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1. Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States

Author

Cramer, Estee Y, Ray, Evan L, Lopez, Velma K, Bracher, Johannes, Brennen, Andrea, Rivadeneira, Alvaro J Castro, Gerding, Aaron, Gneiting, Tilmann, House, Katie H, Huang, Yuxin, Jayawardena, Dasuni, Kanji, Abdul H, Khandelwal, Ayush, Le, Khoa, Mühlemann, Anja, Niemi, Jarad, Shah, Apurv, Stark, Ariane, Wang, Yijin, Wattanachit, Nutcha, Zorn, Martha W, Gu, Youyang, Jain, Sansiddh, Bannur, Nayana, Deva, Ayush, Kulkarni, Mihir, Merugu, Srujana, Raval, Alpan, Shingi, Siddhant, Tiwari, Avtansh, White, Jerome, Abernethy, Neil F, Woody, Spencer, Dahan, Maytal, Fox, Spencer, Gaither, Kelly, Lachmann, Michael, Meyers, Lauren Ancel, Scott, James G, Tec, Mauricio, Srivastava, Ajitesh, George, Glover E, Cegan, Jeffrey C, Dettwiller, Ian D, England, William P, Farthing, Matthew W, Hunter, Robert H, Lafferty, Brandon, Linkov, Igor, Mayo, Michael L, Parno, Matthew D, Rowland, Michael A, Trump, Benjamin D, Zhang-James, Yanli, Chen, Samuel, Faraone, Stephen V, Hess, Jonathan, Morley, Christopher P, Salekin, Asif, Wang, Dongliang, Corsetti, Sabrina M, Baer, Thomas M, Eisenberg, Marisa C, Falb, Karl, Huang, Yitao, Martin, Emily T, McCauley, Ella, Myers, Robert L, Schwarz, Tom, Sheldon, Daniel, Gibson, Graham Casey, Yu, Rose, Gao, Liyao, Ma, Yian, Wu, Dongxia, Yan, Xifeng, Jin, Xiaoyong, Wang, Yu-Xiang, Chen, YangQuan, Guo, Lihong, Zhao, Yanting, Gu, Quanquan, Chen, Jinghui, Wang, Lingxiao, Xu, Pan, Zhang, Weitong, Zou, Difan, Biegel, Hannah, Lega, Joceline, McConnell, Steve, Nagraj, VP, Guertin, Stephanie L, Hulme-Lowe, Christopher, Turner, Stephen D, Shi, Yunfeng, Ban, Xuegang, Walraven, Robert, Hong, Qi-Jun, Kong, Stanley, and van de Walle, Axel

Subjects
Bioengineering, Good Health and Well Being, COVID-19, Data Accuracy, Forecasting, Humans, Pandemics, Probability, Public Health, United States, forecasting, ensemble forecast, model evaluation
Abstract

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.

