Statistical Science

Evidence Synthesis for Stochastic Epidemic Models

Paul J. Birrell, Daniela De Angelis, and Anne M. Presanis

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In recent years, the role of epidemic models in informing public health policies has progressively grown. Models have become increasingly realistic and more complex, requiring the use of multiple data sources to estimate all quantities of interest. This review summarises the different types of stochastic epidemic models that use evidence synthesis and highlights current challenges.

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Statist. Sci., Volume 33, Number 1 (2018), 34-43.

First available in Project Euclid: 2 February 2018

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Evidence synthesis state-space models epidemic modelling mechanistic modelling


Birrell, Paul J.; De Angelis, Daniela; Presanis, Anne M. Evidence Synthesis for Stochastic Epidemic Models. Statist. Sci. 33 (2018), no. 1, 34--43. doi:10.1214/17-STS631.

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  • [1] Ades, A. E. and Sutton, A. J. (2006). Multiparameter evidence synthesis in epidemiology and medical decision-making: Current approaches. J. Roy. Statist. Soc. Ser. A 169 5–35.
  • [2] Albert, I., Espié, E., De Valk, H. and Denis, J. B. (2011). A Bayesian evidence synthesis for estimating campylobacteriosis prevalence. Risk Anal. 31 1141–1155.
  • [3] Anderson, R. M. and May, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford Univ. Press, Oxford.
  • [4] Andrianakis, I., McCreesh, N., Vernon, I., McKinley, T. J., Oakley, J. E., Nsubuga, R. N., Goldstein, M. and White, R. G. (2017). Efficient history matching of a high dimensional individual-based HIV transmission model. SIAM/ASA J. Uncertain. Quantificat. 5 694–719.
  • [5] Baguelin, M., Flasche, S., Camacho, A., Demiris, N., Miller, E. and Edmunds, W. J. (2013). Assessing optimal target populations for influenza vaccination programmes: An evidence synthesis and modelling study. PLoS Med. 10 Article ID e1001527+.
  • [6] Birrell, P. J., Chadborn, T. R., Gill, O. N., Delpech, V. C. and De Angelis, D. (2012). Estimating trends in incidence, time-to-diagnosis and undiagnosed prevalence using a CD4-based Bayesian back-calculation. Stat. Commun. Infec. Dis. 4 Article ID 6.
  • [7] Birrell, P. J., De Angelis, D., Wernisch, L., Tom, B. D. M., Roberts, G. O. and Pebody, R. G. (2016). Efficient real-time monitoring of an emerging influenza epidemic: How feasible? ArXiv preprint. Available at
  • [8] Birrell, P. J., Ketsetzis, G., Gay, N. J., Cooper, B. S., Presanis, A. M., Harris, R. J., Charlett, A., Zhang, X.-S., White, P. J., Pebody, R. G. and De Angelis, D. (2011). Bayesian modeling to unmask and predict influenza A/H1N1pdm dynamics in London. Proc. Natl. Acad. Sci. USA 108 18238–18243.
  • [9] Birrell, P. J., Zhang, X.-S., Pebody, R. G., Gay, N. J. and De Angelis, D. (2016). Reconstructing a spatially heterogeneous epidemic: Characterising the geographic spread of 2009 A/H1N1pdm infection in England. Sci. Rep. 6 29004.
  • [10] Brockwell, P. J. and Davis, R. A. (2002). Introduction to Time Series and Forecasting, 2nd ed. Springer, New York. With 1 CD-ROM (Windows).
  • [11] Conti, S., Presanis, A. M., van Veen, M. G., Xiridou, M., Donoghoe, M. C., Stengaard, A. R. and De Angelis, D. (2011). Modeling of the HIV infection epidemic in the Netherlands: A multi-parameter evidence synthesis approach. Ann. Appl. Stat. 5 2359–2384.
