Time-varying associations between daily SARS-CoV-2 positive rates, positive deaths, and total deaths in Germany

Hagen Scherb

German Research Center for Environmental Health, Institute of Computational Biology, Ingolstädter Landstr. 1, D-85764 Neuherberg, Germany

Corresponding author: Hagen Scherb, German Research Center for Environmental Health, Institute of Computational Biology, Ingolstädter Landstr. 1, D-85764 Neuherberg, Germany, E-Mail:  hagen.scherb@gmail.com

Abstract

Background: Highly aggregated ecologic SARS-CoV-2 statistics about positive cases and positive deaths were used to make predictions and to decree public health control measures. Daily death counts correlated with daily positive rates 10 to 30 days earlier, worldwide. In Germany, this lagged association revealed a distinct temporal clustering suggesting uncontrolled determinants of key pandemic metrics. Ignoring the secular mortality upward-trend in Germany, scientists, official institutions, and the media compared the total deaths in 2020 with the average deaths from 2016 to 2019 and, thereby, overestimated COVID-19 excess deaths. Ad hoc corona metrics and statistics, predictions, and control measures based on this have been called into question.

Methods: The German Robert-Koch Institute reported daily SARS-CoV-2 positive cases and daily positive deaths until 5/26/2021, and the number of tests performed per week until 5/23/2021. The German Statistisches Bundesamt documented annual and daily deaths from 1990 until 5/16/2021. The optimum lag between positive rate and positive deaths was determined as the lag maximizing Spearman rank correlation. Inverse variance weighted (generalized) linear regression, Poisson regression, and logistic regression served to analyse the associations between positive rate, positive deaths, and total deaths with emphasis on the temporal developments of these associations.

Results: The estimated optimum lag between positive rate and positive deaths was 16.9 (11.1, 23.1) days, with a rank correlation of 0.927 (0.913, 0.939). The association between positive deaths and 17d-lagged positive rates showed a distinct four-phasic temporal clustering. The annual deaths per 1000 population in Germany from 1990 to 2019 followed a cubic logistic trend, which the deaths in 2020 exceeded by 1.3% equivalent to 12 667 (-20 886, 45 115) total excess cases, p-value 0.4543.

Conclusion: The association between positive rate and positive deaths revealed a significant temporal clustering, and the preliminary total deaths in Germany in 2020 did not significantly deviate from the secular trend from 1990 to 2019. These findings indicate potential deficits in SARS-CoV-2 metrics and statistics possibly due to unknown pandemic determinants and non-representative data generation. Characterization and control of the pandemic should be based on clearly defined, representative, and population-specific testing strategies of cases and deaths.

Keywords: Covid-19, excess deaths, optimum time lag, secular trend in total deaths, temporal clustering  

Abbreviations

95%-CI or (. , .): 95%-confidence interval; Chi²: Chi-squared distributed test statistic; COVID-19: Coronavirus disease 2019; CW: Calendar Week; DESTATIS: Statistisches Bundesamt, Germany; DF: Degree of freedom; GLM: Generalized linear model; IFR: Infection Fatality Rate; OR: Odds Ratio; OWID: Our World in Data; RKI: Robert Koch-Institute; SAS: Statistical Analysis System, software produced by SAS Institute Inc; SARS-CoV-2: Severe acute respiratory syndrome coronavirus 2; SE: Standard Error; UK: United Kingdom; VIF: Variance Inflation Factor.

Introduction

The assessment of COVID-19 prevalence, incidence, and risk depends on ecological ad-hoc data reported on the coronavirus pandemic. Despite their highly aggregated preliminary nature, daily data on SARS-CoV-2 positive persons and positive deaths are employed for the estimation of indicators such as the reproduction rate (R), the case fatality rate (CFR), the infection fatality rate (IFR), the mortality rate (MR), and years of life lost (YLL). Ioannidis presented a global perspective of COVID-19 epidemiology [1]. Since COVID-19 metrics and statistics depend on differing definitions and reporting rules, the general conceptual and technical quality, validity, and stability of COVID-19 related metrics and statistics play a key role in the subjective and scientific perception as well as in the administration of the pandemic [2]. Pre-analytical factors, such as specimen selection and collection, are crucial for RT-PCR, and any suboptimal collection may contribute to false results [3]. Recent large national and international cohorts described the input characteristics and outcome of hospitalized patients with COVID-19, but these reports were limited in detail [4]. Petti and Cowling emphasized the ecologic nature of COVID-19 mortality statistics. They recommended, e.g., influenza mortality as a predictor for multivariable COVID-19 mortality prediction models since influenza and COVID-19 mortality rates were significantly associated [5].