Published
2022

3. The United States COVID-19 Forecast Hub dataset

Author

US COVID-19 Forecast Hub Consortium, Cramer, Estee Y., Huang, Yuxin, Wang, Yijin, Ray, Evan L., Cornell, Matthew, Bracher, Johannes, Brennen, Andrea, Rivadeneira, Alvaro J. Castro, Gerding, Aaron, House, Katie, Jayawardena, Dasuni, Kanji, Abdul Hannan, Khandelwal, Ayush, Le, Khoa, Mody, Vidhi, Mody, Vrushti, Niemi, Jarad, Stark, Ariane, Shah, Apurv, Wattanchit, Nutcha, Zorn, Martha W., Reich, Nicholas G., Gneiting, Tilmann, Mühlemann, Anja, Gu, Youyang, Chen, Yixian, Chintanippu, Krishna, Jivane, Viresh, Khurana, Ankita, Kumar, Ajay, Lakhani, Anshul, Mehrotra, Prakhar, Pasumarty, Sujitha, Shrivastav, Monika, You, Jialu, Bannur, Nayana, Deva, Ayush, Jain, Sansiddh, Kulkarni, Mihir, Merugu, Srujana, Raval, Alpan, Shingi, Siddhant, Tiwari, Avtansh, White, Jerome, Adiga, Aniruddha, Hurt, Benjamin, Lewis, Bryan, Marathe, Madhav, Peddireddy, Akhil Sai, Porebski, Przemyslaw, Venkatramanan, Srinivasan, Wang, Lijing, Dahan, Maytal, Fox, Spencer, Gaither, Kelly, Lachmann, Michael, Meyers, Lauren Ancel, Scott, James G., Tec, Mauricio, Woody, Spencer, Srivastava, Ajitesh, Xu, Tianjian, Cegan, Jeffrey C., Dettwiller, Ian D., England, William P., Farthing, Matthew W., George, Glover E., Hunter, Robert H., Lafferty, Brandon, Linkov, Igor, Mayo, Michael L., Parno, Matthew D., Rowland, Michael A., Trump, Benjamin D., Chen, Samuel, Faraone, Stephen V., Hess, Jonathan, Morley, Christopher P., Salekin, Asif, Wang, Dongliang, Zhang-James, Yanli, Baer, Thomas M., Corsetti, Sabrina M., Eisenberg, Marisa C., Falb, Karl, Huang, Yitao, Martin, Emily T., McCauley, Ella, Myers, Robert L., Schwarz, Tom, Gibson, Graham Casey, Sheldon, Daniel, Gao, Liyao, Ma, Yian, Wu, Dongxia, Yu, Rose, Jin, Xiaoyong, Wang, Yu-Xiang, Yan, Xifeng, Chen, YangQuan, Guo, Lihong, Zhao, Yanting, Chen, Jinghui, Gu, Quanquan, Wang, Lingxiao, Xu, Pan, Zhang, Weitong, Zou, Difan, Chattopadhyay, Ishanu, Huang, Yi, Lu, Guoqing, Pfeiffer, Ruth, Sumner, Timothy, Wang, Dongdong, Wang, Liqiang, Zhang, Shunpu, Zou, Zihang, Biegel, Hannah, Lega, Joceline, Hussain, Fazle, Khan, Zeina, Van Bussel, Frank, McConnell, Steve, Guertin, Stephanie L., Hulme-Lowe, Christopher, Nagraj, V. P., Turner, Stephen D., Bejar, Benjamín, Choirat, Christine, Flahault, Antoine, Krymova, Ekaterina, Lee, Gavin, Manetti, Elisa, Namigai, Kristen, Obozinski, Guillaume, Sun, Tao, Thanou, Dorina, Ban, Xuegang, Shi, Yunfeng, Walraven, Robert, Hong, Qi-Jun, Van De Walle, Axel, Ben-Nun, Michal, Riley, Steven, Riley, Pete, Turtle, James, Cao, Duy, Galasso, Joseph, Cho, Jae H., Jo, Areum, DesRoches, David, Forli, Pedro, Hamory, Bruce, Koyluoglu, Ugur, Kyriakides, Christina, Leis, Helen, Milliken, John, Moloney, Michael, Morgan, James, Nirgudkar, Ninad, Ozcan, Gokce, Piwonka, Noah, Ravi, Matt, Schrader, Chris, Shakhnovich, Elizabeth, Siegel, Daniel, Spatz, Ryan, Stiefeling, Chris, Wilkinson, Barrie, Wong, Alexander, Cavany, Sean, España, Guido, Moore, Sean, Oidtman, Rachel, Perkins, Alex, Ivy, Julie S., Mayorga, Maria E., Mele, Jessica, Rosenstrom, Erik T., Swann, Julie L., Kraus, Andrea, Kraus, David, Bian, Jiang, Cao, Wei, Gao, Zhifeng, Ferres, Juan Lavista, Li, Chaozhuo, Liu, Tie-Yan, Xie, Xing, Zhang, Shun, Zheng, Shun, Chinazzi, Matteo, Vespignani, Alessandro, Xiong, Xinyue, Davis, Jessica T., Mu, Kunpeng, Piontti, Ana Pastore Y, Baek, Jackie, Farias, Vivek, Georgescu, Andreea, Levi, Retsef, Sinha, Deeksha, Wilde, Joshua, Zheng, Andrew, Lami, Omar Skali, Bennouna, Amine, Ndong, David