Extensions of the distributed lag non-linear model (DLNM) to account for cumulative mortality

The effects of meteorological factors on health outcomes have gained popularity due to climate change, resulting in a general rise in temperature and abnormal climatic extremes. Instead of the conventional cross-sectional analysis that focuses on the association between a predictor and the single dependent variable, the distributed lag non-linear model (DLNM) has been widely adopted to examine the effect of multiple lag environmental factors health outcome. We propose several novel strategies to model mortality with the effects of distributed lag temperature measures and the delayed effect of mortality. Several attempts are derived by various statistical concepts, such as summation, autoregressive, principal component analysis, baseline adjustment, and modeling the offset in the DLNM. Five strategies are evaluated by simulation studies based on permutation techniques. The longitudinal climate and daily mortality data in Taipei, Taiwan, from 2012 to 2016 were implemented to generate the null distribution. According to simulation results, only one strategy, named MVDLNM, could yield valid type I errors, while the other four strategies demonstrated much more inflated type I errors. With a real-life application, the MVDLNM that incorporates both the current and lag mortalities revealed a more significant association than the conventional model that only fits the current mortality. The results suggest that, in public health or environmental research, not only the exposure may post a delayed effect but also the outcome of interest could provide the lag association signals. The joint modeling of the lag exposure and the delayed outcome enhances the power to discover such a complex association structure. The new approach MVDLNM models lag outcomes within 10 days and lag exposures up to 1 month and provide valid results.