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We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse set of skills in data science and applied statistics. We describe the context and aims of the course, and discuss design parameters like the selection of target variables, the forecast submission process, the evaluation of forecast performance, and the feedback provided to students. Furthermore, we describe empirical properties of students' probabilistic forecasts, as well as some lessons learned on our part. [ABSTRACT FROM AUTHOR]

In many forecasting settings, there is a specific interest in predicting the sign of an outcome variable correctly in addition to its magnitude. For instance, when forecasting armed conflicts, positive and negative log-changes in monthly fatalities represent escalation and de-escalation, respectively, and have very different implications. In the ViEWS forecasting challenge, a prediction competition on state-based violence, a novel evaluation score called targeted absolute deviation with direction augmentation (TADDA) has therefore been suggested, which accounts for both for the sign and magnitude of log-changes. While it has a straightforward intuitive motivation, the empirical results of the challenge show that a no-change model always predicting a log-change of zero outperforms all submitted forecasting models under the TADDA score. We provide a statistical explanation for this phenomenon. Analyzing the properties of TADDA, we find that in order to achieve good scores, forecasters often have an incentive to predict no or only modest log-changes. In particular, there is often an incentive to report conservative point predictions considerably closer to zero than the forecaster's actual predictive median or mean. In an empirical application, we demonstrate that a no-change model can be improved upon by tailoring predictions to the particularities of the TADDA score. We conclude by outlining some alternative scoring concepts. [ABSTRACT FROM AUTHOR]

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic‐epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model‐based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time‐varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany. [ABSTRACT FROM AUTHOR]

The article reports that the epidemiological modeling has been in the public eye since the beginning of the COVID-19 pandemic and has significantly influenced political decisions. Topics include considered that in addition to retrospective classifications and long-term scenario forecasts, they can also be used to forecast short-term trends.

In subsection 3.2 two example values of the weighted interval score (a score for forecast accuracy described in the paper) were incorrect. Logarithmic score, absolute error, interval score (with = 0.2), CRPS, and 2 versions of the weighted interval score. [Extracted from the article]

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. Author summary: During the COVID-19 pandemic, model-based probabilistic forecasts of case, hospitalization, and death numbers can help to improve situational awareness and guide public health interventions. The COVID-19 Forecast Hub (https://covid19forecasthub.org/) collects such forecasts from numerous national and international groups. Systematic and statistically sound evaluation of forecasts is an important prerequisite to revise and improve models and to combine different forecasts into ensemble predictions. We provide an intuitive introduction to scoring methods, which are suitable for the interval/quantile-based format used in the Forecast Hub, and compare them to other commonly used performance measures. [ABSTRACT FROM AUTHOR]

Introduction The impact of outdoor air pollution exposure on long-term lung development and potential periods of increased lung susceptibility remain unknown. This study assessed associations between early-life and current residential exposure to air pollution and lung function at 15-years of age in two German birth cohorts. Methods Fifteen year-old participants living in an urban and rural area in Germany underwent spirometry before and after bronchodilation ( N = 2266). Annual average (long-term) exposure to nitrogen dioxide (NO 2 ), particles with aerodynamic diameters less than 2.5 μg/m 3 (PM 2.5 ) mass and less than 10 μg/m 3 (PM 10 ) mass, PM 2.5 absorbance and ozone were estimated to each participant's birth-, 10- and 15-year home address using land-use regression and kriging (ozone only) modelling. Associations between lung function variables and long-term pollutant concentrations were assessed using linear regression models adjusted for host and environmental covariates and recent short-term air pollution exposures. Results Long-term air pollution concentrations assessed to the birth-, 10- and 15-year home addresses were not associated with lung function variables, before and after bronchodilation, in the complete or study area specific populations. However, several lung function variables were negatively associated with long-term NO 2 concentrations among asthmatics. For example, NO 2 estimated to the 15-year home address was associated with the ratio of forced expiratory volume in one second to forced vital capacity (FEV 1 /FVC) and the mean flow rate between 25% and 75% of FVC (−3.5%, 95% confidence interval [−6.0, −1.0] and −297.4 ml/s [−592.6, −2.1] per 5.9 μg/m 3 increase in NO 2 , respectively). Nearly all effect estimates for the associations between the short-term PM 2.5 mass, PM 10 mass and ozone concentrations and the lung function variables were negative in the complete population. Conclusions Early-life and current long-term air pollution exposures and lung function at the age of 15 years were not associated in the complete study population. Asthmatics may represent a vulnerable group. [ABSTRACT FROM AUTHOR]

