key: cord-0748058-df65w0lx
authors: Wieland, T.
title: Change points in the spread of COVID-19 question the effectiveness of nonpharmaceutical interventions in Germany
date: 2020-07-07
journal: nan
DOI: 10.1101/2020.07.05.20146837
sha: dd304441bf061ec86feffedb7190698b70b971b5
doc_id: 748058
cord_uid: df65w0lx

Aims: Nonpharmaceutical interventions against the spread of SARS-CoV-2 in Germany included the cancellation of mass events (from March 8), closures of schools and child day care facilities (from March 16) as well as a "lockdown" (from March 23). This study attempts to assess the effectiveness of these interventions in terms of revealing their impact on infections over time. Methods: Dates of infections were estimated from official German case data by incorporating the incubation period and an empirical reporting delay. Exponential growth models for infections and reproduction numbers were estimated and investigated with respect to change points in the time series. Results: A significant decline of daily and cumulative infections as well as reproduction numbers is found at March 8 (CI [7, 9]), March 10 (CI [9, 11] and March 3 (CI [2, 4]), respectively. Further declines and stabilizations are found in the end of March. There is also a change point in new infections at April 19 (CI [18, 20]), but daily infections still show a negative growth. From March 19 (CI [18, 20]), the reproduction numbers fluctuate on a level below one. Conclusions: The decline of infections in early March 2020 can be attributed to relatively small interventions and voluntary behavioural changes. Additional effects of later interventions cannot be detected clearly. Liberalizations of measures did not induce a re-increase of infections. Thus, the effectiveness of most German interventions remains questionable. Moreover, assessing of interventions is impeded by the estimation of true infection dates and the influence of test volume.

Assessing the effectiveness of nonpharmaceutical interventions (NPIs) in the SARS-CoV-2/COVID-19 context is a topic of growing relevance. Nevertheless, findings documenting the impact of these measures have not been homogeneous within the literature; whether with respect to single countries [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] , or in terms of international comparisons [12] [13] [14] [15] [16] [17] . The question of whether "lockdowns"including contact bans, curfews or closures of schools and child day care facilitiessucceed or fail in reducing infections is a key concern for policymakers, as such measures are accompanied by consequences in terms of economic, social and psychological effects on societies. All European countries introduced NPIs to reduce infections, ranging from appeals to voluntary behaviour changes and the cancellation of mass events (Sweden) to strict curfews (e.g. France, Italy). Being one of the most affected countries (in terms of confirmed prevalence), Germany introduced a strict strategy incorporating three bundles of measures (1. cancellation of mass events after March 8, 2. closure of schools and child day care facilities between March 16 and 18, and 3. a contact ban, bans of gatherings and closures of "nonessential" services from March 23).

There have been some approaches to assessing the interventions in Germany: Dehning et al. [1] utilized epidemiological models (the SIR [susceptible-infected-recovered] model and its extensions) combined with Bayesian inference to find change points in infections over time with respect to the aforementioned measures. They identified impacts of all three bundles of interventions and on this basis have explicitly outlined the importance and necessity of the contact ban for reducing new infections. In a series of studies [2] [3] [4] [5] , German economists investigated structural breaks in time series of cumulated infections and growth rates. Their inferred change points have been interpreted in a similar way, i.e., in support of the measures.

An additional modelling approach using a modified SIR model [4] also outlines the impact of NPIs on infections.

The common denominator in the approaches mentioned above [1] [2] [3] [4] [5] is the application of disease case data from the Johns Hopkins University (JHU). This data differs from the official German case data provided by the Robert Koch Institute (RKI) in terms of both precision and . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint detail, with importantly, the latter dataset including information about the date of onset of symptoms for most cases [18, 19] . This information is essential because it helps to estimate the true infection dates. In the aforementioned studies [1] [2] [3] [4] [5] , information of this type was not available, which has therefore required assumptions to be formulated regarding the time between infection and reporting. The SIR modeling study [1] has already been criticized in terms of its underestimation of this delay and the related results [20] . Moreover, studies utilizing epidemiological models [1, 4, 6] require assumptions on the transmission process of the disease (e.g., spreading rate, contacts per capita) or other unknown epidemiological parameters. Both aspects raise the question whether the previous assessments of NPIs in Germany are reliable.

