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      Nonmechanistic forecasts of seasonal influenza with iterative one-week-ahead distributions

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          Abstract

          Accurate and reliable forecasts of seasonal epidemics of infectious disease can assist in the design of countermeasures and increase public awareness and preparedness. This article describes two main contributions we made recently toward this goal: a novel approach to probabilistic modeling of surveillance time series based on “delta densities”, and an optimization scheme for combining output from multiple forecasting methods into an adaptively weighted ensemble. Delta densities describe the probability distribution of the change between one observation and the next, conditioned on available data; chaining together nonparametric estimates of these distributions yields a model for an entire trajectory. Corresponding distributional forecasts cover more observed events than alternatives that treat the whole season as a unit, and improve upon multiple evaluation metrics when extracting key targets of interest to public health officials. Adaptively weighted ensembles integrate the results of multiple forecasting methods, such as delta density, using weights that can change from situation to situation. We treat selection of optimal weightings across forecasting methods as a separate estimation task, and describe an estimation procedure based on optimizing cross-validation performance. We consider some details of the data generation process, including data revisions and holiday effects, both in the construction of these forecasting methods and when performing retrospective evaluation. The delta density method and an adaptively weighted ensemble of other forecasting methods each improve significantly on the next best ensemble component when applied separately, and achieve even better cross-validated performance when used in conjunction. We submitted real-time forecasts based on these contributions as part of CDC’s 2015/2016 FluSight Collaborative Comparison. Among the fourteen submissions that season, this system was ranked by CDC as the most accurate.

          Author summary

          Seasonal influenza is associated with 250 000 to 500 000 deaths worldwide each year (WHO estimates). In the United States and other temperate regions, seasonal influenza epidemics occur annually, but their timing and intensity varies significantly; accurate and reliable forecasts that quantify their uncertainty can assist policymakers when planning countermeasures such as vaccination campaigns, and increase awareness and preparedness of hospitals and the general public. Starting with the 2013/2014 flu season, CDC has solicited, collected, evaluated, and compared weekly forecasts from external research groups. We developed a new method for forecasting flu surveillance data, which stitches together models of changes that happen each week, and a way of combining its output with other forecasts. The resulting forecasting system produced the most accurate forecasts in CDC’s 2015/2016 FluSight comparison of fourteen forecasting systems. We describe our new forecasting methods, analyze their performance in the 2015/2016 comparison and on data from previous seasons, and describe idiosyncrasies of epidemiological data that should be considered when constructing and evaluating forecasting systems.

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          Most cited references27

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            Using internet searches for influenza surveillance.

            The Internet is an important source of health information. Thus, the frequency of Internet searches may provide information regarding infectious disease activity. As an example, we examined the relationship between searches for influenza and actual influenza occurrence. Using search queries from the Yahoo! search engine ( http://search.yahoo.com ) from March 2004 through May 2008, we counted daily unique queries originating in the United States that contained influenza-related search terms. Counts were divided by the total number of searches, and the resulting daily fraction of searches was averaged over the week. We estimated linear models, using searches with 1-10-week lead times as explanatory variables to predict the percentage of cultures positive for influenza and deaths attributable to pneumonia and influenza in the United States. With use of the frequency of searches, our models predicted an increase in cultures positive for influenza 1-3 weeks in advance of when they occurred (P < .001), and similar models predicted an increase in mortality attributable to pneumonia and influenza up to 5 weeks in advance (P < .001). Search-term surveillance may provide an additional tool for disease surveillance.
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              Forecasting seasonal outbreaks of influenza.

              Influenza recurs seasonally in temperate regions of the world; however, our ability to predict the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited. Here we develop a framework for initializing real-time forecasts of seasonal influenza outbreaks, using a data assimilation technique commonly applied in numerical weather prediction. The availability of real-time, web-based estimates of local influenza infection rates makes this type of quantitative forecasting possible. Retrospective ensemble forecasts are generated on a weekly basis following assimilation of these web-based estimates for the 2003-2008 influenza seasons in New York City. The findings indicate that real-time skillful predictions of peak timing can be made more than 7 wk in advance of the actual peak. In addition, confidence in those predictions can be inferred from the spread of the forecast ensemble. This work represents an initial step in the development of a statistically rigorous system for real-time forecast of seasonal influenza.
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                Author and article information

                Contributors
                Role: InvestigationRole: MethodologyRole: VisualizationRole: Writing – original draft
                Role: InvestigationRole: MethodologyRole: VisualizationRole: Writing – review & editing
                Role: InvestigationRole: MethodologyRole: VisualizationRole: Writing – review & editing
                Role: InvestigationRole: MethodologyRole: VisualizationRole: Writing – review & editing
                Role: InvestigationRole: MethodologyRole: VisualizationRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                June 2018
                15 June 2018
                : 14
                : 6
                : e1006134
                Affiliations
                [1 ] School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
                [2 ] Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
                National Institutes of Health, UNITED STATES
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0003-0877-4978
                http://orcid.org/0000-0003-0377-897X
                http://orcid.org/0000-0002-2158-8304
                http://orcid.org/0000-0002-3274-5862
                Article
                PCOMPBIOL-D-17-00748
                10.1371/journal.pcbi.1006134
                6034894
                29906286
                0a505eb1-47ee-40c9-85e1-2adafbabf6e7
                © 2018 Brooks et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 12 May 2017
                : 10 April 2018
                Page count
                Figures: 7, Tables: 0, Pages: 29
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/100000057, National Institute of General Medical Sciences;
                Award ID: U54 GM088491
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000057, National Institute of General Medical Sciences;
                Award ID: U54 GM088491
                Award Recipient :
                Funded by: funder-id http://dx.doi.org/10.13039/100000001, National Science Foundation;
                Award ID: DGE-1252522
                Award Recipient :
                LCB, DCF, and RR were supported by the National Institute Of General Medical Sciences of the National Institutes of Health under Award Number U54 GM088491. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant Nos. 0946825, DGE-1252522, and DGE-1745016. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Statistical Methods
                Forecasting
                Physical Sciences
                Mathematics
                Statistics (Mathematics)
                Statistical Methods
                Forecasting
                Medicine and Health Sciences
                Infectious Diseases
                Viral Diseases
                Influenza
                Earth Sciences
                Seasons
                Medicine and Health Sciences
                Epidemiology
                Disease Surveillance
                Infectious Disease Surveillance
                Medicine and Health Sciences
                Infectious Diseases
                Infectious Disease Control
                Infectious Disease Surveillance
                Physical Sciences
                Mathematics
                Probability Theory
                Probability Distribution
                Physical Sciences
                Materials Science
                Material Properties
                Density
                Physical Sciences
                Materials Science
                Materials Physics
                Density
                Physical Sciences
                Physics
                Materials Physics
                Density
                Physical Sciences
                Mathematics
                Applied Mathematics
                Algorithms
                Kernel Methods
                Research and Analysis Methods
                Simulation and Modeling
                Algorithms
                Kernel Methods
                Computer and Information Sciences
                Information Technology
                Data Processing
                Custom metadata
                vor-update-to-uncorrected-proof
                2018-07-06
                The latest ILINet report is available from a Fluview Interactive web module ( https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html). Past ILINet reports (in addition to the latest one) are available from our delphi-epidata API ( https://github.com/cmu-delphi/delphi-epidata). (Past and current Delphi-Stat, Delphi-Epicast, and Delphi-Archefilter forecasts, as well as ILI-Nearby nowcasts, are also available from our delphi-epidata API ( https://github.com/cmu-delphi/delphi-epidata).)

                Quantitative & Systems biology
                Quantitative & Systems biology

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