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Explaining transmission rate variations and forecasting epidemic spread in multiple regions with a semiparametric mixed effects SIR model

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  • David A. Buch
  • James E. Johndrow
  • David B. Dunson

Abstract

The transmission rate is a central parameter in mathematical models of infectious disease. Its pivotal role in outbreak dynamics makes estimating the current transmission rate and uncovering its dependence on relevant covariates a core challenge in epidemiological research as well as public health policy evaluation. Here, we develop a method for flexibly inferring a time‐varying transmission rate parameter, modeled as a function of covariates and a smooth Gaussian process (GP). The transmission rate model is further embedded in a hierarchy to allow information borrowing across parallel streams of regional incidence data. Crucially, the method makes use of optional vaccination data as a first step toward modeling of endemic infectious diseases. Computational techniques borrowed from the Bayesian spatial analysis literature enable fast and reliable posterior computation. Simulation studies reveal that the method recovers true covariate effects at nominal coverage levels. We analyze data from the COVID‐19 pandemic and validate forecast intervals on held‐out data. User‐friendly software is provided to enable practitioners to easily deploy the method in public health research.

Suggested Citation

  • David A. Buch & James E. Johndrow & David B. Dunson, 2023. "Explaining transmission rate variations and forecasting epidemic spread in multiple regions with a semiparametric mixed effects SIR model," Biometrics, The International Biometric Society, vol. 79(4), pages 2987-2997, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:2987-2997
    DOI: 10.1111/biom.13901
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    References listed on IDEAS

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    1. Corbin Quick & Rounak Dey & Xihong Lin, 2021. "Regression Models for Understanding COVID-19 Epidemic Dynamics With Incomplete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1561-1577, October.
    2. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    3. Dave Osthus & Kelly R. Moran, 2021. "Multiscale influenza forecasting," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    4. Corbin Quick & Rounak Dey & Xihong Lin, 2021. "Rejoinder: Regression Models for Understanding COVID-19 Epidemic Dynamics With Incomplete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1591-1594, October.
    5. Anjishnu Banerjee & David B. Dunson & Surya T. Tokdar, 2013. "Efficient Gaussian process regression for large datasets," Biometrika, Biometrika Trust, vol. 100(1), pages 75-89.
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