Analysis of the early Covid-19 epidemic curve in Germany by regression models with change points

  1. Helmut Küchenhoff
  2. Felix Günther
  3. Michael Höhle
  4. Andreas Bender

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Abstract

We analyze the Covid-19 epidemic curve from March to end of April 2020 in Germany. We use statistical models to estimate the number of cases with disease onset on a given day and use back-projection techniques to obtain the number of new infections per day. The respective time series are analyzed by a trend regression model with change points. The change points are estimated directly from the data. We carry out the analysis for the whole of Germany and the federal state of Bavaria, where we have more detailed data. Both analyses show a major change between March 9th and 13th for the time series of infections: from a strong increase to a decrease. Another change was found between March 25th and March 29th, where the decline intensified. Furthermore, we perform an analysis stratified by age. A main result is a delayed course of the epidemic for the age group 80+ resulting in a turning point at the end of March.

Our results differ from those by other authors as we take into account the reporting delay, which turned out to be time dependent and therefore changes the structure of the epidemic curve compared to the curve of newly reported cases.

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  1. Version published to 10.1101/2020.10.29.20222265v2 on medRxiv
  2. Version published to 10.1017/s0950268821000558
  3. ScreenIT

    SciScore for 10.1101/2020.10.29.20222265: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    NIH rigor criteria are not applicable to paper type.

    Table 2: Resources

    Software and Algorithms
    SentencesResources
    A procedure for imputation of missing values regarding the disease onset has been developed by [10], using a flexible generalized additive model for location, scale and shape (GAMLSS; [11]), assuming a Weibull-distribution for the time period between disease onset and reporting date.
    GAMLSS
    suggested: None

    Results from OddPub: Thank you for sharing your data.

    Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
    4.1 Limitations: The analysis only includes reported cases. If the proportion of undetected cases changes over time, e.g., due to different test criterion, this can distort the curve and thus the determination of the change points. Therefore, additional data on daily deaths and hospital admissions and the number of tests performed should be considered. Furthermore, it is possible to estimate the proportion of undetected cases with the help of representative studies such as the one currently conducted in Munich, see [20]. In a recent paper [21] performed an time varying estimation of the case detection ratio (CDR) for different age groups. They find a linear decreasing CDR from March 2nd until April 12th in the main age groups. The CDR was only half as large at the end of the period as it was at the beginning. This can only partly explain the curve, where we observe much a much higher increase. Our analysis is based to a considerable extent on imputed data, see [10], which is a results of missing data w.r.t. the disease onset. We have performed a sensitivity analysis using only cases with available disease onset date and based on imputing missing disease onset dates by the reporting date of the cases (Figure S2 in the supplementary material). The back-projection procedure is based on an assumption of the distribution of the incubation time. There are some recent papers showing some evidence for a longer incubation time in elderly cases, see [22] and [23]. Therefore, we perform...

    Results from TrialIdentifier: No clinical trial numbers were referenced.

    Results from Barzooka: We did not find any issues relating to the usage of bar graphs.

    Results from JetFighter: We did not find any issues relating to colormaps.

    Results from rtransparent:
    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
    • Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
    • No protocol registration statement was detected.

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  4. Version published to 10.1101/2020.10.29.20222265v1 on medRxiv