The rate of positive individuals (positive rate) is a central, however imprecise measure. Its interpretation depends among others on the clinical false positive rate, e.g., due to unspecific signals [6, 7], the number of PCR cycles and contaminations of laboratory equipment [8], as well as the composition of individuals tested in relation to the accuracy of the tests employed (PCR vs. antigen vs. antibody tests) [9, 10]. Backhaus discussed several pitfalls about the interpretation of corona data [11]. Kennedy and Yam investigated at the international level the possibility of uncovering fabrication of COVID-19 case figures employing statistical methods [12].

Although considerable scientific efforts concerning detection of the virus, diagnosis of COVID-19 disease, and the optimization of pandemic control have been undertaken globally [13-20], simple notorious unresolved problems remain. The distinction between ‘died with corona’ vs. ‘died due to corona’ is a big issue and may distort findings and burden the entire narrative [21, 22]. The CDC emphasized ‘Getting high-quality cause-of-death information can be challenging, especially during emergencies. Certifiers may be faced with heavy workloads, may not have access to complete information about the death, or may not be well trained in how to prepare good quality cause-of-death statements.’ [23]. From these perspectives it is problematic that in Germany the attribution to death from COVID-19 may be based on the positivity of a PCR test alone: ‘The infection with SARS-CoV-2 presents itself with a broad but unspecific spectrum of symptoms so that the virological diagnosis is the mainstay in the context of the detection of the infection, the reporting and the control of measures’ [24].

In several countries considered, SARS-CoV-2 positive deaths were correlated with lagged positive rates. In Germany, this correlation was subject to a distinct temporal clustering in the period from February 2020 to January 2021 [25]. Because of their preliminary and aggregated nature, epidemiologic pandemic descriptors should be subject to continuous quality and validity control [26-28]. Observations of established associations, e.g., between infection and death [29], or between lagged positive rate and positive deaths [25] provide opportunities for monitoring of pandemic metrics and control measures. Using publicly available OWID data [30] from December 2019 to August 2020 it was found that globally as well as for selected countries the daily SARS-CoV-2 positive rates showed delays to proportional counts of positive deaths as follows: World 20.6 days with 95%-CI (8.4, 32.8), USA 19.8 (9.3, 30.4), Germany 18.8 (6.1, 31.6), and Italy 2.4 (-10.2, 15.0) [25]. Employing the most recent German data from 2/24/2020 until 5/26/2021, the present article updates and scrutinizes the association between optimum lagged daily positive rate, positive deaths, and total deaths for temporal stability or heterogeneity. Data from India and the United States were considered for comparison.

Schreiner et al. observed a median delay from symptom onset to death of 11 days with high variability across European countries including the UK. For Germany, this delay was 11.2 days [29]. Scherb estimated a delay of 15.7 (10.8, 19.8) days between the reporting of positivity and the reporting of death [25]. Considering reporting delays for cases and deaths of up to one week, these both observations fit together. Despite the drawbacks of the involved corona metrics and statistics emphasized above, the association between positive deaths and lagged positive rate, taken at its face value, provides an opportunity for continuous outcome monitoring and plausibility checks.

Morfeld and Erren [31] and Morfeld et al. [32] emphasized the necessity of considering the mortality in 2020 in the context of preceding years. Giattino et al. cautioned against under- or overestimation of the excess with decreasing or increasing mortality trends: ‘For instance, for countries that have an increasing trend in mortality like the US and South Korea the five-year average will overestimate excess deaths; while for countries that have a decreasing trend in mortality like Russia it will underestimate excess deaths’ [33]. Scherb noted: ‘… the total deaths in Germany in 2020 are in line with the previous upward trend from 2005-2019’ [25]. Therefore, the provisional deaths per 1000 population in Germany in 2020 reported by DESTATIS were compared with the expected deaths deduced from an optimum cubic trend from 1990 through 2019. The purpose of this was (1) to estimate the likely excess deaths in 2020 and (2) to investigate whether the daily positive deaths reported by the RKI are consistent with the total deaths of the year 2020 reported by DESTATIS [34,35].