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. Author Summary: Mathematical models of COVID-19 have played a key role in informing governments across the world. While mathematical models are informed by our knowledge of infectious disease dynamics, they are ultimately developed and iteratively adjusted by the researchers and shaped by their subjective opinions. To investigate what modelling is able to add beyond the subjective opinion of the researcher alone, we compared human forecasts with model-based predictions of COVID-19 cases and deaths submitted to the so-called German/Polish Forecast Hub (which collates a variety of models from a range of teams). | We found that our human forecasts consistently outperformed an aggregate of all available model-based forecasts when predicting cases, but not when predicting deaths. Our findings suggest that human insight may be most valuable when forecasting highly uncertain quantities, which depend on many factors that are hard to model using equations, while mathematical models may be most useful in settings like predicting deaths, where leading indicators with a clear connection to the target variable are available. This potentially has very relevant policy implications, as agencies informing policy-makers could benefit from routinely eliciting human forecasts in addition to model-based predictions to inform policies. [ABSTRACT FROM AUTHOR]

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. Author summary: As SARS-CoV-2 began to spread throughout the world in early 2020, modelers played a critical role in predicting how the epidemic could take shape. Short-term forecasts of epidemic outcomes (for example, infections, cases, hospitalizations, or deaths) provided useful information to support pandemic planning, resource allocation, and intervention. Yet, infectious disease forecasting is still a nascent science, and the reliability of different types of forecasts is unclear. We retrospectively evaluated COVID-19 case forecasts, which were often unreliable. For example, forecasts did not anticipate the speed of increase in cases in early winter 2020. This analysis provides insights on specific problems that could be addressed in future research to improve forecasts and their use. Identifying the strengths and weaknesses of forecasts is critical to improving forecasting for current and future public health responses. [ABSTRACT FROM AUTHOR]

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates. Author summary: The effective reproductive number describes how many new infections an individual infected with a given disease causes on average in a population which is subject to a certain degree of immunity and intervention measures. Public health agencies and researchers commonly attempt to keep track of its value over time using various data sources and statistical methods. In this work we compare estimates produced by different research groups in a case study on COVID-19 in Germany. We find pronounced differences between different estimates and shed light on how these are shaped by varying analytical choices. Our results indicate that the employed statistical method has some influence on results, but surrounding analytical choices including epidemiological parameterizations and tuning parameter choices are at least as influential. As estimates are subject to regular updates, we moreover assess how strongly real-time estimates based on different methods were revised retrospectively. While for some methods hardly any retrospective changes occurred, for others there were strong revisions, often incoherent with the uncertainty intervals provided for previous estimates. Our results will be helpful for analysts aiming to set up estimation schemes for the effective reproductive number, and for users confronted with a multitude of potentially disagreeing estimates. [ABSTRACT FROM AUTHOR]

