# How to Calculate Self Financing Capacity

Is the incidence value as it is currently calculated “useless”? A young math student from Bayerisch Gmain put forward this thesis on March 10th in a video that spreads virally on social networks. He criticizes that the incidence value does not include the number of tests carried out in a region: In counties with the same proportion of corona cases per inhabitant, those who would test more allegedly have a higher incidence. He therefore proposes an alternative calculation method.

"In this video I am trying to briefly describe why the incidence value, which is so important for all of us, is currently mathematically incorrectly calculated, and how it could be made better," he wrote about his video on Youtube. "This has serious effects, especially for border districts, which test significantly more than the German average."

Several media reported about it, first the local newspaper Traunsteiner Tagblatton March 15th and recently the Mercury and Focus Online. In the meantime the original video is no longer available on Youtube; it was apparently removed by the author. Copies are still circulating on the net, however, with titles like "Lockdown is based on calculation errors - Merkel, bet, six!". According to research by CORRECTIV.Faktencheck, these formulations are misleading.

The incidence value does not include a “calculation error”. Nevertheless, there is basically something to the criticism. Because there is a problem with the incidence: the incomplete data basis for the test numbers. Researchers have long asked whether the incidence value should be used as the only indicator of the pandemic situation in Germany. The alternative calculation method suggested by the student is also no better. Because it is based on a wrong assumption.

### What is the incidence value?

The 7-day incidence describes the number of newly reported corona cases confirmed with a PCR test per 100,000 inhabitants over a period of seven days. It is calculated as follows: You add up all new cases in a region over seven days. You divide it by the number of inhabitants and multiply the value by 100,000. In this way, an incidence per 100,000 inhabitants can be calculated for various cities, districts, federal states and nationwide. The value creates comparability for regions with different populations.

If the new cases per 100,000 inhabitants exceed certain limit values, this is linked to stricter corona protective measures, how exactly this is regulated can be different in each federal state. Chancellor Angela Merkel explained the reason at a press conference on May 6, 2020: The threshold of 50 new cases per 100,000 inhabitants is being used because it is believed that the chains of infection can still be traced with this amount.

However, there is always criticism of the focus on the incidence value. According to various media reports (here, here or here), experts criticized that it is used as the only parameter for the corona measures. The mirror quoted the epidemiologist Gérard Krause from the Helmholtz Center for Infection Research in November 2020, who said that one should also look at the number of free intensive care beds or the age distribution of the cases. The new infections are also laboratory findings - and their frequency is highly dependent on who is being tested and how.

### Do regions that test more have a higher incidence?

The math student from Bayerisch Gmain criticizes something similar: As a "mathematical problem" he describes the fact that the total number of tests carried out in one place is not included in the incidence calculation (from minute 1:29). If there were the same number of infections in two counties, the county that tested more would have more positive cases and the incidence would be higher, he claims.

Using the example of Berchtesgadener Land, he explains his alternative calculation method. He assumes that nationwide about 1.5 percent of the total population are tested every week. In the Berchtesgadener Land, however, much more was tested: 6.4 percent of the population (6,817 tests). 1.2 percent of the tests there were positive (positive rate) and the official incidence is 78.3.

He suggests that the calculation of the incidence should be based on the nationwide average of the tests carried out, the aforementioned 1.5 percent. This results in an incidence of 18 for the Berchtesgadener Land - this number is the "corrected incidence", the student claims. The incidence values ​​of different counties can be better compared with his method, because the number of tests carried out there no longer plays a role.

According to the physicist Viola Priesemann from the Max Planck Institute for Dynamics and Self-Organization, there is a fundamental mistake in the video.

### The positive rate is not always the same

On March 14, Priesemann criticized on Twitter that the video assumes that the population is randomly tested for Covid-19. That is wrong - it will be tested if there is a specific suspicion such as symptoms of the disease, a positive rapid test or contact with an infected person. This is also what the National Test Strategy says.

The student's assumption that the positive rate of tests in a district would always be the same, no matter how many people are tested there, is therefore wrong. A positive rate of 1.2 percent does not mean that 1.2 percent of all people in Berchtesgadener Land are infected with the corona virus.

Priesemann wrote on Twitter: “The video sounds logical, but it makes the wrong assumption. And so the conclusion is wrong. ”The possibility that more tests will be carried out in a region because there are more suspected cases is completely ignored.

She also wrote: “According to the calculation in the video, one could simply reduce the incidences in the district: For every test for suspicion, do a test on people who are very likely to be negative (or a random test). The incidence has already been halved. "

On March 25, the student spoke up again on Facebook and wrote that he wanted to distance himself from the fact that his video had been picked up by “conspiracy theorists and populist parties”. But he also received many constructive letters. "I would like to emphasize again that I did not want to show a 'correct solution' with my proposal." In the statistics, there is always only an approximation of reality. "The simplified assumption with the same probability of infection in the example in the video does not match reality (keyword test strategy)." Of course, his suggestion has "potential for improvement".

