temperature variations as well as spatial trends in age and gender.