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Brockhaus EK, Wolffram D, Stadler T, Osthege M, Mitra T, Littek JM, Krymova E, Klesen AJ, Huisman JS, Heyder S, Helleckes LM, an der Heiden M, Funk S, Abbott S, Bracher J. Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany. PLoS Comput Biol 2023; 19:e1011653. [PMID: 38011276 PMCID: PMC10703420 DOI: 10.1371/journal.pcbi.1011653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 12/07/2023] [Accepted: 11/03/2023] [Indexed: 11/29/2023] Open
Abstract
The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.
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Affiliation(s)
- Elisabeth K. Brockhaus
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Daniel Wolffram
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
| | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Michael Osthege
- Institute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich GmbH, Jülich, Germany
- Institute of Biotechnology, RWTH Aachen University, Aachen, Germany
| | - Tanmay Mitra
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology (BRICS), Helmholtz Centre for Infection Research, Braunschweig, Germany
- Current address: Kennedy Institute of Rheumatology, Nuffield Department of Orthopedics, Rheumatology and Musculoskeletal Sciences, University of Oxford, Oxford, United Kingdom
| | - Jonas M. Littek
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Ekaterina Krymova
- Swiss Data Science Center, EPF Lausanne and ETH Zurich, Zurich, Switzerland
| | - Anna J. Klesen
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Jana S. Huisman
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Stefan Heyder
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - Laura M. Helleckes
- Institute of Bio- and Geosciences, IBG-1: Biotechnology, Forschungszentrum Jülich GmbH, Jülich, Germany
- Institute of Biotechnology, RWTH Aachen University, Aachen, Germany
| | | | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Sam Abbott
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Johannes Bracher
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
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2
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Wolffram D, Abbott S, an der Heiden M, Funk S, Günther F, Hailer D, Heyder S, Hotz T, van de Kassteele J, Küchenhoff H, Müller-Hansen S, Syliqi D, Ullrich A, Weigert M, Schienle M, Bracher J. Collaborative nowcasting of COVID-19 hospitalization incidences in Germany. PLoS Comput Biol 2023; 19:e1011394. [PMID: 37566642 PMCID: PMC10446237 DOI: 10.1371/journal.pcbi.1011394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Revised: 08/23/2023] [Accepted: 07/28/2023] [Indexed: 08/13/2023] Open
Abstract
Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges.
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Affiliation(s)
- Daniel Wolffram
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
| | - Sam Abbott
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | | | - Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Felix Günther
- Department of Mathematics, Stockholm University, Stockholm, Sweden
| | - Davide Hailer
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Stefan Heyder
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - Thomas Hotz
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - Jan van de Kassteele
- Center for Infectious Disease Control, National Institute for Public Health and the Environment (RIVM), Bilthoven, the Netherlands
| | - Helmut Küchenhoff
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig Maximilian University of Munich, Munich, Germany
- Munich Center for Machine Learning (MCML), Munich, Germany
| | | | - Diellë Syliqi
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig Maximilian University of Munich, Munich, Germany
| | | | - Maximilian Weigert
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig Maximilian University of Munich, Munich, Germany
- Munich Center for Machine Learning (MCML), Munich, Germany
| | - Melanie Schienle
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
| | - Johannes Bracher
- Chair of Statistical Methods and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
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3
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Sherratt K, Gruson H, Grah R, Johnson H, Niehus R, Prasse B, Sandmann F, Deuschel J, Wolffram D, Abbott S, Ullrich A, Gibson G, Ray EL, Reich NG, Sheldon D, Wang Y, Wattanachit N, Wang L, Trnka J, Obozinski G, Sun T, Thanou D, Pottier L, Krymova E, Meinke JH, Barbarossa MV, Leithäuser N, Mohring J, Schneider J, Włazło J, Fuhrmann J, Lange B, Rodiah I, Baccam P, Gurung H, Stage S, Suchoski B, Budzinski J, Walraven R, Villanueva I, Tucek V, Smid M, Zajíček M, Pérez Álvarez C, Reina B, Bosse NI, Meakin SR, Castro L, Fairchild G, Michaud I, Osthus D, Alaimo Di Loro P, Maruotti A, Eclerová V, Kraus A, Kraus D, Pribylova L, Dimitris B, Li ML, Saksham S, Dehning J, Mohr S, Priesemann V, Redlarski G, Bejar B, Ardenghi G, Parolini N, Ziarelli G, Bock W, Heyder S, Hotz T, Singh DE, Guzman-Merino M, Aznarte JL, Moriña D, Alonso S, Álvarez E, López D, Prats C, Burgard JP, Rodloff A, Zimmermann T, Kuhlmann A, Zibert J, Pennoni F, Divino F, Català M, Lovison G, Giudici P, Tarantino B, Bartolucci F, Jona Lasinio G, Mingione M, Farcomeni A, Srivastava A, Montero-Manso P, Adiga A, Hurt B, Lewis B, Marathe M, Porebski P, Venkatramanan S, Bartczuk RP, Dreger F, Gambin A, Gogolewski K, Gruziel-Słomka M, Krupa B, Moszyński A, Niedzielewski K, Nowosielski J, Radwan M, Rakowski F, Semeniuk M, Szczurek E, Zieliński J, Kisielewski J, Pabjan B, Kirsten H, Kheifetz Y, Scholz M, Biecek P, Bodych M, Filinski M, Idzikowski R, Krueger T, Ozanski T, Bracher J, Funk S. Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations. eLife 2023; 12:81916. [PMID: 37083521 DOI: 10.7554/elife.81916] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 02/20/2023] [Indexed: 04/22/2023] Open
