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Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods

Author

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  • Philip D. O'Neill
  • David J. Balding
  • Niels G. Becker
  • Mervi Eerola
  • Denis Mollison

Abstract

The analysis of infectious disease data presents challenges arising from the dependence in the data and the fact that only part of the transmission process is observable. These difficulties are usually overcome by making simplifying assumptions. The paper explores the use of Markov chain Monte Carlo (MCMC) methods for the analysis of infectious disease data, with the hope that they will permit analyses to be made under more realistic assumptions. Two important kinds of data sets are considered, containing temporal and non‐temporal information, from outbreaks of measles and influenza. Stochastic epidemic models are used to describe the processes that generate the data. MCMC methods are then employed to perform inference in a Bayesian context for the model parameters. The MCMC methods used include standard algorithms, such as the Metropolis–Hastings algorithm and the Gibbs sampler, as well as a new method that involves likelihood approximation. It is found that standard algorithms perform well in some situations but can exhibit serious convergence difficulties in others. The inferences that we obtain are in broad agreement with estimates obtained by other methods where they are available. However, we can also provide inferences for parameters which have not been reported in previous analyses.

Suggested Citation

  • Philip D. O'Neill & David J. Balding & Niels G. Becker & Mervi Eerola & Denis Mollison, 2000. "Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 517-542.
  • Handle: RePEc:bla:jorssc:v:49:y:2000:i:4:p:517-542
    DOI: 10.1111/1467-9876.00210
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    Cited by:

    1. Ioannis Andrianakis & Ian R Vernon & Nicky McCreesh & Trevelyan J McKinley & Jeremy E Oakley & Rebecca N Nsubuga & Michael Goldstein & Richard G White, 2015. "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-18, January.
    2. McKinley Trevelyan & Cook Alex R & Deardon Robert, 2009. "Inference in Epidemic Models without Likelihoods," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-40, July.
    3. Gyanendra Pokharel & Rob Deardon, 2022. "Emulation‐based inference for spatial infectious disease transmission models incorporating event time uncertainty," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 455-479, March.
    4. Baey, Charlotte & Smith, Henrik G. & Rundlöf, Maj & Olsson, Ola & Clough, Yann & Sahlin, Ullrika, 2023. "Calibration of a bumble bee foraging model using Approximate Bayesian Computation," Ecological Modelling, Elsevier, vol. 477(C).
    5. Poggi, Ambra & Ramos, Xavier, 2007. "Empirical Modeling of Deprivation Contagion among Social Exclusion Dimensions (Using MCMC Methods)," IZA Discussion Papers 2614, Institute of Labor Economics (IZA).
    6. Akira Endo & Mitsuo Uchida & Adam J Kucharski & Sebastian Funk, 2019. "Fine-scale family structure shapes influenza transmission risk in households: Insights from primary schools in Matsumoto city, 2014/15," PLOS Computational Biology, Public Library of Science, vol. 15(12), pages 1-18, December.
    7. Cai Xiaoxuan & Loh Wen Wei & Crawford Forrest W., 2021. "Identification of causal intervention effects under contagion," Journal of Causal Inference, De Gruyter, vol. 9(1), pages 9-38, January.
    8. Yang, Yang & Longini Jr., Ira M. & Elizabeth Halloran, M., 2007. "A data-augmentation method for infectious disease incidence data from close contact groups," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6582-6595, August.
    9. McKinley, Trevelyan J. & Ross, Joshua V. & Deardon, Rob & Cook, Alex R., 2014. "Simulation-based Bayesian inference for epidemic models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 434-447.

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