Inference in epidemic models without likelihoods

International Journal of Biostatistics

Volumn 5, Issue 1, 2009, Pages

  McKinley, Trevelyan ^a   Cook, Alex R ^b   Deardon, Robert ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF GUELPH   (Canada)

Author keywords

Approximate Bayesian computation; Infectious disease modelling; Inference; Markov Chain Monte Carlo; Sequential Monte Carlo

Indexed keywords

ALGORITHM; ARTICLE; BAYES THEOREM; CONGO; EPIDEMIC; GOLD STANDARD; LIKELIHOOD BASED INFERENCE MODEL; MARKOV CHAIN MONTE CARLO ALGORITHM; MATHEMATICAL MODEL; MONTE CARLO METHOD; PROBABILITY; SEIR MODEL; SEQUENTIAL MONTE CARLO ALGORITHM; SIMULATION; STATISTICAL CONCEPTS; STATISTICAL MODEL; VIRUS HEMORRHAGIC FEVER;

EID: 68249147597     PISSN: 15574679     EISSN: None     Source Type: Journal    
DOI: 10.2202/1557-4679.1171     Document Type: Article

References (63)

1. Anderson, R. and May, R. (1991), Infectious Diseases of Humans, Oxford University Press.
2. Andersson, H. and Britton, T. (2000), Stochastic Epidemic Models and their Statistical Analysis, New York: Springer.
3. Anon. (1978a), "Ebola haemorrhagic fever in Sudan, 1976. Report of a WHO/international study team," Bull World Health Organ, 56, 247-270. (Pubitemid 8360403)
4. Anon. (1978b), "Ebola haemorrhagic fever in Zaire, 1976. Report of a WHO/international study team," Bull World Health Organ, 56, 271-293. (Pubitemid 8360404)
5. Anon. (1995), "Ebola haemorrhagic fever in Zaire," Wkly Epidemiol Rec, 70, 241-242.
6. Bailey, N. T. (1975), The Mathematical Theory of Infectious Diseases, Charles Griffin and Company Ltd., London and High Wycombe, 2nd ed.
7. Beaumont, M., Zhang, W., and Balding, D. (2002), "Approximate Bayesian Computation in population genetics," Genetics, 162, 2025-2035.
8. Beaumont, M.A. (2008), "A note on the ABC-PRC algorithm of Sisson et al. (2007)," http://arxiv.org/abs/0805.3079v1.
9. Becker, N. (1976), "On a general stochastic epidemic model," Theoretical Population Biology, 11, 23-26.
10. Becker, N. (1989), Analysis of Infectious Disease Data, Chapman and Hall/CRC.
11. Bortot, P., Coles, S., and Sisson, S. (2007), "Inference for stereological extremes," Journal of the American Statistical Association, 102, 84-92.
12. Buckland, S. T., Newman, K. B., Ferńandez, C., Thomas,L., and Harwood, J. (2007), "Embedding Population Dynamics Models in Inference," Stat Sci, 22, 44-58.
13. Capṕe, O., Godsill, S., and Moulines, E. (2007), "An overview of existing methods and recent advances in Sequential Monte Carlo," Proceedings of the IEEE, 95, 899-924.
14. Cauchemez, S. and Ferguson, N. M. (2008), "Likelihood-based estimation of continuous-time epidemic models from time-series data: Application to measles transmission in London," Journal of the Royal Society Interface, 5, 885-897. (Pubitemid 351882153)
15. Chowell, G., Hengartner, N., Castillo-Chavez, C., Fenimore, P., and Hyman, J. (2004), "The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda," Journal of Theoretical Biology, 229, 119-126. (Pubitemid 38721255)
16. Chowell, G., Nishiura, H., Bettencourt, L.M.A. (2007), "Comparative estimation of the reproduction number for pandemic influenza from daily case notification data", J Roy Soc: Interface, 4, 155-166.
17. Cook, A., Otten, W., Marion, G., Gibson, G., and Gilligan, C. (2007), "Estimation of multiple transmission rates for epidemics in heterogeneous populations," Proceedings of the National Academy of Sciences USA, 104, 20392-20397.
