The Mean Unfulfilled Lifespan (MUL): A new indicator of the impact of mortality shocks on the individual lifespan, with application to global 2020 quarterly mortality from COVID-19

Declines in period life expectancy at birth (PLEB) provide intuitive indicators of the impact of a cause of death on the individual lifespan. Derived under the assumption that future mortality conditions will remain indefinitely those observed during a reference period, however, the intuitive interpretation of a PLEB becomes problematic when that period conditions reflect a temporary mortality “shock”, resulting from a natural disaster or the diffusion of a new epidemic in the population for instance. Rather than to make assumptions about future mortality, I propose measuring the difference between a period average age at death and the average expected age at death of the same individuals (death cohort): the Mean Unfulfilled Lifespan (MUL). For fine-grained tracking of the mortality impact of an epidemic, I also provide an empirical shortcut to MUL estimation for small areas or short periods. For illustration, quarterly MUL values in 2020 are derived from estimates of COVID-19 deaths in 159 national populations and 122 sub-national populations in Italy, Mexico, Spain and the US. The highest quarterly values in national populations are obtained for Ecuador (5.12 years, second quarter) and Peru (4.56 years, third quarter) and, in sub-national populations, for New York (5.52 years), New Jersey (5.56 years, second quarter) and Baja California (5.19 years, fourth quarter). Using a seven-day rolling window, the empirical shortcut suggests the MUL peaked at 9.12 years in Madrid, 9.20 years in New York, and 9.15 years in Baja California, and in Guayas (Ecuador) it even reached 12.6 years for the entire month of April. Based on reported COVID-19 deaths that might substantially underestimate overall mortality change in affected populations, these results nonetheless illustrate how the MUL tracks the mortality impact of the pandemic, or any mortality shock, retaining the intuitive metric of differences in PLEB, without their problematic underlying assumptions.