A check for the expected mortality -

Hans Lugtigheid

Abstract

For calculating expected mortality one usually uses life expectancy tables etc. With these one makes calculations for year-groups, cohorts, male/female-numbers etc. This gives a lot of useful information. However, with so much details one can loose oversight. With a significant disturbance like the pandemic it is good to have a control-mechanism to check the totals. In this article I give a method to make a calculation to check for the total expected mortality. I adjust the earlier expected mortality for a year to the expected mortality as a consequence of the disturbance. The check only tests the reliability of the size of the excess mortality. Differences that occur can then be analyzed.

Introduction

The article begins with estimating the consequences that the excess mortality in a year has for later later years.

I give some examples to show how we can get a logical check for the validity of the excess mortality numbers. This clarifies the idea here presented.

At the end conclusions and recommendations.

The annual expected mortality

In this article I calculate the new expected mortality, and hence the excess mortality, under de assumption that there is one disturbing factor, in this case covid. I then compare these numbers with the official numbers.

In 2020 many (older) people died from covid who without the pandemic would have died also in 2020 or in 2021 or in later years. These numbers can be determined or estimated at January first 2021. Then we can and must lower the expected mortality for 2021 and later years by these numbers.

An example. Suppose 25K people died from covid in 2020. Without covid some would have died in 2020 and the remaining people in later years. I made three estimates. See table 1.

The estimates are ‘rough’. At the moment those numbers are unknown. Is is difficult to make an estimate for 2021 like, say, 8.659 with a 95%-confidence interval of [8.659-383, 8.659+383]. Hence these estimates don’t seem very useful.

The estimates however are useful in another way. The 25K are divided over the years. This distribution is important. With the first two estimates most people would have died without the pandemic in 2020 or 2021. This is in line with the observation that many older and weak people died from covid in 2020. The effect on the expected mortality is significantly higher than zero. With the third estimate most people would have lived until 2023 or later. That is not likely. Therefore the first estimates are a better indicator for the decrease of the expected mortality.

With the estimates we can calculate the expected mortality. For the expected mortality without covid I take the last pre-pandemic estimate. So for the current pandemic I would use the expected mortality for 2021 published in 2019 as a base. See table 2.

Suppose an estimate of the expected mortality for 2021 comes near estimate III. That is an indication that the expected mortality is overestimated.

This might be explained by another disturbing factor besides covid. However I assumed only one disturbing factor. If a second factor changes the excess mortality then we must deal with this separately to get a good comparison.

Also the following can be the case. The life expectancy tables are annually corrected according to the population at the beginning of the year. This is usually done with an estimate based on previous years. However, covid strikes hardest at the weak. This changes the distribution in the year-groups. Then the percentage has to be adjusted for this effect. The numbers in the year-groups decrease. But the average expected life-expectancy in the groups increase. And with that the expected mortality of the groups decrease. For more on this subject see Lugtigheid (2023).

The above is important with establishing excess mortality. Suppose that in 2021 the actual death is measured at 221. Table 3 gives the excess mortality per estimate.

The differences are significant. With estimate III the excess mortality is (strongly) underestimated.

Conclusion and recommendation

The method in this article gives a logical check on the annual expected mortality in a country. The estimates are rough, but the overall view gives a good indication. It is recommendable to check this for appropriate numbers.

Develop methods to improve the required estimates.

Literature

Lugtigheid, Hans. (2023, september) Expected mortality adjusted for distribution https://www.hanslugtigheid.nl/expected-mortality-adjusted-for-distribution