Amsterdam, August 2025
In the pandemic we work with baselines as expected mortality. These baselines usually are in some way extrapolated mortality rates from the years before the pandemic that are applied to the new population numbers. However the pandemic also changes the mortality rates that are expected. Below an example to show this effect. When calculating baselines one should be cautious because of this.
Situation without covid/pandemic
For a baseline we assume that every year on Jan. 1 there are 10,000 people of age x of whom 2,000 die in that year. We consider two groups: A and B.
Group A: All people aged x on Jan. 1 of year one.
Group B: All people aged x on Jan. 1 of year two.
Group A has (pre-pandemic) three subgroups:
A0: 1,000 people who die each year before year one
A1: 2,000 people who die in year one
A2: 8,000 people who don’t die in year one
Likewise group B has B0, B1 and B2.
See tables below. The colored parts begin when the people in each group at Jan. 1 have age $x$. Group B is shifted one year from group A.
When we estimate the expected mortality of the group of age x in a year from the past years, allways 2,000 or 20%, we get an estimate of 2,000 or 20% of the 10,000 at the beginning of the year.
One could thus estimate the expected mortality of group B in year two by applying the 20% from group A in year one to the population of group B (10,000) at Jan. 1 of year two.
2. Situation with covid/pandemic
In year one the pandemic starts. The pandemic changes things. People in group A1 die in year one. Either from natural causes or possibly earlier from covid. In group A2 nobody was expected to die in year one, but now, say, 1,000 people die in group A2 from covid. Thus in group A 3,000 people die, 1,000 more than expected. This is 30% and higher than the expected 20%. See table.
Group B has 11,000 people at Jan. 1 of year one. Without the pandemic we expect that the 1,000 people in group B0 die in year one. With the pandemic people also will die in the groups B1 and B2. The people in group B1 are expected to die in year one so their chance of dying in year one from covid is higher than those in B2 (covid hits harder with weak people). Say 1,000 from B1 die in year one from covid and 1000 in B2. At Jan 1. in year two we then have 8,000 people of age x. 1,000 in group B1 and 7,000 in group B2. In year two the remaining 1,000 from group B1 die (natural or from covid) and, say, 500 from group B2 from covid. See table.
At Jan. 1 in year two we want to estimate expected mortality in group B in year two as if year two has no pandemic. This is the (adjusted) baseline. Then we would expect that all remaining 1,000 people in B1 die and none of the remaining in group B2. So we expect 1,000 / 8,000 = 12.5% from this age group to die in year two. This is the adjusted baseline.
When we extrapolate the probability of dying in group B from the years before year one we get a probability of 20%. Then we expect 20% x 8,000 is 1,600 to die. This is 600 more than the 1,000 above.
When we add year one to the years to extrapolate from we get a higher probability than 20% because year one had 30% mortality.
The most realistic is a probability/rate of 12.5%. The values 20% or higher overestimate expected mortality and thus underestimate excess mortality.
Conclusion
Thus we see that one has to be cautious when estimating mortality from the probabilities/’mortality rates’ from the past in a situation of excess mortality.
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