The aim of this study is to assess the effectiveness of NPIs towards the SARS-CoV-2 spread in Germany (from March 8, 16 and 23, respectively), while overcoming the data-related problems mentioned above. The measures are analysed in terms of revealing their impact on infections over time. By using official case data [19] , true dates of infection are estimated.

Inspired by the methodical approach in previous studies [2] [3] [4] 11] , change points in time series of three indicators (daily and cumulative infections as well as reproduction numbers, all of which were calculated based on the estimated infection dates) were detected. The data covers infections from February 15 to May 31, 2020, which means that also possible effects of the easing of measures (from April 20) and the introduction of face masks (from April 27) can be assessed.

To assess the effectiveness of NPIs, it is the dates of infections of the reported cases which must be regarded, rather than the date of report. However, the real time of infection is unknown, thus, it must be estimated using the reported cases. In simple terms, the time between infection and reporting consists of two time periods: a) the time between infection . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint and onset of symptoms (incubation period), and b) the time between onset of symptoms and the date of report (reporting delay). Thus, to estimate the date of infection, both periods must be subtracted from the date of report [1] [2] [3] [4] [5] 8, 11] .

There are several estimations of the SARS-CoV-2/COVID-19 incubation period, ranging from median values of 5.0 to 6.4 days [21, 22] . Incorporating the reporting delay, however, is much more difficult. Previous studies investigating the effectiveness of interventions in Germany [1] [2] [3] [4] [5] have employed data from the Johns Hopkins University (JHU) which only includes daily infection and death cases. The reporting delay is either assumed to be equal to 2-3 days [2] [3] [4] or estimated in the model parametrization [1, 5] . In contrast, the data on German cases from the Robert Koch Institute (RKI) includes the reporting date and, for the majority of cases, casespecific dates of onset of symptoms, socio-demographic information (age group, gender), and the corresponding county [18, 19] . The data used here is the RKI dataset from June 28, 2020 [19] . In this dataset, there were 193,467 reported infections, for which, the date of onset of symptoms is known in 135,967 cases (70.28 %). The arithmetic mean of the time between onset of symptoms and report (reporting delay) is equal to 6.71 days (SD = 6.19) and the corresponding median equals 5 days. 95 % of the reporting delays lie between 0 (2.5 % percentile) and 21 (97.5 percentile) days. On this basis, we clearly see that assuming this value to be equal to 2-3 days [2] [3] [4] is an obvious underestimation. Moreover, exploring the dataset reveals that the reporting delay varies between the age and gender groups of the reported cases and over time, as well as between German counties. These differences indicate that it is difficult to assume or estimate average values for the reporting delay [1, 5] .

Thus, the estimation of the true infection dates of reported cases was conducted using the information from the RKI case data. In line with previous studies [1] [2] [3] [4] [5] , the incubation period is assumed to equal 5 days, which is the minimum value reported in the literature [21, 22] . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint = − Based on the cases with full information, a dummy variable regression model was estimated for the interpolation of the reporting delay for the remaining 57,500 cases. As the reporting delay differs across case-specific attributes, the reporting delay for case i (RDi,agcwt) was estimated by including dummy variables for age group a (a = 1, …, A), gender group g (g = 1, …, G), county c (c = 1, …, C) and weekday w (w = 1, …, W) as well as the time trend t:

where α is the estimated constant, βa, γg, δc and ζw represent sets of empirically estimated parameters for the A-1 age groups, G-1 gender groups, C-1 counties and W-1 weekdays, φ is the empirically estimated parameter for the time trend and εi,agcwt is the stochastic disturbance term. The model parametrization was conducted via Ordinary Least Squares (OLS) estimation.

In those cases lacking the information on onset of symptoms, the date of infection was calculated as the date of report (DRi) subtracted by the estimated reporting delay and the incubation period:

Previous studies with respect to the assessment of interventions have focused on only one indicator such as daily infections [1] , cumulative infections [2] [3] [4] [5] 8, 11, 15] , or reproduction numbers [7, 17] . To arrive at a more holistic picture, three indicators are used: a) the daily new is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint [18] as the quotient of infections in two succeeding 4-day intervals (implying a generation period of 4 days):

The period under study includes the infections from February 15 (first proven "super spreading event" in Germany, the "Kappensitzung" in Gangelt, North Rhine Westphalia) to May 31, resulting in N = 107 daily observations. The final date is estimated by the last available date of report (June 27) subtracted by the 97.5 % percentile of the incubation period (5.6 days) and the 97.5 % percentile of the reporting delay (21 days).