  • [12] De Angelis, D. (2011). Back-calculation. In Encyclopaedic Companion to Medical Statistics, 2nd ed. (B. S. Everitt and C. R. Palmer, eds.) 23–24. Wiley, New York.
  • [13] De Angelis, D., Presanis, A. M., Birrell, P. J., Scalia Tomba, G. and House, T. (2014). Four key challenges in infectious disease modelling using data from multiple sources. Epidemics 10 83–87.
  • [14] De Angelis, D., Presanis, A. M., Conti, S. and Ades, A. E. (2014). Estimation of HIV burden through Bayesian evidence synthesis. Statist. Sci. 29 9–17.
  • [15] De Maio, N., Wu, C.-H. and Wilson, D. J. (2016). SCOTTI: Efficient reconstruction of transmission within outbreaks with the structured coalescent. PLoS Comput. Biol. 12 Article ID e1005130.
  • [16] Dorigatti, I., Cauchemez, S. and Ferguson, N. M. (2013). Increased transmissibility explains the third wave of infection by the 2009 H1N1 pandemic virus in England. Proc. Natl. Acad. Sci. USA 110 13422–13427.
  • [17] Dureau, J., Kalogeropoulos, K. and Baguelin, M. (2013). Capturing the time-varying drivers of an epidemic using stochastic dynamical systems. Biostatistics 14 541–555.
  • [18] Farah, M., Birrell, P., Conti, S. and Angelis, D. D. (2014). Bayesian emulation and calibration of a dynamic epidemic model for A/H1N1 influenza. J. Amer. Statist. Assoc. 109 1398–1411.
  • [19] Goudie, R. J. B., Presanis, A. M., Lunn, D., De Angelis, D. and Wernisch, L. (2016). Model surgery: Joining and splitting models with Markov melding. ArXiv preprint. Available at
  • [20] Gross, E., Harrington, H. A., Rosen, Z. and Sturmfels, B. (2016). Algebraic systems biology: A case study for the Wnt pathway. Bull. Math. Biol. 78 21–51.
  • [21] Heesterbeek, H., Anderson, R. M., Andreasen, V., Bansal, S., De Angelis, D., Dye, C., Eames, K. T. D., Edmunds, W. J., Frost, S. D. W., Funk, S., Hollingsworth, T. D., House, T., Isham, V., Klepac, P., Lessler, J., Lloyd-Smith, J. O., Metcalf, C. J. E., Mollison, D., Pellis, L., Pulliam, J. R. C., Roberts, M. G. and Viboud, C. (2015). Modeling infectious disease dynamics in the complex landscape of global health. Science 347 Article ID aaa4339. DOI:10.1126/science.aaa4339.
  • [22] Jackson, C., Presanis, A., Conti, S. and De Angelis, D. (2017). Value of information: Sensitivity analysis and research design in Bayesian evidence synthesis. ArXiv preprint. Availabe at arXiv:1703.08994.
  • [23] Klinkenberg, D., Backer, J. A., Didelot, X., Colijn, C. and Wallinga, J. (2017). Simultaneous inference of phylogenetic and transmission trees in infectious disease outbreaks. PLoS Comput. Biol. 13 Article ID e1005495.
  • [24] Lau, M. S. Y., Marion, G., Streftaris, G., Gibson, G., Chase-Topping, M. and Haydon, D. (2015). A systematic Bayesian integration of epidemiological and genetic data. PLoS Comput. Biol. 11 Article ID e1004633.
  • [25] Lauritzen, S. L. (1996). Graphical Models. Oxford Statistical Science Series 17. Clarendon Press, Oxford.
  • [26] Lessler, J., Azman, A. S., Grabowski, M. K., Salje, H. and Rodriguez-Barraquer, I. (2016). Trends in the mechanistic and dynamic modeling of infectious diseases. Curr. Epidemiol. Rep. 3 212–222.
  • [27] Presanis, A. M., De Angelis, D., Goubar, A., Gill, O. N. and Ades, A. E. (2011). Bayesian evidence synthesis for a transmission dynamic model for HIV among men who have sex with men. Biostatistics 12 666–681.
