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

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 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. Results: Over 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. 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 two weeks.

Evaluating Forecasts with scoringutils in R (preprint)

Evaluating forecasts is essential in order to understand and improve forecasting and make forecasts useful to decision-makers. Much theoretical work has been done on the development of proper scoring rules and other scoring metrics that can help evaluate forecasts. In practice, however, conducting a forecast evaluation and comparison of different forecasters remains challenging. In this paper we introduce scoringutils, an R package that aims to greatly facilitate this process. It is especially geared towards comparing multiple forecasters, regardless of how forecasts were created, and visualising results. The package is able to handle missing forecasts and is the first R package to offer extensive support for forecasts represented through predictive quantiles, a format used by several collaborative ensemble forecasting efforts. The paper gives a short introduction to forecast evaluation, discusses the metrics implemented in scoringutils and gives guidance on when they are appropriate to use, and illustrates the application of the package using example data of forecasts for COVID-19 cases and deaths submitted to the European Forecast Hub between May and September 2021

Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States (preprint)

The U.S. COVID-19 Forecast Hub aggregates forecasts of the short-term burden of COVID-19 in the United States from many contributing teams. We study methods for building an ensemble that combines forecasts from these teams. These experiments have informed the ensemble methods used by the Hub. To be most useful to policy makers, ensemble forecasts must have stable performance in the presence of two key characteristics of the component forecasts: (1) occasional misalignment with the reported data, and (2) instability in the relative performance of component forecasters over time. Our results indicate that in the presence of these challenges, an untrained and robust approach to ensembling using an equally weighted median of all component forecasts is a good choice to support public health decision makers. In settings where some contributing forecasters have a stable record of good performance, trained ensembles that give those forecasters higher weight can also be helpful.

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

Forecasts 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 (preprint)

We report on the second and final part of a pre-registered forecasting study on COVID-19 cases and deaths in Germany and Poland. Fifteen independent research teams provided forecasts at lead times of one through four weeks from January through mid-April 2021. Compared to the first part (October--December 2020), the number of participating teams increased, and a number of teams started providing subnational-level forecasts. The addressed time period is characterized by rather stable non-pharmaceutical interventions in both countries, making short-term predictions more straightforward than in the first part of our study. In both countries, case counts declined initially, before rebounding due to the rise of the B.1.1.7 variant. Deaths declined through most of the study period in Germany while in Poland they increased after a prolonged plateau. Many, though not all, models outperformed a simple baseline model up to four weeks ahead, with ensemble methods showing very good relative performance. Major trend changes in reported cases, however, remained challenging to predict.

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

Background: Forecasting 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. Methods: We 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. Results: All 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. Conclusions: Assuming 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.

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

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 (preprint)

Background: Short-term forecasts of infectious disease can create situational awareness and inform 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. Methods: We 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 to ensemble forecasts using a simple mean as well as a quantile regression average that aimed to maximise performance. We further compared model performance to a null model of no change. Results: In 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. Conclusions: Ensembles 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 (preprint)

Background: To assess the viability of isolation and contact tracing to control onwards transmission from imported cases of 2019-nCoV. Methods: We 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. Findings: While 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. Interpretation: We 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.