For the analysis of infections over time, phenomenological models have the advantage that they only incorporate time series of infections and do not require further assumptions concerning the transmission process of the disease under study [23, 24] . Thus, the time series of all three indicators were analysed using exponential growth models in their semilog form, which means that the dependent variables (I where α D , α C , α R , λ D , λ C and λ R are the parameters to be estimated and μ D t, μ C t and μ R t represent the stochastic disturbance term in each model.

The detection and dating of change points was conducted using a fluctuation test (recursive estimation test) and F statistics, which incorporates comparing the regression coefficients of a time series with M breakpoints (and, thus, M+1 segments) to the full sample estimates (no segmentation). Within these tests, structural breaks in the time series can be identified. The . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint optimal number of breakpoints and their attribution to the specific observation at which point they occur (which means a dating of the breakpoint, including the computation of confidence intervals) was conducted using the Bai-Perron algorithm. The statistically optimal number of M breakpoints is inferred by comparing model variants with zero to five breakpoints (corresponding to one to six segments). The variant which minimizes the residual sum of squares (RSS) and the Bayesian information criterion (BIC) is considered to be the optimal solution [25, 26] . Thus, the exponential growth functions shown above are divided into M+1 segments, in which the regression coefficients in each m segment (m = 1, …, M+1) are constant. The analysis was conducted in R [27] using the package strucchange [26] . [insert Figure 1] [insert Figure 2 ]

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. The second break on March 26 (CI [25, 27] ) documents a further decrease in daily growth . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint from 6.8 % to 1.9 % (0.019, CI [0.017, 0.020]). The last structural change is detected on April 13 (CI [12, 14] ), at which time the daily growth rate shifted from 1.9 % to 0.4 % (0.004, CI [0.003, 0.004]).

With respect to the reproduction number (R), three structural breaks can also be identified.

After the first break on March 3 (CI [2, 4] ), R starts to decrease by 9. In the last third of April, we find structural changes with respect to daily infections and reproduction numbers, but the growth rate of infections still remains negative. From March 19, the reproduction numbers, with few exceptions, fluctuate on a level below one (ln R < 0).

Regarding all three indicators, we find consistent results with respect to a significant decline of infections in the first third of Marchabout one week before the closing of schools and child . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint day care and two weeks before the full "lockdown" (including the contact ban) came into force.

The effect coincides with the cancellation of mass events recommended by the German minister of health, Spahn, on March 8. However, the increased awareness in the general population could have also had a significant impact in terms of voluntary changes in daily behaviour (e.g., physical distancing to strangers, careful coughing and sneezing, thorough and frequent hand washing). Surveys demonstrate an increased awareness towards the Corona threat already in the middle of February [29] . Additionally, voluntary cautious behaviour in the Corona context could also explain the abrupt and unusual decline of other infectious respiratory diseases in Germany starting in early March [30] .

Previous studies have also found a first slowing of infections in the first third of march [1] [2] [3] [4] [5] , but the results of the present analysis contradict their findings as the change point in the 10th calendar week is a) the clearest structural break given that it is present for all three indicators, b) the break which initiated a trend change in terms of a decline of daily new infections and c) the most influential break with respect to cumulative infections. Dehning et al. [1] state: "Our results indicate that the full extent of interventions was necessary to stop exponential growth

[…] Only with the third intervention, the contact ban, we found that the epidemic changed from growth to decay". These statements are based on a negative growth rate (-3 %) having not become apparent before the contact ban came into force. In contrast, given the estimated infection dates in the present study, we see that the growth rates of new infections and reproduction numbers already turn negative on March 3 and 8, respectively. At the same time, the growth rate of the cumulative infections has its biggest decrease across all four segments of the time series. Thus, a decline in infections occurred before school closures and the contact ban came into force.

