Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations
Authors: Sherratt Katharine , Gruson Hugo , Grah Rok , Johnson Helen , Niehus Rene , Prasse Bastian , Sandmann Frank , Deuschel Jannik , Wolffram Daniel , Abbott Sam , Ullrich Alexander , Gibson Graham , Ray Evan L , Reich Nicholas G , Sheldon Daniel , Wang Yijin , Wattanachit Nutcha , Wang Lijing , Trnka Jan , Obozinski Guillaume , Sun Tao , Thanou Dorina , Pottier Loic , Krymova Ekaterina , Meinke Jan H , Barbarossa Maria Vittoria , Leithauser Neele , Mohring Jan , Schneider Johanna , Wlazlo Jaroslaw , Fuhrmann Jan , Lange Berit , Rodiah Isti , Baccam Prasith , Gurung Heidi , Stage Steven , Suchoski Bradley , Budzinski Jozef , Walraven Robert , Villanueva Inmaculada , Tucek Vit , Smid Martin , Zajicek Milan , Perez Alvarez Cesar , Reina Borja , Bosse Nikos I , Meakin Sophie R , Castro Lauren , Fairchild Geoffrey , Michaud Isaac , Osthus Dave , Alaimo Di Loro Pierfrancesco , Maruotti Antonello , Eclerova Veronika , Kraus Andrea , Kraus David , Pribylova Lenka , Dimitris Bertsimas , Li Michael Lingzhi , Saksham Soni , Dehning Jonas , Mohr Sebastian , Priesemann Viola , Redlarski Grzegorz , Bejar Benjamin , Ardenghi Giovanni , Parolini Nicola , Ziarelli Giovanni , Bock Wolfgang , Heyder Stefan , Hotz Thomas , Singh David E , Guzman-Merino Miguel , Aznarte Jose L , Morina David , Alonso Sergio , Alvarez Enric , Lopez Daniel , Prats Clara , Burgard Jan Pablo , Rodloff Arne , Zimmermann Tom , Kuhlmann Alexander , Zibert Janez , Pennoni Fulvia , Divino Fabio , Catala Marti , Lovison Gianfranco , Giudici Paolo , Tarantino Barbara , Bartolucci Francesco , Jona Lasinio Giovanna , Mingione Marco , Farcomeni Alessio , Srivastava Ajitesh , Montero-Manso Pablo , Adiga Aniruddha , Hurt Benjamin , Lewis Bryan , Marathe Madhav , Porebski Przemyslaw , Venkatramanan Srinivasan , Bartczuk Rafal P , Dreger Filip , Gambin Anna , Gogolewski Krzysztof , Gruziel-Slomka Magdalena , Krupa Bartosz , Moszyński Antoni , Niedzielewski Karol , Nowosielski Jedrzej , Radwan Maciej , Rakowski Franciszek , Semeniuk Marcin , Szczurek Ewa , Zielinski Jakub , Kisielewski Jan , Pabjan Barbara , Holger Kirsten , Kheifetz Yuri , Scholz Markus , Przemyslaw Biecek , Bodych Marcin , Filinski Maciej , Idzikowski Radoslaw , Krueger Tyll , Ozanski Tomasz , Bracher Johannes , Funk Sebastian 
Published: April 2023

Background:Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022.Methods:We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1–4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models’ predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models’ forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models’ past predictive performance.Results:Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models’ forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models’ forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models’ forecasts of deaths (N=763 predictions from 20 models). Across a 1–4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models.Conclusions:Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks.Funding:AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 (https://www.nfdi4health.de/task-force-covid-19-2) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).