Methods

On 5/26/2021, the Robert Koch Institute (RKI) published on the internet the following cumulative SARS-CoV-2 related counts. Daily positive cases: 3,656,177, daily deaths: 87,726 and weekly performed tests until 5/23/2021: 60,408,571. Daily test counts were derived by linearly interpolating weekly counts (reported on Wednesdays for the week before). The total of the estimated/interpolated daily tests through 5/23/2021of 60,418,862 is practically identical to the total official weekly counts [34]. The deviation is only 0.02%. Table 1 reflects the daily data analysed, summarized by weeks for convenient tabular presentation. The optimum lag between positive rate and positive deaths was determined as the lag in days maximizing Spearman rank correlation of 7-day smoothed daily counts [25,36]. Inverse variance weighted (straight line) regression served to analyse the association between positive deaths and positive rates with an emphasis on temporal stability, variability, or clustering. Table 2 contains the total deaths in Germany from 1990 through 2020 [35,37], whereby the counts for 2020 and 2021 through 5/16/2021 are preliminary as of 5/26/2021. For analyses of raw or smoothed death counts and positive rates, rank correlation, weighted ordinary regression, weighted generalized linear regression (GLM), Poisson regression, and linear logistic regression were employed. Software used was MS-Excel-365 (2016), Wolfram MATHEMATICA 11.3, and mostly SAS/STAT software 9.4 (SAS Institute Inc: SAS/STAT User’s Guide, Cary NC: SAS Institute Inc, 2014).

Results

Optimum lag between positive tests and positive deaths

Spearman rank correlation has been employed previously for estimating an optimum time lag [36] between daily positive deaths and lagged positive rates in Germany [25]. An optimum delay of 15.7 (10.8, 19.8) days was found in data from February to November 2020. Applying the same method to the extended data from 2/24/2020 through 5/26/2021, the updated optimum delay was 16.9 (11.1, 23.1) days, with an optimum rank correlation of 0.927 (0.913, 0.939). See Figure 1 for details of the optimum lag estimation.

Trends of lagged positive rate and positive deaths

Utilizing the time lag of rounded 17 days for an optimum association between positive deaths and lagged positive rate in the RKI data, Figure 2 shows congruence of lagged positive rate and positive deaths up to 11/27/2020. From 11/28/20 this tight initial association increasingly dissolves. A formal change-point analysis [38, 39] based on the minimum deviance criterion (data and statistical parameters not shown) confirmed the significant structural change in November 2020: p-value < 0.0001.

Temporal clustering of positive individuals and positive tests

Figure 3 depicts the highly significantly temporally clustered association between positive deaths and 17 days lagged positive rate from a different viewpoint. In the combined periods 2/24 to 11/27/20 and 03/30 to 05/26/2021, daily positive deaths increased by 24.6 per 1% increase of the positive rate with R2 = 0.940. From 11/28 to 12/15/2020, 12/16 to 03/08/2021, and 03/09 to 03/29/2021, the further period-specific slopes were 156.5 R2 = 0.758, 66.4 R2= 0.958, and -139.7 R2 = 0.803, respectively. An overall interactive GLM, linear in the positive rate, yields R2 = 0.982. If quadratic and cubic terms and corresponding interactions are included, these are highly significant with p < 0.0001, and R2 slightly increases to 0.984. Using Poisson regression, linear in the positive rate, model fit is rather poor with scale 4.1, AIC 9846.2, deviance 7190.3 with 430 degrees of freedom, and thus overdispersion 16.7. The goodness of fit increases considerably when including quadratic and cubic positive rates: scale 2.0, AIC 44064, and deviance 1746.5 with 428 degrees of freedom, and thus overdispersion 4.1. The p-value for the interaction ‘period × lagged positive rate’ is less than 0.0001, for the four periods.

