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Having dealt with apparent contradictions between statistical measures in the last blog post, we now delve deeper into how local incidences are determined. There have been occasional criticisms in the German media that the incidences reported by the RKI are too low in some counties. We want to address the question: How large is this effect and how comparable are incidences in different regions?
A Blog Entry by Jochen Fiedler and Sascha Feth.
After federal regulations were introduced, there were reports that locally some incidence values were too low. Thus, associated relaxations would come too early. Among others, the Tagesschau reported this with a reference to a BR data analysis.
After a health department knows about a positive Corona case, this case is given a reporting date; we call this the GA reporting date (as Gesundheitsamt is the german word for health department). The case is then reported to the RKI via the relevant state authority. Unfortunately, delays keep cropping up in this process.
The basis for the daily incidence, which is issued by the RKI, is the health department reporting data. If, for example, the incidence on May 8 is to be determined for a specific region, the health department reporting data from May 1 to 7 are used. Subsequently, the incidence for May 8 is »frozen« – later reports therefore no longer influence this incidence. This is a policy decision intended to prevent subsequent changes in incidence and associated planning uncertainties.
| GA reporting date | 01.05. | 02.05. | 03.05. | 04.05 | 05.05 | 06.05 | 07.05 | Sum |
| Number of cases (Stand 08.05) |
15.077 |
6.615 |
9.133 |
21.027 |
20.812 |
16.839 |
11.564 |
101.067 |
| Later reports | -6 |
8 |
4 |
55 |
58 |
256 |
3.307 |
3.682 |
| Number of cases (Stand 09.05) |
15.071 |
6.623 |
9.137 |
21.082 |
20.870 |
17.095 |
14.871 |
104.749 |
As a result, delayed reports for the days of May 2-7 will be considered for the May 9 incidences at the earliest.
Consider two fictitious health departments A and B. Health department A reports all cases to the RKI by the following day, health department B only manages to report half of the cases on the following day and needs another day for the other half. For simplicity, both counties have 100,000 inhabitants. In addition, they also each recorded a constant 10 cases in the days from May 1 to May 7. What incidences will the RKI report on May 8?
At Health Office A, it knew all 70 cases for the relevant period, and will announce the incidence 70. For Health Office B, the RKI knew only 65 of the 70 cases (because only half of the May 7 cases were actually reported by May 8). Thus, the incidence reported by the RKI is 65 for county B, a good 7% less, than in county A, even though the situation is the same. Unfortunately, this effect does not simply average away.
Due to the delayed reporting of a portion of the cases, this portion of the cases will only ever be included in six incidence calculations: The five cases with GA reporting dates of May 7, which do not become known to the RKI until May 9, will only factor into the incidence calculations for May 9-14. Accordingly, these cases will receive less weight. Health department B will therefore always push a few cases ahead of itself and, in comparable situations, will be certified by the RKI as having a lower incidence than health department A. Since the incidences are also not subsequently adjusted by subsequent notifications, in practice this can lead to county B being able to open earlier than county A.
How strong can this effect be? Let us take a closer look at the difference between frozen and corrected incidences.
Time for a disclaimer: Of course, we do not know the reporting processes of all health departments in detail. Therefore, we could at most speculate about the causes of the reporting delay. We will not do so and will only look at the effects of the reporting delay.
We take the frozen incidences directly from the RKI Website(accessed 17.05.2021), where in the data sheet »LK_7-day incidence« the incidences reported by the RKI since 18.11.2020 are stored. We calculate the corrected incidences on the basis of the data published at Arcgis, where we have retrieved the data on 17.05.2021. This data also includes all subsequent reports through May 17. In our analysis, we only use cases with GA reporting dates through 05/12/2021, as additional, atypical delays may surface the following days due to the Ascension Day holiday.
Let's compare the incidences from Willhemshaven with Mannheim: in Willhemshaven we have a clear and almost constant difference between frozen and corrected incidence since (at least) mid-November 2020, while the reporting delay in Mannheim is hardly noticeable (about one day delay).
On average, the ratio between frozen and corrected incidence in Mannheim is thus close to 1. If this ratio is determined for all German counties, the following histogram results:
We see that most ratios are quite close to 1 and that 90% of all counties have a value above 0.82 (red dashed line). There are only a few counties on the far left, of which we have already taken a closer look at the most extreme county with Wilhelmshaven above.
Another interesting question is whether the introduction of the federal regulations have now led to improvements in the reporting process in the counties? The regulations went into effect on 04/24/2021, which is why we look at the mean ratios of frozen and corrected incidences before and after that date. To exclude the effects of Christmas and New Year's Eve, we only take values from February 2021. Similarly, we exclude the Easter holiday (02.04.-13.04.2021)
Overall, a shift towards higher ratios and a somewhat lower dispersion can be observed. The results should still be viewed with caution because the database is still small. However, the trend shows a positive effect.
A closer look at individual counties again shows that developments can vary. There are examples of a shift to lower ratios, for example in the Rheinisch-Bergisch district:
Likewise, there are examples of shifts to ratios closer to 1, such as in the Main-Taunus district:
We see how the two incidences diverge for the first county after 04/24/2021 and how they converge for the second county. In addition, however, we also see that the corresponding period after the introduction of the federal emergency brake is small. This does not yet make these preliminary results strongly robust.
The overall reporting process is not uniform across all counties. In some cases, we see strong systematic delays in the figures, which can have a wide variety of causes.
After the introduction of uniform federal regulations, the same figures should be used everywhere as a basis for taking and easing measures. Overall, there has been a slight improvement, although there have also been new delays in individual counties.
Fraunhofer Institute for Industrial Mathematics ITWM