Assessing the causal effects of a stochastic intervention in time series data: Are heat alerts effective in preventing deaths and hospitalizations?

We introduce a new causal inference framework for time series data aimed at assessing the effectiveness of heat alerts in reducing mortality and hospitalization risks. We are interested in addressing the following question: how many deaths and hospitalizations could be averted if we were to increase the frequency of issuing heat alerts in a given location? In the context of time series data, the overlap assumption - each unit must have a positive probability of receiving the treatment - is often violated. This is because, in a given location, issuing a heat alert is a rare event on an average temperature day as heat alerts are almost always issued on extremely hot days. To overcome this challenge, first we introduce a new class of causal estimands under a stochastic intervention (i.e., increasing the odds of issuing a heat alert) for a single time series corresponding to a given location. We develop the theory to show that these causal estimands can be identified and estimated under a weaker version of the overlap assumption. Second, we propose nonparametric estimators based on time-varying propensity scores, and derive point-wise confidence bands for these estimators. Third, we extend this framework to multiple time series corresponding to multiple locations. Via simulations, we show that the proposed estimator has good performance with respect to bias and root mean squared error. We apply our proposed method to estimate the causal effects of increasing the odds of issuing heat alerts in reducing deaths and hospitalizations among Medicare enrollees in 2817 U.S. counties. We found weak evidence of a causal link between increasing the odds of issuing heat alerts during the warm seasons of 2006-2016 and a reduction in deaths and cause-specific hospitalizations across the 2817 counties.