But the video takes up an important topic, explained Viola Priesemann. "Increased testing is 'punished' in the short term, because more of the chains of infection are discovered. In the long term, however, it is worthwhile because it stops the chains. ”As a solution, she suggested“ screening ”,“ that is, around 100,000 random tests that provide an objective picture of the outbreak every week ”.

### The development of the number of cases is related to test numbers, but cannot be explained by that alone

The Robert Koch Institute (RKI) also sees a connection between the test strategy and the number of reported infections. Changes to the test strategy - for example, the testing of return travelers - or an increase in the number of tests can have an impact on the number of cases, the RKI points out on its website (“What is the general connection between increased test numbers and increased case numbers?”).

In recent months, it has therefore been claimed in social networks that an increase or decrease in the number of cases can be explained solely by more or fewer tests. Again, that is not correct - the RKI also points this out. Most recently, 7.91 percent of the PCR tests nationwide were positive and thus significantly less than at the beginning of January (10.44 percent), although fewer tests per week were documented at the time (as of March 24). The RKI writes: "The higher the proportion of positive people with a consistently high number of cases, the higher the number of undetected infected people in a population is estimated (underreporting)." (PDF, pages 11-12)

### Reporting the SARS-CoV-2 test numbers is voluntary for laboratories

The number of weekly tests and their positive rate, which the RKI publishes every Wednesday in its situation reports, only allow a rough guide. They are not complete.

There is always a certain backlog of samples in the laboratories. The limited laboratory capacities also have an impact on the test strategy; if they are overloaded, the focus is on people with symptoms and specific suspected cases (PDF, page 13).

In addition, according to the RKI, there is no obligation for laboratories to report the number of their tests. A total of 259 laboratories in Germany have currently registered for the recording of test numbers (PDF, pages 9-10). However, the number of laboratories reporting weekly has fluctuated between 154 and 213 since the 12th calendar week 2020. The RKI provides the exact data here as an Excel table (as of March 24). Only 74 laboratories are currently reporting further data to the RKI as part of a surveillance system, from which test numbers, age groups and positive rates for individual federal states can be derived (PDF, pages 12-13).

A complete picture is therefore not possible with this data. If the number of tests per week in the RKI's management report increases or decreases, it is unclear what exactly is the reason for this - fewer reporting laboratories, other laboratories, actually fewer tests or fewer suspected corona cases? The RKI itself points out in its management report: "The aggregated data published here do not allow direct comparisons with the reported number of cases."

### Criticism of the incidence value as the sole benchmark

The calculation method in the math student's video is not a good alternative to the 7-day incidence. Nevertheless, there is often criticism of basing the corona measures solely on the incidence value. Partly because it is not known how many PCR tests are actually carried out per week.

Gérard Krause from the Helmholtz Center for Infection Research is one of these critics. In response to our request, he referred us to two expert reports that he had written for the Committee on Health of the German Bundestag - in November 2020 for the hearing on the “Third Civil Protection Act” and then again in February 2021.

In the first report, Krause wrote: "The sole reduction of the assessment of the situation to a single measured value, as provided here, cannot be justified epidemiologically and does not correspond to the state of the available scientific evidence." Proportion of severe and mild illnesses or the number of people in hospital (page 6).

In the more recent report, the epidemiologist dealt with the problem of the test numbers: “Due to the coupling of measures to a single indicator, namely only the incidence value of the case reports, decided in the Third Civil Protection Act, the legislature has given the executive branch depending on a measured value that demonstrably has none has a constant measurement basis, ”he wrote. "In order to properly evaluate the number of cases reported, it is also necessary to collect a reference value for the number of tests actually carried out."

As a solution, Krause suggests a weekly reporting requirement for PCR tests carried out. The reports should contain the age group and zip code of the person tested. So you can "correct the strategy-related fluctuations in test activities".

When asked, a spokesman for the Federal Ministry of Health, Oliver Ewald, informed us by e-mail: “An obligation to collect the PCR tests carried out consistently is not planned. The national test strategy gives nationwide uniform recommendations on which people should be tested for SARS-CoV-2. ”Beyond the 7-day incidence, the RKI analyzes various data sources“ in order to record and assess the situation in Germany as precisely as possible can". In addition to reporting data, this also included information from monitoring systems, such as the one for influenza, or projects and studies. The number of Covid-19 patients in intensive care units is also recorded. "All information is assessed together and published in the daily situation report."

Update, March 26, 2021: We have supplemented the response from the Federal Ministry of Health to our press request.

Editing: Matthias Bau, Sarah Thust

The main public sources for this report:

• RKI management report of March 24, 2021 with test numbers: Link
• RKI test numbers as an Excel table: Link