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BackgroundThe accurate estimation of the effective reproductive number (Re) of epidemic outbreaks is of central relevance to public health policy and decision making. We present estimateR, an R package for the estimation of the reproductive number through time from delayed observations of infection events. Such delayed observations may for example be confirmed cases, hospitalizations or deaths. The Re estimation procedure is modularized which allows easy implementation of new alternatives to the already-available methods. Users can tailor their analyses according to their particular use cases by choosing among implemented variations. The package is based on the methodology of Huisman et al. developed as a response to the COVID-19 pandemic. ResultsThe estimateR R package allows users to estimate the effective reproductive number of an epidemic outbreak based on observed cases, hospitalization, death or any other type of event documenting past infections, in a fast and timely fashion. We validated the implementation with a simulation study, and by comparing results from estimateR to results from the Huisman et al. pipeline on empirical COVID-19 case-confirmation incidence. Compared to existing methods, estimateR implements unique features whose benefit we demonstrated with a simulation study. On simulated data, estimateR yielded estimates of similar, if not better, accuracy than compared alternative publicly available methods while being two to three orders of magnitude faster. In summary, this R package provides a fast and flexible implementation to estimate the effective reproductive number for various diseases and datasets. ConclusionsThe estimateR R package is a modular and extendible tool designed for outbreak surveillance and retrospective outbreak investigation. It extends the method developed for COVID-19 by Huisman et al. and makes it available for a variety of pathogens, outbreak scenarios, and observation types. Estimates obtained with estimateR can be interpreted directly or used to inform more complex epidemic models (e.g. for forecasting) on the value of Re.
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Serosurveys are an important tool to estimate the true extent of the current SARS-CoV-2 pandemic. So far, most serosurvey data have been analysed with cut-off based methods, which dichotomize individual measurements into sero-positives or negatives based on a predefined cutoff. However, mixture model methods can gain additional information from the same serosurvey data. Such methods refrain from dichotomizing individual values and instead use the full distribution of the serological measurements from pre-pandemic and COVID-19 controls to estimate the cumulative incidence. This study presents an application of mixture model methods to SARS-CoV-2 serosurvey data from the SEROCoV-POP study from April and May 2020 in Geneva (2766 individuals). Besides estimating the total cumulative incidence in these data (8.1% (95% CI: 6.8% - 9.8%)), we applied extended mixture model methods to estimate an indirect indicator of disease severity, which is the fraction of cases with a distribution of antibody levels similar to hospitalised COVID-19 patients. This fraction is 51.2% (95% CI: 15.2% - 79.5%) across the full serosurvey, but differs between three age classes: 21.4% (95% CI: 0% - 59.6%) for individuals between 5 and 40 years old, 60.2% (95% CI: 21.5% - 100%) for individuals between 41 and 65 years old and 100% (95% CI: 20.1% - 100%) for individuals between 66 and 90 years old. Additionally, we find a mismatch between the inferred negative distribution of the serosurvey and the validation data of pre-pandemic controls. Overall, this study illustrates that mixture model methods can provide additional insights from serosurvey data.
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The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.
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The numbers of confirmed cases of SARS-CoV-2 infection are increasing in many places. Consequently, the number of individuals placed into quarantine is increasing too. The large number of individuals in quarantine has high societal and economical costs, as well as infringing on the freedom of the individual. This has led to a vigorous debate about the duration of quarantine, particularly in light of the potentially low specificity of quarantine (i.e. low probability of quarantined individuals indeed being infected). We present a mathematical model that leverages empirically determined distributions of incubation period, infectivity, and generation time to quantify how the duration of quarantine affects transmission. With this model we address the impact of shortening the quarantine for returning travellers and traced contacts of confirmed cases, both in terms of prevented transmission and the ratio of prevented transmission to days spent in quarantine. We also consider the impact of i) test-and-release strategies; ii) additional hygiene measures imposed upon release after a negative test; iii) the development of symptoms during quarantine; iv) the relationship between quarantine duration and adherence; and v) the specificity of quarantine. When considering the benefit versus cost utility of quarantine, we find that the diminishing impact of longer quarantine on transmission prevention may support a quarantine duration below 10 days, particularly for returning travellers. A greater gain of utility can be achieved through a test-and-release strategy, and this can be even further strengthened by imposed hygiene measures post-release. We also find that unless a test-and-release strategy is considered, the specificity of quarantine does not affect the optimal duration of quarantine. Therefore, the argument that we should shorten quarantine because of lack of specificity is misguided.
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Estimation of the effective reproductive number, Rt, is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation. Author summaryThe effective reproductive number, Rt, is a key epidemic parameter used to assess whether an epidemic is growing, shrinking or holding steady. Rt estimates can be used as a near real-time indicator of epidemic growth or to assess the effectiveness of interventions. But due to delays between infection and case observation, estimating Rt in near real-time, and correctly inferring the timing of changes in Rt is challenging. Here, we provide an overview of challenges and best practices for accurate, timely Rt estimation.
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Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method -- referred to as mixture-model approach -- for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the tests ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys. Author SummaryAs other pathogens, SARS-CoV-2 elicits antibody responses in infected people that can be detected in their blood serum as early as a week after the infection until long after recovery. The presence of SARS-CoV-2 specific antibodies can therefore be used as a marker of past infection, and the prevalence of seropositive people, i.e. people with specific antibodies, is a key measure to determine the extent of the SARS-CoV-2 pandemic. The serological tests, however, are usually not perfect, yielding false positive and false negative results. Here we exploit an approach that refrains from classifying people as seropositive or negative, but rather compares the antibody level of an individual to that of confirmed cases and controls. This approach leads to more reliable estimates of cumulative incidence, especially for the low prevalence and low test accuracies that we face during the current SARS-CoV-2 pandemic. We also show how this approach can be extended to infer the presence of specific types of cases that have not been used for validating the test, such as people that underwent a mild or asymptomatic infection.
