A Methodological Note on Empirical Confidence Intervals for the GCM-Ensemble Mean in Projecting Climate Change Impacts on Health

In climate–health impact projection studies, projected impacts from multiple general circulation models (GCMs) are commonly aggregated by reporting the mean of GCM-specific impacts as the point estimate alongside a 95% empirical confidence interval (eCI) constructed from the 2.5th and 97.5th percentiles of the simulated pooled distribution of GCM-specific impacts. This study shows that the eCI generally does not yield the nominal coverage probability for the GCM-ensemble mean and constructs an interval aligned with the estimand. In a simulation study, the coverage of the eCI for the GCM-ensemble mean deviates from the nominal level in both directions, whereas the aligned interval yields coverage near 95% across all considered settings. The exact coverages derived analytically under a location-shift model agree with the simulation results. In a reanalysis of a heat-related mortality projection in London, the eCI is consistently wider. The eCI should be distinguished from confidence intervals for the GCM-ensemble mean; rather, the interval may be better described as a simulation-based approximate prediction interval for a GCM-specific impact under the uniformly randomly selected GCM from the considered GCM set.