Estimating the Temperature-Mortality Relationship Using a Novel Local Estimand: Application to the Metropolitan Area of Florence

Abstract

INTRODUCTION: The Average Dose-Response Function (aDRF) is a standard global estimand for evaluating the causal effect of a continuous exposure. The estimation of the aDRF relies, among others, on the assumption that all units share common support. However, when studying the short-term effects of temperature, some units (days) cannot realistically be exposed to certain exposure doses. The lack of common support can lead to problematic extrapolations.

OBJECTIVE: We propose a method to estimate local aDRFs within a Potential Outcomes (PO) framework, and use it to identify the short-term relationship between average temperature (lag 0-3) and natural deaths in the Florence metropolitan area, Italy (2010-2019).

METHODS: Under the Stable Unit Treatment Value, we define for each day the number of deaths that would have occurred for different temperature levels, i.e. the POs. Only the PO corresponding to the actually observed exposure is available, whereas the remaining POs are missing and must be imputed. We impute them using the following procedure. We do it according to the following procedure. Under local weak unconfoundedness, we first estimate the Generalized Propensity Score (GPS), defined as the conditional density of temperature given confounders. Then, for each day, we estimate the GPS at the observed temperature, R_i, and over a pre-specified grid of temperature values. Finally, we fit a flexible model on daily mortality given temperature and the R_i and use it to impute the POs for every day at each temperature level in the grid. Most existing methods rely on a global overlap assumption and target a global aDRF, estimated by averaging the imputed potential outcomes across all days for each temperature level. In contrast, we rely on a local overlap assumption and estimate local aDRFs for subgroups of days for which local overlap holds. We define temperature intervals and for each interval we identify the subgroup of days based on the overlap between the R_i estimated for the days with temperature within the interval and the GPS predicted in the middle of the interval for the days with temperature outside the interval. The aDRF is then estimated for each interval, by averaging the imputed POs over the selected subgroup at each temperature level within the interval. We perform a simulation study to evaluate the performance of our method.

RESULTS: Our procedure has good performance in terms of Absolute Bias and Root Mean Square Error. For the study area, we estimate 5 local aDRFs for the temperature intervals [0-6], [6-12], [12-18], [18-24], [24-30]. The local aDRFs are consistent with the literature, highlighting the U-shaped risk related to extreme temperatures.

CONCLUSIONS: Our local approach addresses the common support problem, avoiding inappropriate extrapolation. It yields dose–response curves that have causal interpretation and can be readily used to conduct impact evaluations under counterfactual scenarios.