Abstract
Background: Short-term forecasts of infectious disease contribute to situational awareness and capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise forecasts' predictive performance by combining independent models into an ensemble. Here we report the performance of ensemble predictions of COVID-19 cases and deaths across Europe from March 2021 to March 2022. Methods: We created the European COVID-19 Forecast Hub, an online open-access platform where modellers upload weekly forecasts for 32 countries with results publicly visualised and evaluated. We created a weekly ensemble forecast from the equally-weighted average across individual models' predictive quantiles. We measured forecast accuracy using a baseline and relative Weighted Interval Score (rWIS). We retrospectively explored ensemble methods, including weighting by past performance. Results: We collected weekly forecasts from 48 models, of which we evaluated 29 models alongside the ensemble model. The ensemble had a consistently strong performance across countries over time, performing better on rWIS than 91% of forecasts for deaths (N=763 predictions from 20 models), and 83% forecasts for cases (N=886 predictions from 23 models). Performance remained stable over a 4-week horizon for death forecasts but declined with longer horizons for cases. Among ensemble methods, the most influential choice came from using a median average instead of the mean, regardless of weighting component models. Conclusions: Our results support combining independent models into an ensemble forecast to improve epidemiological predictions, and suggest that median averages yield better performance than methods based on means. We highlight that forecast consumers should place more weight on incident death forecasts than case forecasts at horizons greater than two weeks. Funding: European Commission, Ministerio de Ciencia, Innovación y Universidades, FEDER; Agència de Qualitat i Avaluació Sanitàries de Catalunya; Netzwerk Universitätsmedizin; Health Protection Research Unit; Wellcome Trust; European Centre for Disease Prevention and Control; Ministry of Science and Higher Education of Poland; Federal Ministry of Education and Research; Los Alamos National Laboratory; German Free State of Saxony; NCBiR; FISR 2020 Covid-19 I Fase; Spanish Ministry of Health / REACT-UE (FEDER); National Institutes of General Medical Sciences; Ministerio de Sanidad/ISCIII; PERISCOPE European H2020; PERISCOPE European H2021; InPresa; National Institutes of Health, NSF, US Centers for Disease Control and Prevention, Google, University of Virginia, Defense Threat Reduction Agency.
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Affiliation(s)
- Katharine Sherratt
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Hugo Gruson
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Rok Grah
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Helen Johnson
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Rene Niehus
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Bastian Prasse
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | - Frank Sandmann
- European Centre for Disease Prevention and Control, Stockholm, Sweden
| | | | | | - Sam Abbott
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | | | - Graham Gibson
- University of Massachusetts Amherst, Amherst, United States
| | - Evan L Ray
- University of Massachusetts Amherst, Amherst, United States
| | | | - Daniel Sheldon
- University of Massachusetts Amherst, Amherst, United States
| | - Yijin Wang
- University of Massachusetts Amherst, Amherst, United States
| | | | - Lijing Wang
- Boston Children's Hospital, Boston, United States
| | - Jan Trnka
- Department of Biochemistry, Cell and Molecular Biology, Charles University, Prague, Czech Republic
| | | | - Tao Sun
- École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Dorina Thanou
- École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | | | | | | | | | - Neele Leithäuser
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Jan Mohring
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Johanna Schneider
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | - Jaroslaw Włazło
- Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
| | | | - Berit Lange
- Helmholtz Centre for Infection Research, Braunschweig, Germany
| | - Isti Rodiah
- Helmholtz Centre for Infection Research, Braunschweig, Germany
| | | | | | | | | | | | | | - Inmaculada Villanueva
- Institut d'Investigacions Biomediques August Pi i Sunyer, Universitat Pompeu Fabra, Barcelona, Spain
| | - Vit Tucek
- Institute of Computer Science, Prague, Czech Republic
| | - Martin Smid
- Institute of Information Theory and Automation, Prague, Czech Republic
| | - Milan Zajíček
- Institute of Information Theory and Automation, Prague, Czech Republic
| | | | | | - Nikos I Bosse
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Sophie R Meakin
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
| | - Lauren Castro
- Los Alamos National Laboratory, Los Alamos, United States
| | | | - Isaac Michaud
- Los Alamos National Laboratory, Los Alamos, United States
| | - Dave Osthus
- Los Alamos National Laboratory, Los Alamos, United States
| | | | | | | | | | | | | | | | | | - Soni Saksham
- Massachusetts Institute of Technology, Cambridge, United States
