It is well-known that the relationship between human all-cause mortality risk and age can be represented by the Gompertz model 鈥 one of the oldest mathematical formulations in actuarial science and human demography.
Our research shows that the risk of dying with COVID-19 can also be modelled using a Gompertz parametric description, allowing some important differences by age, gender, and country to be highlighted.
In this research brief, we draw on publicly available data to help understand who is at greatest risk of dying with COVID-19. Figure 1 below shows COVID-19 mortality rates per 1,000 population (as of June 2, 2020) by age and gender in adults aged 40 years and above for ten countries: the UK, Belgium, Spain, the Netherlands, Italy, France, the U.S., Germany, South Korea, and Australia. Figure 2 presents the data in Figure 1 on the log10 scale.
Note: Some data have been smoothed in order to show consistent age segments.
In people aged 40 years and older, Figures 1 and 2 highlight that COVID-19 mortality risk increases with age and is higher in males compared to females. Further, Figure 2 demonstrates that COVID-19 mortality rates exhibit a precise pattern of exponential increase with age.
The exponential pattern observed with respect to COVID-19鈥檚 mortality rate with age suggests it can be modelled using the Gompertz function, with formula:
where m(t) is the mortality rate for an adult with age (t), while 伪 and A are free parameter to estimate; 伪 is the rate of age-related increase in mortality (also known as the 鈥渟enescent component鈥) and A represents the baseline mortality, which can be thought of as an aggregate of different environmental factors.
Estimating 伪 enables the derivation of the mortality rate doubling time (MRDT) for COVID-19 鈥 the age increment necessary for COVID-19鈥檚 mortality rate to double:
Estimate of COVID-19鈥檚 Mortality Rate Doubling Time | Countries |
|---|---|
5 years | Netherlands |
6 years | Italy, Germany, Spain, South Korea, Belgium, Australia |
7 years | France, U.K. |
8 years | USA |
In over half of the countries analyzed, COVID-19鈥檚 MRDT is estimated as 6 years. This suggests that, compared to a 20-year-old, an 80-year-old (being 60 years older) has approximately 210 times the risk of dying from COVID-19 (roughly 1000 times the risk).
Figure 3 illustrates all-cause MRDTs and COVID-19 MRDTs for the ten countries analyzed. All-cause mortality estimates of the MRDT were calculated using data from the .
Population all-cause MRDTs are all in the range of 7 to 8, with the exception of the U.S. which has an MRDT of 9. These estimates are consistent with . COVID-19鈥檚 MRDT is shorter than the equivalent all-cause MRDT in every country, implying COVID-19鈥檚 mortality rate by age is steeper. Moreover, within a country, the MRDTs for each sex are similar, but steeper for males.
COVID-19 could be viewed as having an 鈥渁dditional mortality鈥 impact on populations across the age segments shown here, due to its similar MRDT to population all-cause mortality. COVID-19 mortality rates reflect the average risk of dying with COVID-19 for a particular age, but an individual鈥檚 risk of dying will very much depend on his or her underlying health and other risk factors. Nonetheless, MRDTs are shorter for COVID-19 (i.e., the risk with age is steeper) compared with all-cause in all countries as well as for males compared with females. The shorter MRDT associated with COVID-19 may, in part, be driven by an 鈥榠ntensification鈥 or an 鈥榓cceleration鈥 to the risk of dying in some people with underlying health conditions or other risk factors.
Finally, the limitations of these data are important to consider and differ by country, which we discussed in this article. Most notably, different countries have adopted different definitions with respect to reporting COVID-19 deaths.