Expected versus observed total deaths in the year 2020

Table 2 compiles the official annual population and total death counts for Germany from 1990 to 2019, as well as corresponding preliminary counts for 2020 [35, 37]. A parsimonious optimum cubic polynomial logistic trend (R2=0.91) was fit to these data in the period 1990 to 2019. This yielded the expected counts per 1000 population in table 2. The total deaths in 2020 are 1.3% more than predicted by the trend from 1990 through 2019. The excess of 1.3% translates to 12,667 (-20,886, 45,115) additional cases in 2020. The p-value for the excess in 2020 is 0.4543. Figure 4 depicts the cubic trend of total deaths per 1000 population in Germany from 1990 through 2020. Figure 4 includes 95%-confidence bands for annual mean values, and it highlights the insignificant excess mortality in 2020 compared to the overall variability of the secular total mortality trend from 1970 to 2019.

COVID-19-status of deaths during periods

In view of the total deaths and the positive deaths in table 1 and considering the four distinct periods identified in Figure 3, we can assess the temporal development of the odds of negative tested or not at all tested deaths versus positive deaths. Table 3 presents these calculations by choosing period 1 as the reference period. It turns out that the odds ratio of not dying with or due to corona infection during the first period versus the remaining periods varies between 2 and 7. On average the odds ratio is 5.56. This could imply that the virus was up to 6 times more deadly during winter compared to the rest of the year. Or it could mean overcounting [40] of positive deaths due to unspecific signals, false positives (insufficient discrimination from influenza [5]), and disproportional more testing among the elderly and moribund compared with younger parts of the population. Table 3, last row, implies 49,475 excess or overcounted deaths in the second and third waves under the assumption that the virus or the pandemic was as deadly in the second and third waves as they were in the first.

Discussion

The associations between the daily SARS-CoV-2 positive deaths, the 17 days lagged positive rate, and the daily total deaths during the first 458 days of the corona pandemic in Germany 2/24/20 through 5/26/2021 were updated and scrutinized with a focus on temporal stability or variability. A strong artificial four-phasic temporal clustering of the association between positive deaths and 17 days lagged positive rate was found. Two possible explanations for this clustering exist in principle: (1) unknown or unacknowledged natural determinants driving the pandemic, e.g., seasonality [5] and the spread of unnoticed more deadly virus variants from November 2020 onward, or (2) discontinuities and artefacts in not representative corona metrics, reporting regimes, and statistics. Beginning the series of autumn/winter lockdowns in Germany on 11/3/2020, testing of asymptomatic persons reportedly decreased. Nevertheless, testing was still mandatory for healthy people for traveling and other access reasons and the ensuing daily positive rates did not profoundly change, whereas the positive deaths sharply increased [25, 41], especially so in nursing homes despite the lockdowns [42]. Of special interest is the strict negative correlation between lagged positive rate and deaths in the 4th period in Figure 3. The slope is: -139.7 (-172.6, -106.9), p-value < 0.0001, R2 = 0.803. It is conjectured that this behaviour is not due to biologic and epidemiologic causes, but is rather an artefact of disproportionate testing frequencies of younger versus older patients, e.g., children versus the moribund parts of the population.

In view of figure 2, Figure 3, Figure 5, and table 3, the question arises: Was the virus or the pandemic more deadly during the second and third waves compared to the first, or reflects this discrepancy an overcounting of the COVID-19 deaths in the second and third waves, for whatever reason? Morfeld et al. [32] analysed total mortality in Germany, January to October 2020. They found no overall excess mortality expressed as total-SMR of 1.01 (0.99, 1.04). However, their approach was biased since they did not consider the secular upward trend in mortality from 2004, see Figure 4. They rather compared the mortality in 2020 with ‘ … an average (arithmetic and geometric) of the death counts in the reference years 2016 bis 2019’ [32]. Figure 4 demonstrates no significant excess mortality in Germany in 2020, and table 3 implies nearly 50,000 possibly overcounted deaths in the second and third waves under the assumption that the virus or the pandemic was as deadly in the second and third waves as they had been in the first. The large differences in the presumed COVID-19 deaths between the first and the subsequent waves described here call for clarification. Bassetti et al. emphasized the perils that lie in the subjective perception of information: ‘... we must recognize that our judgment could theoretically be at risk ... to be influenced by the numerator and the denominator we see in our everyday life [2]. In view of the findings of this paper, we may complement the warnings by Bassetti et al. with the insight that our scientific perception may also be misled by seemingly hard official figures in case the underlying scientific and administrative testing and pandemic control concepts are not sound, not stable, or not representative.