| | - Jonas Dehning
- Max-Planck-Institut fur Dynamik und Selbstorganisation, Göttingen, Germany
| | - Sebastian Mohr
- Max-Planck-Institut fur Dynamik und Selbstorganisation, Göttingen, Germany
| | - Viola Priesemann
- MPRG Priesemann, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | | | | | | | | | | | - Wolfgang Bock
- Technical University of Kaiserlautern, Kaiserslautern, Germany
| | | | - Thomas Hotz
- Technische Universitat Ilmenau, Ilmenau, Germany
| | | | | | - Jose L Aznarte
- Universidad Nacional de Educacion a Distancia, Madrid, Spain
| | | | - Sergio Alonso
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Enric Álvarez
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Daniel López
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | - Clara Prats
- Universitat Politecnica de Catalunya, Barcelona, Spain
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Benjamin Hurt
- University of Virginia, Charlottesville, United States
| | - Bryan Lewis
- University of Virginia, Charlottesville, United States
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Marcin Bodych
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - Maciej Filinski
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | | | - Tyll Krueger
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - Tomasz Ozanski
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | | | - Sebastian Funk
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom
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4
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Bracher J, Wolffram D, Deuschel J, Görgen K, Ketterer JL, Ullrich A, Abbott S, Barbarossa MV, Bertsimas D, Bhatia S, Bodych M, Bosse NI, Burgard JP, Castro L, Fairchild G, Fuhrmann J, Funk S, Gogolewski K, Gu Q, Heyder S, Hotz T, Kheifetz Y, Kirsten H, Krueger T, Krymova E, Li ML, Meinke JH, Michaud IJ, Niedzielewski K, Ożański T, Rakowski F, Scholz M, Soni S, Srivastava A, Zieliński J, Zou D, Gneiting T, Schienle M. A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. Nat Commun 2021; 12:5173. [PMID: 34453047 PMCID: PMC8397791 DOI: 10.1038/s41467-021-25207-0] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 07/28/2021] [Indexed: 12/31/2022] Open
Abstract
Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.
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Affiliation(s)
- J Bracher
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany.
| | - D Wolffram
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
| | - J Deuschel
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - K Görgen
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - J L Ketterer
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - A Ullrich
- Robert Koch Institute (RKI), Berlin, Germany
| | - S Abbott
- London School of Hygiene and Tropical Medicine, London, UK
| | - M V Barbarossa
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
| | - D Bertsimas
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - S Bhatia
- MRC Centre for Global Infectious Disease Analysis, Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), Imperial College London, London, UK
| | - M Bodych
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - N I Bosse
- London School of Hygiene and Tropical Medicine, London, UK
| | - J P Burgard
- Economic and Social Statistics Department, University of Trier, Trier, Germany
| | - L Castro
- Information Systems and Modeling, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - G Fairchild
- Information Systems and Modeling, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - J Fuhrmann
- Frankfurt Institute for Advanced Studies, Frankfurt, Germany
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - S Funk
- London School of Hygiene and Tropical Medicine, London, UK
| | - K Gogolewski
- Institute of Informatics, University of Warsaw, Warsaw, Poland
| | - Q Gu
- Department of Computer Science, University of California, Los Angeles, CA, USA
| | - S Heyder
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - T Hotz
- Institute of Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
| | - Y Kheifetz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - H Kirsten
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - T Krueger
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - E Krymova
- Swiss Data Science Center, ETH Zurich and EPFL, Lausanne, Switzerland
| | - M L Li
- Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - J H Meinke
- Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany
| | - I J Michaud
- Statistical Sciences Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - K Niedzielewski
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - T Ożański
- Wroclaw University of Science and Technology, Wroclaw, Poland
| | - F Rakowski
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - M Scholz
- Institute for Medical Informatics, Statistics and Epidemiology, University of Leipzig, Leipzig, Germany
| | - S Soni
- Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - A Srivastava
- Ming Hsieh Department of Computer and Electrical Engineering, University of Southern California, Los Angeles, CA, USA
| | - J Zieliński
- Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
| | - D Zou
- Department of Computer Science, University of California, Los Angeles, CA, USA
| | - T Gneiting
- Computational Statistics Group, Heidelberg Institute for Theoretical Studies (HITS), Heidelberg, Germany
- Institute for Stochastics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - M Schienle
- Chair of Statistics and Econometrics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
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