Forecast evaluation is essential for the development of predictive epidemic models and can inform their use for public health decision-making. Common scores to evaluate epidemiological forecasts are the Continuous Ranked Probability Score (CRPS) and the Weighted Interval Score (WIS), which can be seen as measures of the absolute distance between the forecast distribution and the observation. However, applying these scores directly to predicted and observed incidence counts may not be the most appropriate due to the exponential nature of epidemic processes and the varying magnitudes of observed values across space and time. In this paper, we argue that transforming counts before applying scores such as the CRPS or WIS can effectively mitigate these difficulties and yield epidemiologically meaningful and easily interpretable results. Using the CRPS on log-transformed values as an example, we list three attractive properties: Firstly, it can be interpreted as a probabilistic version of a relative error. Secondly, it reflects how well models predicted the time-varying epidemic growth rate. And lastly, using arguments on variance-stabilizing transformations, it can be shown that under the assumption of a quadratic mean-variance relationship, the logarithmic transformation leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. Applying a transformation of log(x + 1) to data and forecasts from the European COVID-19 Forecast Hub, we find that it changes model rankings regardless of stratification by forecast date, location or target types. Situations in which models missed the beginning of upward swings are more strongly emphasised while failing to predict a downturn following a peak is less severely penalised when scoring transformed forecasts as opposed to untransformed ones. We conclude that appropriate transformations, of which the natural logarithm is only one particularly attractive option, should be considered when assessing the performance of different models in the context of infectious disease incidence. Author summary: Scores like the Continuous Ranked Probability Score (CRPS) or the Weighted Interval Score (WIS) are commonly used to evaluate epidemiological forecasts and are a measure of absolute distance between forecast and observation. Due to the exponential nature of epidemic processes, evaluating the absolute distance between forecast and observation may not be ideal. We argue that transforming counts before applying the CRPS or WIS can yield more meaningful results. The natural logarithm is a particularly attractive transformation in epidemiological settings. Scores computed on log-transformed values can be interpreted as a probabilistic version of a relative error and reflect how well forecasters predict the time-varying epidemic growth rate. If the data-generating process has a quadratic mean-variance relationship, the logarithmic transformation also leads to expected CRPS values which are independent of the order of magnitude of the predicted quantity. We illustrate these properties using data from the European COVID-19 Forecast Hub and find that scoring transformed counts changes model rankings. Stronger emphasis is given to situations in which forecasters missed the beginning of upward swings, while failing to predict a downturn following a peak is less severely penalised. We generally recommend including evaluations of transformed counts when assessing forecaster performance. [ABSTRACT FROM AUTHOR]

Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges. Author summary: Current trends in epidemiological indicators are often obscured by the fact that recent values are still incomplete. This is due to reporting delays and other types of delays. Statistical nowcasting methods can be used to account for these biases and reveal yet unobserved trends, thereby improving situational awareness and supporting public health decision-making. While numerous methods exist for this purpose, little is known about their behavior in real-time settings and their relative performance. In this paper, we compared eight different nowcasting methods in an application to COVID-19 hospitalization incidences in Germany from November 2021 to April 2022. Additionally, we combined the predictions of these methods to create so-called ensemble nowcasts. Our findings indicate that while all methods yielded practically useful results, some systematic biases in nowcasts occurred and the remaining uncertainty was generally underestimated. Combined ensemble nowcasts showed promising performance relative to individual models and thus represent a promising avenue for future research. [ABSTRACT FROM AUTHOR]

Routine surveillance of notifiable infectious diseases gives rise to daily or weekly counts of reported cases stratified by region and age group. From a public health perspective, forecasts of infectious disease spread are of central importance. We argue that such forecasts need to properly incorporate the attached uncertainty, so they should be probabilistic in nature. However, forecasts also need to take into account temporal dependencies inherent to communicable diseases, spatial dynamics through human travel and social contact patterns between age groups. We describe a multivariate time series model for weekly surveillance counts on norovirus gastroenteritis from the 12 city districts of Berlin, in six age groups, from week 2011/27 to week 2015/26. The following year (2015/27 to 2016/26) is used to assess the quality of the predictions. Probabilistic forecasts of the total number of cases can be derived through Monte Carlo simulation, but first and second moments are also available analytically. Final size forecasts as well as multivariate forecasts of the total number of cases by age group, by district and by week are compared across different models of varying complexity. This leads to a more general discussion of issues regarding modelling, prediction and evaluation of public health surveillance data. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We use Mechanical Turk 's diverse participant pool to conduct online bargaining games in India and the US. First, we assess internal validity of crowdsourced experimentation through variation of stakes ($0, $1, $4, and $10) in the Ultimatum and Dictator Game. For cross-country equivalence we adjust the stakes following differences in purchasing power. Our marginal totals correspond closely to laboratory findings. Monetary incentives induce more selfish behavior but, in line with most laboratory findings, the particular size of a positive stake appears irrelevant. Second, by transporting a homogeneous decision situation into various living conditions crowdsourced experimentation permits identification of context effects on elicited behavior. We explore context-dependency using session-level variation in participants' geographical location, regional affluence, and local social capital. Across “virtual pools” behavior varies in the range of stake effects. We argue that quasi-experimental variation of the characteristics people bring to the experimental situation is the key potential of crowdsourced online designs. [ABSTRACT FROM AUTHOR]

The authors discuss the significance of collaboration in the development of modeling and data curation during the COVID-19 pandemic in the U.S.