  • [28] Prevost, T. C., Presanis, A. M., Taylor, A., Goldberg, D. J., Hutchinson, S. J. and De Angelis, D. (2015). Estimating the number of people with hepatitis C virus who have ever injected drugs and have yet to be diagnosed: An evidence synthesis approach for Scotland. Addiction 110 1287–1300.
  • [29] Rasmussen, D. A., Ratmann, O. and Koelle, K. (2011). Inference for nonlinear epidemiological models using genealogies and time series. PLoS Comput. Biol. 7 Article ID e1002136+.
  • [30] Ratmann, O., Donker, G., Meijer, A., Fraser, C. and Koelle, K. (2012). Phylodynamic inference and model assessment with approximate Bayesian computation: Influenza as a case study. PLoS Comput. Biol. 8 Article ID e1002835+.
  • [31] Rosinska, M., Gwiazda, P., De Angelis, D. and Presanis, A. M. (2016). Bayesian evidence synthesis to estimate HIV prevalence in men who have sex with men in Poland at the end of 2009. Epidemiol. Infect. 144 1175–1191.
  • [32] Shaman, J., Karspeck, A., Yang, W., Tamerius, J. and Lipsitch, M. (2013). Real-time influenza forecasts during the 2012–2013 season. Nat. Commun. 4 Article ID 2837. DOI:10.1038/ncomms3837.
  • [33] Sheinson, D. M., Niemi, J. and Meiring, W. (2014). Comparison of the performance of particle filter algorithms applied to tracking of a disease epidemic. Math. Biosci. 255 21–32.
  • [34] Shubin, M., Lebedev, A., Lyytikäinen, O. and Auranen, K. (2016). Revealing the true incidence of pandemic A(H1N1)pdm09 influenza in Finland during the first two seasons—An analysis based on a dynamic transmission model. PLoS Comput. Biol. 12 Article ID e1004803.
  • [35] Shubin, M., Virtanen, M., Toikkanen, S., Lyytikäinen, O. and Auranen, K. (2014). Estimating the burden of A(H1N1)pdm09 influenza in Finland during two seasons. Epidemiol. Infect. 142 964–974. DOI:10.1017/s0950268813002537.
  • [36] Si, Y., Pillai, N. S. and Gelman, A. (2015). Bayesian nonparametric weighted sampling inference. Bayesian Anal. 10 605–625.
  • [37] te Beest, D. E., Birrell, P. J., Wallinga, J., De Angelis, D. and van Boven, M. (2015). Joint modelling of serological and hospitalization data reveals that high levels of pre-existing immunity and school holidays shaped the influenza A pandemic of 2009 in the Netherlands. J. R. Soc. Interface 12 Article ID 20141244. DOI:10.1098/rsif.2014.1244.
  • [38] Welton, N. J. and Ades, A. E. (2005). A model of toxoplasmosis incidence in the UK: Evidence synthesis and consistency of evidence. J. Roy. Statist. Soc. Ser. C 54 385–404.
  • [39] Worby, C. J., O’Neill, P. D., Kypraios, T., Robotham, J. V., De Angelis, D., Cartwright, E. J. P., Peacock, S. J. and Cooper, B. S. (2016). Reconstructing transmission trees for communicable diseases using densely sampled genetic data. Ann. Appl. Stat. 10 395–417.
  • [40] Wu, H. and Tan, W. Y. (2000). Modelling the HIV epidemic: A state-space approach. Math. Comput. Modelling 32 197–215.
  • [41] Xu, X., Kypraios, T. and O’Neill, P. D. (2016). Bayesian nonparametric inference for stochastic epidemic models using Gaussian processes. Biostatistics 17 619–633.
  • [42] Yaari, R., Katriel, G., Stone, L., Mendelson, E., Mandelboim, M. and Huppert, A. (2016). Model-based reconstruction of an epidemic using multiple datasets: Understanding influenza A/H1N1 pandemic dynamics in Israel. J. R. Soc. Interface 13 Article ID 20160099.
  • [43] Yan, P., Zhang, F. and Wand, H. (2011). Using HIV diagnostic data to estimate HIV incidence: Method and simulation. Stat. Commun. Infec. Dis. 3 Article ID 6.