IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i4p3954-3967.html
   My bibliography  Save this article

A proportional incidence rate model for aggregated data to study the vaccine effectiveness against COVID‐19 hospital and ICU admissions

Author

Listed:
  • Ping Yan
  • Muhammad Abu Shadeque Mullah
  • Ashleigh Tuite

Abstract

We develop a proportional incidence model that estimates vaccine effectiveness (VE) at the population level using conditional likelihood for aggregated data. Our model assumes that the population counts of clinical outcomes for an infectious disease arise from a superposition of Poisson processes with different vaccination statuses. The intensity function in the model is calculated as the product of per capita incidence rate and the at‐risk population size, both of which are time‐dependent. We formulate a log‐linear regression model with respect to the relative risk, defined as the ratio between the per capita incidence rates of vaccinated and unvaccinated individuals. In the regression analysis, we treat the baseline incidence rate as a nuisance parameter, similar to the Cox proportional hazard model in survival analysis. We then apply the proposed models and methods to age‐stratified weekly counts of COVID‐19–related hospital and ICU admissions among adults in Ontario, Canada. The data spanned from 2021 to February 2022, encompassing the Omicron era and the rollout of booster vaccine doses. We also discuss the limitations and confounding effects while advocating for the necessity of more comprehensive and up‐to‐date individual‐level data that document the clinical outcomes and measure potential confounders.

Suggested Citation

  • Ping Yan & Muhammad Abu Shadeque Mullah & Ashleigh Tuite, 2023. "A proportional incidence rate model for aggregated data to study the vaccine effectiveness against COVID‐19 hospital and ICU admissions," Biometrics, The International Biometric Society, vol. 79(4), pages 3954-3967, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3954-3967
    DOI: 10.1111/biom.13915
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13915
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13915?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. Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
    2. Simon N. Wood, 2003. "Thin plate regression splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 95-114, February.
    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. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, Universität Innsbruck.
    2. Paul Ghelasi & Florian Ziel, 2024. "From day-ahead to mid and long-term horizons with econometric electricity price forecasting models," Papers 2406.00326, arXiv.org, revised Aug 2024.
    3. Valtiala, Juho & Niskanen, Olli & Torvinen, Mikael & Riekkinen, Kirsikka & Suokannas, Antti, 2023. "The relationship between agricultural land parcel size and cultivation costs," Land Use Policy, Elsevier, vol. 131(C).
    4. David C. Broadstock & Shunsuke Managi & Roman Matousek & Nickolaos G. Tzeremes, 2019. "Does doing “good” always translate into doing “well”? An eco‐efficiency perspective," Business Strategy and the Environment, Wiley Blackwell, vol. 28(6), pages 1199-1217, September.
    5. Longhi, Christian & Musolesi, Antonio & Baumont, Catherine, 2014. "Modeling structural change in the European metropolitan areas during the process of economic integration," Economic Modelling, Elsevier, vol. 37(C), pages 395-407.
    6. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    7. Musolesi Antonio & Mazzanti Massimiliano, 2014. "Nonlinearity, heterogeneity and unobserved effects in the carbon dioxide emissions-economic development relation for advanced countries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 521-541, December.
    8. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    9. Paciorek, Christopher J., 2007. "Computational techniques for spatial logistic regression with large data sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3631-3653, May.
    10. Bo Sun & Derek T. Robinson, 2018. "Comparison of Statistical Approaches for Modelling Land-Use Change," Land, MDPI, vol. 7(4), pages 1-33, November.
    11. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.
    12. Scott Tainsky & Brian M. Mills & Jason A. Winfree, 2015. "Further Examination of Potential Discrimination Among MLB Umpires," Journal of Sports Economics, , vol. 16(4), pages 353-374, May.
    13. Sun, Tianyu & Chand, Satish & Sharpe, Keiran, 2018. "Effect of aging on housing prices: evidence from a panel data," MPRA Paper 94418, University Library of Munich, Germany, revised 01 Mar 2019.
    14. Roman Matousek & Nickolaos G. Tzeremes, 2021. "The asymmetric impact of human capital on economic growth," Empirical Economics, Springer, vol. 60(3), pages 1309-1334, March.
    15. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    16. Fukuyama, Hirofumi & Matousek, Roman & Tzeremes, Nickolaos G., 2020. "A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system," Omega, Elsevier, vol. 95(C).
    17. Audrey C. Luo & Valerie J. Sydnor & Adam Pines & Bart Larsen & Aaron F. Alexander-Bloch & Matthew Cieslak & Sydney Covitz & Andrew A. Chen & Nathalia Bianchini Esper & Eric Feczko & Alexandre R. Franc, 2024. "Functional connectivity development along the sensorimotor-association axis enhances the cortical hierarchy," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    18. Rodríguez-Álvarez, María Xosé & Lee, Dae-Jin & Kneib, Thomas & Durbán, María & Eilers, Paul, 2013. "Fast algorithm for smoothing parameter selection in multidimensional generalized P-splines," DES - Working Papers. Statistics and Econometrics. WS ws133026, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    20. Ferrara, Giancarlo & Vidoli, Francesco & Canello, Jacopo & Campagna, Arianna, 2013. "Labour-use Efficiency in the Italian Machinery Industry: a Non-parametric Stochastic Frontier Perspective," MPRA Paper 94359, University Library of Munich, Germany.

    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:79:y:2023:i:4:p:3954-3967. 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.