In the time series studies on the German case [2] [3] [4] [5] , the closing of infrastructures (schools etc.) in mid-March was found to be the most influential break with respect to cumulative infections. This conclusion cannot be confirmed in the present study, as we cannot find any referring breakpoint with respect to the daily and cumulative infections. If the closures of schools and child day care facilities would have had an impact on infections, there would have . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint been a significant decline of new infections from March 16 to 18 on. The structural break in the reproduction numbers on March 19 initiates a stabilization of the reproduction numbers but not a further decline. Therefore, an impact of school and child day care closures cannot be detected. The influence of the third intervention ("lockdown" including contact ban), which was found to be the most influent factor in the SIR modelling study [1] , and an important factor in the previous time series analyses [2] [3] [4] [5] , remains unclear in the present study as well. There is no structural break in the reproduction numbers which coincides with the contact ban.

Significant breaks in daily and cumulative infections occur after the social ban came into force, but not immediately. The mismatches between the present and previous results are obviously related to different data sources, a point underscored by the fact that the modelling approach is similar to some of the previous studies [2] [3] [4] .

The impact of first liberalizations of measures from April 20 (e.g., reopening of some "nonessential" retail shops) is plausibly reflected in the temporal development of new infections and reproduction numbers. However, there is no re-increase of new infections as the corresponding growth rate remains negative and the reproduction numbers remain, with few exceptions, below the critical value of one. Moreover, no effect of the implementation of compulsory face masks in retail shops and public transport (starting from April 27) can be detected, as there is no further significant structural break. However, this intervention was implemented at a time where infections were already on a low level. Thus, the effectiveness of this measure cannot be definitely assessed. Further liberalizations starting in the first half of May (e.g., reopening of schools for some age groups, extending emergency childcare) do not show any impact as well.

The current findings support results for Germany inferred from logistic growth models which show a trend change before the contact ban came into force [8] . In addition, a Spanish time series study revealed breakpoints in cumulative infections, with the first occurring about two weeks before the nationwide "lockdown" [11] . Furthermore, the present results tend to support other studies of international comparisons which have found a decline of infections with or without strict interventions [12] [13] [14] [15] [16] .

. CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint

One strength of the present study is the relative simplicity of the analysis. The current approach allows for a time-related analysis of NPIs based on a rather simple model which CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint [16] [17] [18] and the third bundle of interventions (March 23) is questionable because a) the related effects on infections (if any) cannot be unequivocally validated, b) a trend change had already occurred long before they came into force, and c) liberalizations of these measures did not induce a re-increase of infections. We cannot deduce conclusions towards the necessity of compulsory face masks, as this intervention was introduced late. Furthermore, the time series of (confirmed) infections is substantially influenced by temporal changes in the test volume, which leads to a high degree of uncertainty with respect to the data source. Therefore, a future evaluation of NPIs towards SARS-CoV-2/COVID-19 in Germany should consider these questionable effects and uncertainties.

The study reveals three methodological issues for assessing the impact of NPIs which may influence the results enormously. Firstly, the key challenge is the estimation of realistic infections dates from official statistics (which typically do not include this information). This information is essential for the assessment of measures which aim at the reduction of new infections. It is particularly important to include a realistic and differentiated reporting delay.

An underestimation of the time between infection and reporting leads to the estimation of infections to a later date than actually occurred in reality. As a consequence, trend changes will also be dated too late, and thus, are attributed erroneously to specific interventions.

Secondly, it is important to incorporate several indicators for the pandemic spread. Daily and cumulative infections as well as reproduction numbers, though based on the same initial data, have different meanings. As the results of this study show, significant change points may be found for some indicators but not for others. Thus, assessment of effectiveness of nonpharmaceutical interventions depends on the indicator used which leads to the conclusion that the temporal development of the indicators chosen should be carefully compared. And lastly, quantitative investigations based on empirical case data implicitly assume constant test volumes, which is obviously not true. In the German case, the number of conducted tests for SARS-CoV-2 is not constant over time. An increase (or decrease) of tests may result in an artificial increase (or decrease) of reported infections. Thus, increasing test capacitywhich is a key parameter in fighting a pandemicmay result in a statistical source of error when . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint analyzing pandemics over time. All these issues exist regardless of the chosen modeling approach, which suggests a need to shift study design toward prioritizing the handling of data sources rather than refining models.

The author declares that there is no conflict of interest.

The author received no specific funding for this work.

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The copyright holder for this preprint this version posted July 7, 2020. . https://doi.org/10.1101/2020.07.05.20146837 doi: medRxiv preprint

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