Nze, Perakis, Georgia, Singhvi, Divya, Spantidakis, Ioannis, Thayaparan, Leann, Tsiourvas, Asterios, Weisberg, Shane, Jadbabaie, Ali, Sarker, Arnab, Shah, Devavrat, Celi, Leo A., Penna, Nicolas D., Sundar, Saketh, Berlin, Abraham, Gandhi, Parth D., McAndrew, Thomas, Piriya, Matthew, Chen, Ye, Hlavacek, William, Lin, Yen Ting, Mallela, Abhishek, Miller, Ely, Neumann, Jacob, Posner, Richard, Wolfinger, Russ, Castro, Lauren, Fairchild, Geoffrey, Michaud, Isaac, Osthus, Dave, Wolffram, Daniel, Karlen, Dean, Panaggio, Mark J., Kinsey, Matt, Mullany, Luke C., Rainwater-Lovett, Kaitlin, Shin, Lauren, Tallaksen, Katharine, Wilson, Shelby, Brenner, Michael, Coram, Marc, Edwards, Jessie K., Joshi, Keya, Klein, Ellen, Hulse, Juan Dent, Grantz, Kyra H., Hill, Alison L., Kaminsky, Kathryn, Kaminsky, Joshua, Keegan, Lindsay T., Lauer, Stephen A., Lee, Elizabeth C., Lemaitre, Joseph C., Lessler, Justin, Meredith, Hannah R., Perez-Saez, Javier, Shah, Sam, Smith, Claire P., Truelove, Shaun A., Wills, Josh, Gardner, Lauren, Marshall, Maximilian, Nixon, Kristen, Burant, John C., Budzinski, Jozef, Chiang, Wen-Hao, Mohler, George, Gao, Junyi, Glass, Lucas, Qian, Cheng, Romberg, Justin, Sharma, Rakshith, Spaeder, Jeffrey, Sun, Jimeng, Xiao, Cao, Gao, Lei, Gu, Zhiling, Kim, Myungjin, Li, Xinyi, Wang, Yueying, Wang, Guannan, Wang, Lily, Yu, Shan, Jain, Chaman, Bhatia, Sangeeta, Nouvellet, Pierre, Barber, Ryan, Gaikedu, Emmanuela, Hay, Simon, Lim, Steve, Murray, Chris, Pigott, David, Reiner, Robert C., Baccam, Prasith, Gurung, Heidi L., Stage, Steven A., Suchoski, Bradley T., Fong, Chung-Yan, Yeung, Dit-Yan, Adhikari, Bijaya, Cui, Jiaming, Prakash, B. Aditya, Rodríguez, Alexander, Tabassum, Anika, Xie, Jiajia, Asplund, John, Baxter, Arden, Keskinocak, Pinar, Oruc, Buse Eylul, Serban, Nicoleta, Arik, Sercan O., Dusenberry, Mike, Epshteyn, Arkady, Kanal, Elli, Le, Long T., Li, Chun-Liang, Pfister, Tomas, Sinha, Rajarishi, Tsai, Thomas, Yoder, Nate, Yoon, Jinsung, Zhang, Leyou, Wilson, Daniel, Belov, Artur A., Chow, Carson C., Gerkin, Richard C., Yogurtcu, Osman N., Ibrahim, Mark, Lacroix, Timothee, Le, Matthew, Liao, Jason, Nickel, Maximilian, Sagun, Levent, Abbott, Sam, Bosse, Nikos I., Funk, Sebastian, Hellewell, Joel, Meakin, Sophie R., Sherratt, Katharine, Kalantari, Rahi, Zhou, Mingyuan, Karimzadeh, Morteza, Lucas, Benjamin, Ngo, Thoai, Zoraghein, Hamidreza, Vahedi, Behzad, Wang, Zhongying, Pei, Sen, Shaman, Jeffrey, Yamana, Teresa K., Bertsimas, Dimitris, Li, Michael L., Soni, Saksham, Bouardi, Hamza Tazi, Adee, Madeline, Ayer, Turgay, Chhatwal, Jagpreet, Dalgic, Ozden O., Ladd, Mary A., Linas, Benjamin P., Mueller, Peter, Xiao, Jade, Bosch, Jurgen, Wilson, Austin, Zimmerman, Peter, Wang, Qinxia, Wang, Yuanjia, Xie, Shanghong, Zeng, Donglin, Bien, Jacob, Brooks, Logan, Green, Alden, Hu, Addison J., Jahja, Maria, McDonald, Daniel, Narasimhan, Balasubramanian, Politsch, Collin, Rajanala, Samyak, Rumack, Aaron, Simon, Noah, Tibshirani, Ryan J., Tibshirani, Rob, Ventura, Valerie, Wasserman, Larry, Drake, John M., O’Dea, Eamon B., Abu-Mostafa, Yaser, Bathwal, Rahil, Chang, Nicholas A., Chitta, Pavan, Erickson, Anne, Goel, Sumit, Gowda, Jethin, Jin, Qixuan, Jo, HyeongChan, Kim, Juhyun, Kulkarni, Pranav, Lushtak, Samuel M., Mann, Ethan, Popken, Max, Soohoo, Connor, Tirumala, Kushal, Tseng, Albert, Varadarajan, Vignesh, Vytheeswaran, Jagath, Wang, Christopher, Yeluri, Akshay, Yurk, Dominic, Zhang, Michael, Zlokapa, Alexander, Pagano, Robert, Jain, Chandini, Tomar, Vishal, Ho, Lam, Huynh, Huong, Tran, Quoc, Lopez, Velma K., Walker, Jo W., Slayton, Rachel B., Johansson, Michael A., and Biggerstaff, Matthew

