Evaluating infectious disease forecasts with allocation scoring rules (preprint)

Recent years have seen increasing efforts to forecast infectious disease burdens, with a primary goal being to help public health workers make informed policy decisions. However, there has only been limited discussion of how predominant forecast evaluation metrics might indicate the success of policies based in part on those forecasts. We explore one possible tether between forecasts and policy: the allocation of limited medical resources so as to minimize unmet need. We use probabilistic forecasts of disease burden in each of several regions to determine optimal resource allocations, and then we score forecasts according to how much unmet need their associated allocations would have allowed. We illustrate with forecasts of COVID-19 hospitalizations in the US, and we find that the forecast skill ranking given by this allocation scoring rule can vary substantially from the ranking given by the weighted interval score. We see this as evidence that the allocation scoring rule detects forecast value that is missed by traditional accuracy measures and that the general strategy of designing scoring rules that are directly linked to policy performance is a promising direction for epidemic forecast evaluation.

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.

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.

The United States COVID-19 Forecast Hub dataset (preprint)

Academic researchers, government agencies, industry groups, and individuals have produced forecasts at an unprecedented scale during the COVID-19 pandemic. To leverage these forecasts, the United States Centers for Disease Control and Prevention (CDC) partnered with an academic research lab at the University of Massachusetts Amherst to create the US COVID-19 Forecast Hub. Launched in April 2020, the Forecast Hub is a dataset with point and probabilistic forecasts of incident hospitalizations, incident cases, incident deaths, and cumulative deaths due to COVID-19 at national, state, and county levels in the United States. Included forecasts represent a variety of modeling approaches, data sources, and assumptions regarding the spread of COVID-19. The goal of this dataset is to establish a standardized and comparable set of short-term forecasts from modeling teams. These data can be used to develop ensemble models, communicate forecasts to the public, create visualizations, compare models, and inform policies regarding COVID-19 mitigation. These open-source data are available via download from GitHub, through an online API, and through R packages.

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

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. In 2020, the COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized hundreds of thousands of specific predictions from more than 50 different academic, industry, and independent research groups. This manuscript systematically evaluates 23 models that regularly submitted forecasts of reported weekly incident COVID-19 mortality counts in the US at the state and national level. One of these models was a multi-model ensemble that combined all available forecasts each week. The performance of individual models showed high variability across time, geospatial units, and forecast horizons. Half of the models evaluated showed better accuracy than a naive baseline model. In combining the forecasts from all teams, the ensemble showed the best overall probabilistic accuracy of any model. Forecast accuracy degraded as models made predictions farther into the future, with probabilistic accuracy at a 20-week horizon more than 5 times worse 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. f

Ensemble Forecasts of Coronavirus Disease 2019 (COVID-19) in the U.S. (preprint)

Background The COVID-19 pandemic has driven demand for forecasts to guide policy and planning. Previous research has suggested that combining forecasts from multiple models into a single "ensemble" forecast can increase the robustness of forecasts. Here we evaluate the real-time application of an open, collaborative ensemble to forecast deaths attributable to COVID-19 in the U.S. Methods Beginning on April 13, 2020, we collected and combined one- to four-week ahead forecasts of cumulative deaths for U.S. jurisdictions in standardized, probabilistic formats to generate real-time, publicly available ensemble forecasts. We evaluated the point prediction accuracy and calibration of these forecasts compared to reported deaths. Results Analysis of 2,512 ensemble forecasts made April 27 to July 20 with outcomes observed in the weeks ending May 23 through July 25, 2020 revealed precise short-term forecasts, with accuracy deteriorating at longer prediction horizons of up to four weeks. At all prediction horizons, the prediction intervals were well calibrated with 92-96% of observations falling within the rounded 95% prediction intervals. Conclusions This analysis demonstrates that real-time, publicly available ensemble forecasts issued in April-July 2020 provided robust short-term predictions of reported COVID-19 deaths in the United States. With the ongoing need for forecasts of impacts and resource needs for the COVID-19 response, the results underscore the importance of combining multiple probabilistic models and assessing forecast skill at different prediction horizons. Careful development, assessment, and communication of ensemble forecasts can provide reliable insight to public health decision makers.

The Zoltar forecast archive: a tool to facilitate standardization and storage of interdisciplinary prediction research (preprint)

Forecasting has emerged as an important component of informed, data-driven decision-making in a wide array of fields. We introduce a new data model for probabilistic predictions that encompasses a wide range of forecasting settings. This framework clearly defines the constituent parts of a probabilistic forecast and proposes one approach for representing these data elements. The data model is implemented in Zoltar, a new software application that stores forecasts using the data model and provides standardized API access to the data. In one real-time case study, an instance of the Zoltar web application was used to store, provide access to, and evaluate real-time forecast data on the order of 10$^7$ rows, provided by over 20 international research teams from academia and industry making forecasts of the COVID-19 outbreak in the US. Tools and data infrastructure for probabilistic forecasts, such as those introduced here, will play an increasingly important role in ensuring that future forecasting research adheres to a strict set of rigorous and reproducible standards.

Evaluating epidemic forecasts in an interval format (preprint)

For practical reasons, many forecasts of case, hospitalization and death counts in the context of the current COVID-19 pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation of quantile and interval forecasts can be applied to epidemic forecasts in this format. Specifically, we discuss the computation and interpretation of the weighted interval score, which is a proper score that approximates the continuous ranked probability score. It can be interpreted as a generalization of the absolute error to probabilistic forecasts and allows for a decomposition into a measure of sharpness and penalties for over- and underprediction.