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 multimodel ensemble forecast that combined predictions from dozens of 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 naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk 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. [ABSTRACT FROM AUTHOR]

Background: The elimination programme for visceral leishmaniasis (VL) in India has seen great progress, with total cases decreasing by over 80% since 2010 and many blocks now reporting zero cases from year to year. Prompt diagnosis and treatment is critical to continue progress and avoid epidemics in the increasingly susceptible population. Short-term forecasts could be used to highlight anomalies in incidence and support health service logistics. The model which best fits the data is not necessarily most useful for prediction, yet little empirical work has been done to investigate the balance between fit and predictive performance. Methodology/Principal findings: We developed statistical models of monthly VL case counts at block level. By evaluating a set of randomly-generated models, we found that fit and one-month-ahead prediction were strongly correlated and that rolling updates to model parameters as data accrued were not crucial for accurate prediction. The final model incorporated auto-regression over four months, spatial correlation between neighbouring blocks, and seasonality. Ninety-four percent of 10-90% prediction intervals from this model captured the observed count during a 24-month test period. Comparison of one-, three- and four-month-ahead predictions from the final model fit demonstrated that a longer time horizon yielded only a small sacrifice in predictive power for the vast majority of blocks. Conclusions/Significance: The model developed is informed by routinely-collected surveillance data as it accumulates, and predictions are sufficiently accurate and precise to be useful. Such forecasts could, for example, be used to guide stock requirements for rapid diagnostic tests and drugs. More comprehensive data on factors thought to influence geographic variation in VL burden could be incorporated, and might better explain the heterogeneity between blocks and improve uniformity of predictive performance. Integration of the approach in the management of the VL programme would be an important step to ensuring continued successful control. Author summary: This paper demonstrates a statistical modelling approach for forecasting of monthly visceral leishmaniasis (VL) incidence at block level in India, which could be used to tailor control efforts according to local estimates and monitor deviations from the currently decreasing trend. By fitting a variety of models to four years of historical data and assessing predictions within a further 24-month test period, we found that the model which best fit the observed data also showed the best predictive performance, and predictive accuracy was maintained when making rolling predictions up to four months ahead of the observed data. Since there is a two-month delay between reporting and processing of the data, predictive power more than three months ahead of current data is crucial to make forecasts which can feasibly be acted upon. Some heterogeneity remains in predictive power across the study region which could potentially be improved using unit-specific data on factors believed to be associated with reported VL incidence (e.g. age distribution, socio-economic status and climate). [ABSTRACT FROM AUTHOR]

Bats are strictly protected throughout Europe. They are a highly diverse order of mammals in terms of body size, body weight, migratory behaviour, trophic niche specialisation and habitat use. The latter ranges from urban areas and arable land to forest. Due to their low reproductive rate, environmental stressors can have a major impact on bat populations. Pesticides in particular are discussed as an important driver of bat population declines. In this work, we analysed nearly 400 animals of five different species (Eptesicus serotinus, Myotis myotis, Nyctalus noctula, Pipistrellus pipistrellus, and Plecotus auritus) from all over Germany for residues of 209 pesticides and persistent organic pollutants. Residue analysis was conducted with a previously developed method using a miniaturized quick, easy, cheap, effective, rugged and safe (QuEChERS) sample preparation and gas chromatography-tandem mass spectrometry for separation and detection. These analytical data were statistically correlated with the known data on the animals (e.g. age, sex, place and time of finding). Of 209 pesticides and pollutants investigated, 28 compounds were detected, the most frequent being organochlorine insecticides and polychlorinated biphenyls, which have been banned for decades by the Stockholm Convention on Persistent Organic Pollutants. Detection of more recent pesticides that were legally used for the last decade included azole antifungals and the insecticide fipronil. The bats contained between four and 25 different residues. Statistical data analyses showed that the distribution throughout Germany is largely comparable, and single exceptions were observed in specialized ecological niches. In conclusion, this work provides the largest dataset of pesticide and persistent organic pollutant residues in European bats to date. [Display omitted] • 209 contaminants in 387 animals of five different species were analysed. • The bats contained between four and 25 different residues. • p,p' -DDE and high chlorinated PCBs were found in all samples. • Contamination of bats is largely homogeneous throughout Germany. [ABSTRACT FROM AUTHOR]