IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v77y2021i4p1202-1214.html
   My bibliography  Save this article

A marginal moment matching approach for fitting endemic‐epidemic models to underreported disease surveillance counts

Author

Listed:
  • Johannes Bracher
  • Leonhard Held

Abstract

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.

Suggested Citation

  • Johannes Bracher & Leonhard Held, 2021. "A marginal moment matching approach for fitting endemic‐epidemic models to underreported disease surveillance counts," Biometrics, The International Biometric Society, vol. 77(4), pages 1202-1214, December.
  • Handle: RePEc:bla:biomet:v:77:y:2021:i:4:p:1202-1214
    DOI: 10.1111/biom.13371
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13371
    Download Restriction: no

    File URL: https://libkey.io/10.1111/biom.13371?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    2. King, Aaron A. & Nguyen, Dao & Ionides, Edward L., 2016. "Statistical Inference for Partially Observed Markov Processes via the R Package pomp," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i12).
    3. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    4. Cici Bauer & Jon Wakefield, 2018. "Stratified space–time infectious disease modelling, with an application to hand, foot and mouth disease in China," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1379-1398, November.
    5. Staudenmayer, John & Buonaccorsi, John P., 2005. "Measurement Error in Linear Autoregressive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 841-852, September.
    6. Cui, Yunwei & Zheng, Qi, 2017. "Conditional maximum likelihood estimation for a class of observation-driven time series models for count data," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 193-201.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bracher, Johannes & Held, Leonhard, 2022. "Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1221-1233.
    2. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    3. Yunwei Cui & Rongning Wu & Qi Zheng, 2021. "Estimation of change‐point for a class of count time series models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1277-1313, December.
    4. Alexandre Petkovic & David Veredas, 2009. "Aggregation of linear models for panel data," Working Papers ECARES 2009-012, ULB -- Universite Libre de Bruxelles.
    5. Mamingi Nlandu, 2017. "Beauty and Ugliness of Aggregation over Time: A Survey," Review of Economics, De Gruyter, vol. 68(3), pages 205-227, December.
    6. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    7. Jon Michel, 2020. "The Limiting Distribution of a Non‐Stationary Integer Valued GARCH(1,1) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 351-356, March.
    8. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    9. Huiyu Mao & Fukang Zhu & Yan Cui, 2020. "A generalized mixture integer-valued GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 527-552, September.
    10. Heather Williams & Andrew Scharf & Anna R. Ryba & D. Ryan Norris & Daniel J. Mennill & Amy E. M. Newman & Stéphanie M. Doucet & Julie C. Blackwood, 2022. "Cumulative cultural evolution and mechanisms for cultural selection in wild bird songs," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    11. del Barrio Castro, Tomás & Rachinger, Heiko, 2021. "Aggregation of Seasonal Long-Memory Processes," Econometrics and Statistics, Elsevier, vol. 17(C), pages 95-106.
    12. Aknouche, Abdelhakim & Demouche, Nacer, 2018. "Ergodicity conditions for a double mixed Poisson autoregression," MPRA Paper 88843, University Library of Munich, Germany.
    13. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    14. Alexander, Carol & Rauch, Johannes, 2021. "A general property for time aggregation," European Journal of Operational Research, Elsevier, vol. 291(2), pages 536-548.
    15. Brajendra C. Sutradhar & R. Prabhakar Rao, 2016. "Inferences in Longitudinal Count Data Models with Measurement Errors in Time Dependent Covariates," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 39-65, May.
    16. Jung, Young Cheol & Das, Anupam & McFarlane, Adian, 2020. "The asymmetric relationship between the oil price and the US-Canada exchange rate," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 198-206.
    17. Youngmi Lee & Sangyeol Lee, 2019. "CUSUM test for general nonlinear integer-valued GARCH models: comparison study," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1033-1057, October.
    18. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    19. Götz, Thomas B. & Knetsch, Thomas A., 2019. "Google data in bridge equation models for German GDP," International Journal of Forecasting, Elsevier, vol. 35(1), pages 45-66.
    20. Tomas Havranek & Dominik Herman & Zuzana Irsova, 2018. "Does Daylight Saving Save Electricity? A Meta-Analysis," The Energy Journal, , vol. 39(2), pages 35-61, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:77:y:2021:i:4:p:1202-1214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.