During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub (https://covid19forecasthub.org). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1-4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

In subsection 3.2 two example values of the weighted interval score (a score for forecast accuracy described in the paper) were incorrect.The respective sentence should read:"The WIS (with K = 11 as in the previous section), on the other hand, favors G as its quantiles are generally closer to the observed value y (WIS(F, 190) = 105.3,WIS(G, 190) = 88.9)."These values had erroneously been given as (WIS(F, 190) = 103.9,WIS(G, 190) = 87.

From February to May 2020, experts in the modeling of infectious disease provided quantitative predictions and estimates of trends in the emerging COVID-19 pandemic in a series of 13 surveys. Data on existing transmission patterns were sparse when the pandemic began, but experts synthesized information available to them to provide quantitative, judgment-based assessments of the current and future state of the pandemic. We aggregated expert predictions into a single "linear pool" by taking an equally weighted average of their probabilistic statements. At a time when few computational models made public estimates or predictions about the pandemic, expert judgment provided (a) falsifiable predictions of short- and long-term pandemic outcomes related to reported COVID-19 cases, hospitalizations, and deaths, (b) estimates of latent viral transmission, and (c) counterfactual assessments of pandemic trajectories under different scenarios. The linear pool approach of aggregating expert predictions provided more consistently accurate predictions than any individual expert, although the predictive accuracy of a linear pool rarely provided the most accurate prediction. This work highlights the importance that an expert linear pool could play in flexibly assessing a wide array of risks early in future emerging outbreaks, especially in settings where available data cannot yet support data-driven computational modeling.

For practical reasons, many forecasts of case, hospitalization, and death counts in the context of the current Coronavirus Disease 2019 (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.

With an estimated $10.4 billion in medical costs and 31.4 million outpatient visits each year, influenza poses a serious burden of disease in the United States. To provide insights and advance warning into the spread of influenza, the U.S. Centers for Disease Control and Prevention (CDC) runs a challenge for forecasting weighted influenza-like illness (wILI) at the national and regional level. Many models produce independent forecasts for each geographical unit, ignoring the constraint that the national wILI is a weighted sum of regional wILI, where the weights correspond to the population size of the region. We propose a novel algorithm that transforms a set of independent forecast distributions to obey this constraint, which we refer to as probabilistically coherent. Enforcing probabilistic coherence led to an increase in forecast skill for 79% of the models we tested over multiple flu seasons, highlighting the importance of respecting the forecasting system's geographical hierarchy.

Seasonal influenza results in substantial annual morbidity and mortality in the United States and worldwide. Accurate forecasts of key features of influenza epidemics, such as the timing and severity of the peak incidence in a given season, can inform public health response to outbreaks. As part of ongoing efforts to incorporate data and advanced analytical methods into public health decision-making, the United States Centers for Disease Control and Prevention (CDC) has organized seasonal influenza forecasting challenges since the 2013/2014 season. In the 2017/2018 season, 22 teams participated. A subset of four teams created a research consortium called the FluSight Network in early 2017. During the 2017/2018 season they worked together to produce a collaborative multi-model ensemble that combined 21 separate component models into a single model using a machine learning technique called stacking. This approach creates a weighted average of predictive densities where the weight for each component is determined by maximizing overall ensemble accuracy over past seasons. In the 2017/2018 influenza season, one of the largest seasonal outbreaks in the last 15 years, this multi-model ensemble performed better on average than all individual component models and placed second overall in the CDC challenge. It also outperformed the baseline multi-model ensemble created by the CDC that took a simple average of all models submitted to the forecasting challenge. This project shows that collaborative efforts between research teams to develop ensemble forecasting approaches can bring measurable improvements in forecast accuracy and important reductions in the variability of performance from year to year. Efforts such as this, that emphasize real-time testing and evaluation of forecasting models and facilitate the close collaboration between public health officials and modeling researchers, are essential to improving our understanding of how best to use forecasts to improve public health response to seasonal and emerging epidemic threats.

Accurate and reliable predictions of infectious disease dynamics can be valuable to public health organizations that plan interventions to decrease or prevent disease transmission. A great variety of models have been developed for this task, using different model structures, covariates, and targets for prediction. Experience has shown that the performance of these models varies; some tend to do better or worse in different seasons or at different points within a season. Ensemble methods combine multiple models to obtain a single prediction that leverages the strengths of each model. We considered a range of ensemble methods that each form a predictive density for a target of interest as a weighted sum of the predictive densities from component models. In the simplest case, equal weight is assigned to each component model; in the most complex case, the weights vary with the region, prediction target, week of the season when the predictions are made, a measure of component model uncertainty, and recent observations of disease incidence. We applied these methods to predict measures of influenza season timing and severity in the United States, both at the national and regional levels, using three component models. We trained the models on retrospective predictions from 14 seasons (1997/1998-2010/2011) and evaluated each model's prospective, out-of-sample performance in the five subsequent influenza seasons. In this test phase, the ensemble methods showed average performance that was similar to the best of the component models, but offered more consistent performance across seasons than the component models. Ensemble methods offer the potential to deliver more reliable predictions to public health decision makers.