A Tutorial on Implementing Statistical Methods for Estimating Excess Death With a Case Study and Simulations on...

Excess death estimation, defined as the difference between the observed and expected death counts, is a popular technique for assessing the overall death toll of a public health crisis. The expected death count is defined as the expected number of deaths in the counterfactual scenario where prevailing conditions continued and the public health crisis did not occur. While excess death is frequently obtained by estimating the expected number of deaths and subtracting it from the observed number, some methods calculate this difference directly, based on historic mortality data and direct predictors of excess deaths. This tutorial provides guidance to researchers on the application of four popular methods for estimating excess death: the World Health Organization's Bayesian model; The Economist's gradient boosting algorithm; Acosta and Irizarry's quasi-Poisson model; and the Institute for Health Metrics and Evaluation's ensemble model. We begin with explanations of the mathematical formulation of each method and then demonstrate how to code each method in R, applying the code for a case study estimating excess death in the United States for the post-pandemic period of 2022-2024. An additional simulation study estimating excess death for three different scenarios and three different extrapolation periods further demonstrates general trends in performance across methods; together, these two studies show how the estimates by these methods and their accuracy vary widely depending on the choice of input covariates, reference period, extrapolation period, and tuning parameters. Caution should be exercised when extrapolating for estimating excess death, particularly in cases where the reference period of pre-event conditions is temporally distant (> 5 years) from the period of interest. In place of committing to one method under one setting, we advocate for using multiple excess death methods in tandem, comparing and synthesizing their results and conducting thorough sensitivity analyses as best practice for estimating excess death for a period of interest. We also call for more detailed simulation studies and benchmark datasets to better understand the accuracy and comparative performance of methods estimating excess death.