Numerous studies have reported that the association between ambient temperature and human health may vary over time. However, most studies simply divide the time-series dataset into subsets of different time periods, which may not properly capture the temporal change of the temperature-health association due to modelling instability, particularly for small-size datasets. It is recommended to apply statistical strategies that do not break the structure of original time-series dataset.

This study introduces time-varying distributed lag non-linear model (DLNM) and compare its performance with ordinary DLNM in exploring the temporal change in the association between ambient temperature and daily mortality using data from Chicago between 1987 and 1997 for presenting the advantages of time-varying DLNM.

The mathematic structures of ordinary and time-varying DLNMs were introduced and compared. Daily data on all-cause mortality and environmental exposures including ambient temperature, relative humidity, and inhalable particulate matter were collected from Chicago between 1987 and 1997 from the dlnm package in R software. Quasi-Poisson regression with time-varying DLNM was applied to examine the temporal change in the temperature-mortality association in 1987 and 1997, respectively. Quasi-Poisson regression with ordinary DLNM was applied to examine the temperature-mortality association in 1987-1997, 1987-1989, 1995-1997, 1987, and 1997, respectively, and the results were compared with those using time-varying DLNM.

The association between daily mean temperature and mortality accumulated across lag 0-30 days was V-shaped in Chicago between 1987 and 1997, with the minimum morality temperature (MMT) being 19.2℃. The results of time-varying DLNM indicated that compared with MMT the relative risk (RR) of extremely cold temperature (the 1st percentile of average temperature, -15.8℃) i.e. cold effect, decreased insignificantly from 1.59 (95% CI:1.25-2.01) in 1987 to 1.50 (95% CI:1.13-1.98) in 1997 (P=0.756). By contrast, the RR of extremely high temperature (the 99th percentile of average temperature, 28.9℃), i.e. heat effect, increased significantly from 1.04 (95% CI:0.85-1.28) to 1.75 (95% CI:1.39-2.21) during the same time period (P=0.001). Similar temporal variations were also observed in the 1987-1989 dataset and the 1995-1997 dataset analyzed using ordinary DLNM. The results of ordinary DLNM on single-year datasets (i.e. in 1987 and 1997, respectively) were less stable, compared with the results of time-varying DLNM.

Time-varying DLNM can be used in the time-series analysis to examine the temporal variation in the association between environmental exposures (such as ambient temperature) and health outcomes.