Whether vaccination in Germany starting on 12/27/2020 had already a visible effect on the pandemic until May 2021 is a difficult issue because Germany until May 2021 has vaccinated only about 10% of its population with two doses. German Medical Association President Klaus Reinhardt claimed in May 2021: whereas the vaccination coverage was "still far too low to give the all-clear", it was "nevertheless showing effect" [43]. However, it remains to be scrutinized whether this assumed vaccination effect can be separated properly from the natural seasonal variability of the pandemic. The strong decreases in positive rate and positive deaths visible in Figure 2 from January to May 2021 can thus most likely not be explained by the relatively rare vaccination in that period.

Whereas it is beyond the scope of the present paper, it is nevertheless interesting to look in every detail at the associations between lagged positive rate and positive deaths from an international perspective. Figures 5 to 7 provisionally display the corresponding OWID data [30] for Germany, United States, and India, stratified by five periods. In contrast to Germany, the United States and India show rather dissimilar associations between positive rates and positive deaths in the first and final periods. Therefore, the 1st and 5th periods were not combined in Figures 5 to 7 in contrast to in Figure 4. It shows that in all three countries there is distinct temporal clustering in principle. But the fine structure of the clustering is differing. This is likely due to unknown and unspecified determinants of the data like demographical population characteristics, reporting regimes, country-specific seasonal factors, and so on. Therefore, temporal clustering of lagged cases and deaths can be expected globally.

Major limitations of this study lie in (1) unknown precise dates of infections and deaths, (2) unknown positive rates among the deaths, as well as (3) unknown testing strategies, i.e., unknown representativeness of positive rates and positive deaths. As the weekly deaths in Germany during 2020 range from 16,168 in calendar week 28 to 25,499 in calendar week 52 the collective of the daily total deaths can be considered a relatively stable surrogate reference for the daily positive deaths. This justifies the consideration of the positive deaths without denominator or offset. The unavoidable overdispersion inherent to this approach is accounted for by ordinary regression automatically, as well as by deviance-scaled Poisson or logistic regression. The daily positive rate applies to all of Germany and can thus be taken at its face value.

Minor limitations are the provisional total deaths for 2020 by DESTATIS and the preliminary nature of the volatile RKI-data, which change from day to day because of continuous updates. However, in most cases, these changes are at most in the one-digit percent range. Another limitation is the unknown number of tests performed per day. Unfortunately, only positive cases are reported. Reporting is not mandatory for negative cases, which is a considerable scientific drawback. As a substitute, the RKI reports the number of performed tests per week, which can be interpolated to tests per day. The problem is that these weekly test counts contain multiple tests for individual persons. However, it may be assumed that the number of tests reported is a reasonable proportional surrogate for the individual tests performed [25].

Conclusion

The presented findings demonstrate that COVID-19 death count variability may not only be high between locations [1] but may also be extremely variable within locations across periods. Ad-hoc highly aggregated ecologic SARS-CoV-2 metrics and statistics are too crude and thus inappropriate for meaningful pandemic description and control due to unknown determinants and non-representative data generation. Seasonality and other diseases are among the important, however, neglected, competing risk factors of infection and mortality. Total deaths in 2020 fall well within expected limits of random variation derived from the significant mortality upward trend in Germany from 2004 to 2019. Ignoring this upward trend is unreasonable and scientifically unsound. Therefore, the characterization of the pandemic should be based on transparent and representative population-specific testing strategies of cases and deaths. In other countries, similar but not identical time clustering was observed. Analysis of the complex relationships between cases and deaths around the world is beyond the scope of this paper but is planned for future publications.

Declarations

Ethical Approval and Consent to participate

Not applicable. Ethics approval and consent to participate are not required and not necessary, since only publicly available data and previously published information is being used.

Consent for publication

Not applicable. Only anonymous data is being used.

Availability of supporting data

The employed data has exclusively been published previously and/or it is contained in the tables and in the Figures included in this paper.

Competing interests

The author declares that he has no conflicts of interest.

Funding

The author declares that he has no funding for this study.

Authors' contributions

Not applicable.

Acknowledgments

I am most grateful to the reviewers for the details.