Background: The effects of meteorological factors on health outcomes have gained popularity due to climate change, which not only results in a general rise in temperature but also the 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 lagged environmental factors on the health outcome. In this research, we further investigate a more complex association structure between the lagged temperature exposures and the lagged mortality. Method: Derived by various statistical concepts, such as summation, autoregressive, principal component analysis, baseline adjustment, and offset in the DLNM, five strategies are newly proposed and evaluated by a simulation study 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. Results: According to simulation results, only one strategy, named as MV DLNM , could yield valid Type-I errors, while the other 4 strategies demonstrated much more inflated type-I errors. With an illustration using the real data, the MV DLNM that incorporates both the current and lagged mortalities demonstrates a more significant association comparing to the conventional DLNM that only relies on the current mortality. Conclusions: In public health research, not only the exposure may post a delayed effect, but also the outcome of interest could provide the lagged association signals. The joint modeling of the lagged exposure and the lagged outcome would discover such complex association structure.