Efficiency of case-crossover versus time-series study designs for extreme heat exposures

Time-stratified case-crossover (CC) and Poisson time series (TS) are two popular methods for relating acute health outcomes to time-varying ubiquitous environmental exposures. Our aim is to compare the performance of these methods in estimating associations with rare, extreme heat exposures and mortality-an increasingly relevant exposure in our changing climate.

Daily mortality data were simulated in various scenarios similar to observed Los Angeles County data from 2014 to 2019 (N = 367,712 deaths). We treated observed temperature as either a continuous or dichotomized variable and controlled for day of week and a smooth function of time. Five temperature dichotomization cutoffs between the 80th and 99th percentile were chosen to investigate the effects of extreme heat events. In each of 10,000 simulations, the CC and several TS models with varying degrees of freedom for time were fit to the data. We reported bias, variance, and relative efficiency (ratio of variance for a "reference" TS method to variance of another method) of temperature association estimates.

CC estimates had larger uncertainty than TS methods, with the relative efficiency of CC ranging from 91% under the 80th percentile cutoff to 80% under the 99th percentile cutoff. As previously reported, methods best capturing data-generating time trends generally had the least bias. Additionally, TS estimates for observed Los Angeles data were larger with less uncertainty.

We provided new evidence that, compared with TS, CC has increasingly poor efficiency for rarer exposures in ecological study settings with shared, regional exposures, regardless of underlying time trends. Analysts should consider these results when applying either TS or CC methods.