Subjects
ddc:510, Mathematics
Abstract

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 cases, incident hospitalizations, incident deaths, and cumulative deaths due to COVID-19 at county, state, and national, 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.

Published
2022

4. Isotonic regression for elicitable functionals and their Bayes risk

Author

Mühlemann, Anja and Ziegel, Johanna F.

Subjects
Statistics and Probability, 510 Mathematics, 510 Mathematik, Statistics, Probability and Uncertainty
Abstract

We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and (Value-at-Risk, Expected Shortfall), where the latter pair consists of important risk measures in finance. We present our results for totally ordered covariates but extenstions to partial orders are given in the appendix.

Published
2022
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6. The Role of Loss Functions in Regression Problems

Author

Mühlemann, Anja

Subjects
510 Mathematics
Abstract

In regression analysis, the goal is to capture the influence of one or more explanatory variables X1, . . . ,Xm on a response variable Y in terms of a regression function g : Rm -> R. An estimate ĝ of g is then found or evaluated in terms of its ability to predict a prespecified statistical functional T of the conditional distribution L(Y |X1, . . . ,Xm). This is done with the help of a loss function that penalizes estimates that perform poorly in predicting T(L(Y |X1, . . . ,Xm)). More precisely, it is done by using loss functions that are consistent for T. Clearly, the outcome of the evaluation or estimation strongly depends on the functional T. However, when we focus on a specific functional T a vast collection of suitable loss functions may be available and the result can still be sensitive to the choice of loss function. There are several viable solution strategies to approach this issue. We can, for instance, impose additional properties on the loss function or the resulting estimate so that only one of the possible loss functions remains reasonable. In this doctoral thesis we adopt another approach. The underlying idea is that we would naturally prefer an estimate ĝ that is optimal with respect to several consistent loss functions for T, as then the choice of loss function seems to impact the outcome less severely. In Chapter 1, we consider the nonparametric isotonic regression problem. We show that this regression problem is special in that for identifiable functionals T, solutions which are simultaneously optimal with respect to an entire class of consistent losses exist and can be characterized. There are, however, several functionals of interest that are not identifiable. The expected shortfall is just one prominent example. However, some of those functionals can be obtained as a function of a vector-valued elicitable functional. In the second Chapter, we investigate when simultaneous optimality with respect to a class of consistent losses holds for these functionals and introduce the solution to the isotonic regression problem for a specific loss in the case where simultaneous optimality is not fulfilled. In parametric regression, on the other hand, different consistent loss functions often yield different parameter estimates under misspecification. This motivates to consider the set of these parameters as a way to measure misspecification. We introduce this approach in Chapter 3 and show how the set of these model parameters can be calculated on the population and on the sample level for an isotonic regression function g.

Published
2021
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8. Challenges of COVID-19 Case Forecasting in the US, 2020-2021.

Author

Lopez VK, Cramer EY, Pagano R, Drake JM, O'Dea EB, Adee M, Ayer T, Chhatwal J, Dalgic OO, Ladd MA, Linas BP, Mueller PP, Xiao J, Bracher J, Castro Rivadeneira AJ, Gerding A, Gneiting T, Huang Y, Jayawardena D, Kanji AH, Le K, Mühlemann A, Niemi J, Ray EL, Stark A, Wang Y, Wattanachit N, Zorn MW, Pei S, Shaman J, Yamana TK, Tarasewicz SR, Wilson DJ, Baccam S, Gurung H, Stage S, Suchoski B, Gao L, Gu Z, Kim M, Li X, Wang G, Wang L, Wang Y, Yu S, Gardner L, Jindal S, Marshall M, Nixon K, Dent J, Hill AL, Kaminsky J, Lee EC, Lemaitre JC, Lessler J, Smith CP, Truelove S, Kinsey M, Mullany LC, Rainwater-Lovett K, Shin L, Tallaksen K, Wilson S, Karlen D, Castro L, Fairchild G, Michaud I, Osthus D, Bian J, Cao W, Gao Z, Lavista Ferres J, Li C, Liu TY, Xie X, Zhang S, Zheng S, Chinazzi M, Davis JT, Mu K, Pastore Y Piontti A, Vespignani A, Xiong X, Walraven R, Chen J, Gu Q, Wang L, Xu P, Zhang W, Zou D, Gibson GC, Sheldon D, Srivastava A, Adiga A, Hurt B, Kaur G, Lewis B, Marathe M, Peddireddy AS, Porebski P, Venkatramanan S, Wang L, Prasad PV, Walker JW, Webber AE, Slayton RB, Biggerstaff M, Reich NG, and Johansson MA

Subjects
Humans, United States epidemiology, Computational Biology, Models, Statistical, COVID-19 epidemiology, COVID-19 transmission, Forecasting methods, SARS-CoV-2, Pandemics statistics & numerical data
Abstract

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., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: APP report grants from Metabiota Inc outside the submitted work. J.S. and Columbia University declare partial ownership of SK Analytics. No other authors have competing interests to declare., (Copyright: This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.)

Published
2024
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