Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations

BackgroundShort-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. MethodsWe 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 from a standardised source over the next one to four 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. ResultsOver 52 weeks we collected and combined up to 28 forecast models for 32 countries. 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 84% of participating models forecasts of incident cases (with a total N=862), and 92% of participating models forecasts of deaths (N=746). Across a one to four week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over four 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. ConclusionsOur 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 two weeks. Code and data availabilityAll data and code are publicly available on Github: covid19-forecast-hub-europe/euro-hub-ensemble.

Comparing human and model-based forecasts of COVID-19 in Germany and Poland

1Forecasts based on epidemiological modelling have played an important role in shaping public policy throughout the COVID-19 pandemic. This modelling combines knowledge about infectious disease dynamics with the subjective opinion of the researcher who develops and refines the model and often also adjusts model outputs. Developing a forecast model is difficult, resource- and time-consuming. It is therefore worth asking what modelling is able to add beyond the subjective opinion of the researcher alone. To investigate this, we analysed different real-time forecasts of cases of and deaths from COVID-19 in Germany and Poland over a 1-4 week horizon submitted to the German and Polish Forecast Hub. We compared crowd forecasts elicited from researchers and volunteers, against a) forecasts from two semi-mechanistic models based on common epidemiological assumptions and b) the ensemble of all other models submitted to the Forecast Hub. We found crowd forecasts, despite being overconfident, to outperform all other methods across all forecast horizons when forecasting cases (weighted interval score relative to the Hub ensemble 2 weeks ahead: 0.89). Forecasts based on computational models performed comparably better when predicting deaths (rel. WIS 1.26), suggesting that epidemiological modelling and human judgement can complement each other in important ways.

National and subnational short-term forecasting of COVID-19 in Germany and Poland, early 2021

BackgroundDuring the COVID-19 pandemic there has been a strong interest in forecasts of the short-term development of epidemiological indicators to inform decision makers. In this study we evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland for the period from January through April 2021. MethodsWe evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland. These were issued by 15 different forecasting models, run by independent research teams. Moreover, we study the performance of combined ensemble forecasts. Evaluation of probabilistic forecasts is based on proper scoring rules, along with interval coverage proportions to assess forecast calibration. The presented work is part of a pre-registered evaluation study and covers the period from January through April 2021. ResultsWe find that many, though not all, models outperform a simple baseline model up to four weeks ahead for the considered targets. Ensemble methods (i.e., combinations of different available forecasts) show very good relative performance. The addressed time period is characterized by rather stable non-pharmaceutical interventions in both countries, making short-term predictions more straightforward than in previous periods. However, major trend changes in reported cases, like the rebound in cases due to the rise of the B.1.1.7 (alpha) variant in March 2021, prove challenging to predict. ConclusionsMulti-model approaches can help to improve the performance of epidemiological forecasts. However, while death numbers can be predicted with some success based on current case and hospitalization data, predictability of case numbers remains low beyond quite short time horizons. Additional data sources including sequencing and mobility data, which were not extensively used in the present study, may help to improve performance. Plain language summaryThe goal of this study is to assess the quality of forecasts of weekly case and death numbers of COVID-19 in Germany and Poland during the period of January through April 2021. We focus on real-time forecasts at time horizons of one and two weeks ahead created by fourteen independent teams. Forecasts are systematically evaluated taking uncertainty ranges of predictions into account. We find that combining different forecasts into ensembles can improve the quality of predictions, but especially case numbers proved very challenging to predict beyond quite short time windows. Additional data sources, in particular genetic sequencing data, may help to improve forecasts in the future.

Comparative assessment of methods for short-term forecasts of COVID-19 admissions in England at the local level

BackgroundForecasting healthcare demand is essential in epidemic settings, both to inform situational awareness and facilitate resource planning. Ideally, forecasts should be robust across time and locations. During the COVID-19 pandemic in England, it is an ongoing concern that demand for hospital care for COVID-19 patients in England will exceed available resources. MethodsWe made weekly forecasts of daily COVID-19 hospital admissions for National Health Service (NHS) Trusts in England between August 2020 and April 2021 using three disease-agnostic forecasting models: a mean ensemble of autoregressive time series models, a linear regression model with 7-day-lagged local cases as a predictor, and a scaled convolution of local cases and a delay distribution. We compared their point and probabilistic accuracy to a mean-ensemble of them all, and to a simple baseline model of no change from the last day of admissions. We measured predictive performance using the Weighted Interval Score (WIS) and considered how this changed in different scenarios (the length of the predictive horizon, the date on which the forecast was made, and by location), as well as how much admissions forecasts improved when future cases were known. ResultsAll models outperformed the baseline in the majority of scenarios. Forecasting accuracy varied by forecast date and location, depending on the trajectory of the outbreak, and all individual models had instances where they were the top- or bottom-ranked model. Forecasts produced by the mean-ensemble were both the most accurate and most consistently accurate forecasts amongst all the models considered. Forecasting accuracy was improved when using future observed, rather than forecast, cases, especially at longer forecast horizons. ConclusionsAssuming no change in current admissions is rarely better than including at least a trend. Using confirmed COVID-19 cases as a predictor can improve admissions forecasts in some scenarios, but this is variable and depends on the ability to make consistently good case forecasts. However, ensemble forecasts can make forecasts that make consistently more accurate forecasts across time and locations. Given minimal requirements on data and computation, our admissions forecasting ensemble could be used to anticipate healthcare needs in future epidemic or pandemic settings.

Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the US

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multi-model ensemble forecast that combined predictions from dozens of different research groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naive baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-week horizon 3-5 times larger than when predicting at a 1-week horizon. This project underscores the role that collaboration and active coordination between governmental public health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks. Significance StatementThis paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the US. Results show high variation in accuracy between and within stand-alone models, and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public health action.

Short-term forecasting of COVID-19 in Germany and Poland during the second wave - a preregistered study

We report insights from ten weeks of collaborative COVID-19 forecasting for 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.

Short-term forecasts to inform the response to the COVID-19 epidemic in the UK

BackgroundShort-term forecasts of infectious disease can aid situational awareness and planning for outbreak response. Here, we report on multi-model forecasts of Covid-19 in the UK that were generated at regular intervals starting at the end of March 2020, in order to monitor expected healthcare utilisation and population impacts in real time. MethodsWe evaluated the performance of individual model forecasts generated between 24 March and 14 July 2020, using a variety of metrics including the weighted interval score as well as metrics that assess the calibration, sharpness, bias and absolute error of forecasts separately. We further combined the predictions from individual models into ensemble forecasts using a simple mean as well as a quantile regression average that aimed to maximise performance. We compared model performance to a null model of no change. ResultsIn most cases, individual models performed better than the null model, and ensembles models were well calibrated and performed comparatively to the best individual models. The quantile regression average did not noticeably outperform the mean ensemble. ConclusionsEnsembles of multi-model forecasts can inform the policy response to the Covid-19 pandemic by assessing future resource needs and expected population impact of morbidity and mortality.

Feasibility of controlling 2019-nCoV outbreaks by isolation of cases and contacts

BackgroundTo assess the viability of isolation and contact tracing to control onwards transmission from imported cases of 2019-nCoV. MethodsWe developed a stochastic transmission model, parameterised to the 2019-nCoV outbreak. We used the model to quantify the potential effectiveness of contact tracing and isolation of cases at controlling a 2019 nCoV-like pathogen. We considered scenarios that varied in: the number of initial cases; the basic reproduction number R0; the delay from symptom onset to isolation; the probability contacts were traced; the proportion of transmission that occurred before symptom onset, and the proportion of subclinical infections. We assumed isolation prevented all further transmission in the model. Outbreaks were deemed controlled if transmission ended within 12 weeks or before 5000 cases in total. We measured the success of controlling outbreaks using isolation and contact tracing, and quantified the weekly maximum number of cases traced to measure feasibility of public health effort. FindingsWhile simulated outbreaks starting with only 5 initial cases, R0 of 1.5 and little transmission before symptom onset could be controlled even with low contact tracing probability, the prospects of controlling an outbreak dramatically dropped with the number of initial cases, with higher R0, and with more transmission before symptom onset. Across different initial numbers of cases, the majority of scenarios with an R0 of 1.5 were controllable with under 50% of contacts successfully traced. For R0 of 2.5 and 3.5, more than 70% and 90% of contacts respectively had to be traced to control the majority of outbreaks. The delay between symptom onset and isolation played the largest role in determining whether an outbreak was controllable for lower values of R0. For higher values of R0 and a large initial number of cases, contact tracing and isolation was only potentially feasible when less than 1% of transmission occurred before symptom onset. InterpretationWe found that in most scenarios contact tracing and case isolation alone is unlikely to control a new outbreak of 2019-nCov within three months. The probability of control decreases with longer delays from symptom onset to isolation, fewer cases ascertained by contact tracing, and increasing transmission before symptoms. This model can be modified to reflect updated transmission characteristics and more specific definitions of outbreak control to assess the potential success of local response efforts. FundingWellcome Trust, Global Challenges Research Fund, and HDR UK. Research in ContextO_ST_ABSEvidence before this studyC_ST_ABSContact tracing and isolation of cases is a commonly used intervention for controlling infectious disease outbreaks. This intervention can be effective, but may require intensive public health effort and cooperation to effectively reach and monitor all contacts. When the pathogen has infectiousness before symptom onset, control of outbreaks using contact tracing and isolation is more challenging. Added value of this studyThis study uses a mathematical model to assess the feasibility of contact tracing and case isolation to control outbreaks of 2019-nCov, a newly emerged pathogen. We used disease transmission characteristics specific to the pathogen and therefore give the best available evidence if contact tracing and isolation can achieve control of outbreaks. Implications of all the available evidenceContact tracing and isolation may not contain outbreaks of 2019-nCoV unless very high levels of contact tracing are achieved. Even in this case, if there is asymptomatic transmission, or a high fraction of transmission before onset of symptoms, this strategy may not achieve control within three months.