Testing the Temperature-Mortality Nonparametric Function Change with an Application to Chicago Mortality

The relationship between temperature and mortality is well-documented, yet most existing studies assume this relationship remains static over time. This study investigates whether the temperature-mortality association in Chicago from 1987 to 2000 has changed in shape or location of key features, such as change points. We apply nonparametric regression techniques to estimate the temperature-mortality functions for each year using daily mortality and temperature data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) database. A permutation-based test is used to assess whether the shapes of these functions differ across time, while a bootstrap procedure evaluates the consistency of change points. Intensive simulation studies are conducted to evaluate the permutation-based test and bootstrap procedure based on Type I error and power. The proposed tests are compared with F tests in terms of Type I error and power. For the real data set, the analysis finds significant variation in the functional shapes across years, indicating evolving mortality responses to temperature. However, the estimated change points—temperatures associated with peak mortality—remain statistically consistent. These findings suggest that while the population’s overall vulnerability pattern may shift, the temperature threshold linked to maximum mortality has remained stable. This study contributes to understanding the temporal dynamics of climate-sensitive health outcomes and highlights the importance of flexible modeling in public health and climate adaptation planning.