18. Cook, A., Gibson, G., Gottwald, T., and Gilligan, C. (2008a), "Constructing the effect of alternative intervention strategies on historic epidemics," Journal of the Royal Society: Interface, 5, 1203-1213.
19. Cook, A. R., Gibson, G. J., and Gilligan, C. A. (2008b), "Optimal observation times in experimental epidemic processes," Biometrics, 64, 860-868.
20. Deardon, R., Brooks, S. P., Grenfell, B. T., Keeling, M. J., Tildesley, M. J., Savill, N. J., Shaw, D. J., and Woolhouse, M. E. (2009), "Inference for individual level models of infectious diseases in large populations," to appear in Statistica Sinica.
21. Diggle, P. (2006), "Spatio-temporal point processes, partial likelihood, footand-mouth disease," Statistical Methods in Medical Research, 15, 325-336.
22. Diggle, P. and Gratton, R. (1984), "MonteCarlo methods of inference for implicit statistical models (with discussion)," Journal of the Royal Statistical Society. Series B, 46, 193-227.
23. Doucet, A., Freitas, N. D., and Gordon, N. (eds.) (2001), Sequential Monte Carlo Methods in Practice, Springer.
24. Fearnhead, P. and Meligkotsidou, L. (2004), "Exact filtering for partiallyobserved continuous time models," Journal of the Royal Statistical Society. Series B (Methodological), 66, 771-789. (Pubitemid 39015912)
25. Filipe, J. and Gibson, G. (2001), "Comparing approximations to spatiotemporal models for epidemics with local spread," Bulletin of Mathematical Biology, 63, 603-624. (Pubitemid 32721005)
26. Formenty, P., Libama, F., Epelboin, A., Allarangar, Y., Leroy, E., Moudzeo, H., Tarangonia, P., Molamou, A., Lenzi, M., Ait-Ikhlef, K., Hewlett, B., Roth, C., Grein, T., and l'equipe de lutte contre l'epidemio d'Ebola, au Congo. (2003), "L'epidemie de fievre hemorragique ́a virus Ebola en Republique du Congo, 2003: une nouvelle strategie?", Med Trop, 63, 291-295. (Pubitemid 46417000)
27. Gamerman, D. and Lopes, H. F. (2006), Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, CRC Press, 2nd ed.
28. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis, Chapman and Hall/CRC, 2nd ed.
29. Gibson, G. J. and Renshaw, E. (1998), "Estimating parameters in stochastic compartmental models using Markov chain methods," IMA Journal of Mathematics Applied in Medicine and Biology, 15, 19-40. (Pubitemid 28264309)
30. Gillespie, D. T. (1977), "Exact stochastic simulation of coupled chemical reactions," The Journal of Physical Chemistry, 81, 2340-2361.
31. Haydon, D., Chase-Topping, M., Shaw, D., Matthews, L., Friar, J., Wilesmith, J., and Woolhouse, M. (2003), "The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak," Proceedings Of The Royal Society Of London Series B - Biological Sciences, 270, 121-127. (Pubitemid 36143362)
32. Ḧohle, M., Jørgensen, E., and O'Neill, P. D. (2005), "Inference in disease transmission experiments by using stochastic epidemic models," Applied Statistics, 54, 349-366. (Pubitemid 40306659)
33. Ionides, E., Bret́o, C., and King, A. (2006), "Inference for nonlinear dynamical systems," Proceedings of the National Academy of Sciences USA, 103, 18438-18443.
34. Jègat, C., Carrat, F., Lajaunie, C., and Wackernagel, H. (2008), "Early Detection and Assessment of Epidemics by Particle Filtering", in Soares, A., Pereira, M. J. and Dimitrakopoulos, R. (eds) geoENV VI - Geostatistics for Environmental Applications, 16, 22-35, Springer Netherlands.
35. Keeling, M. J. and Rohani, P. (2008), Modeling Infectious Diseases in Humans and Animals, Princeton University Press.
36. Khan, A. S., Tshioko, F. K., Heymann, D. L., Guenno, B. L., Nabeth, P., Kerstïens, B., Fleerackers, Y., Kilmarx, P. H., Rodier, G. R., Nkuku, O., Rollin, P. E., Sanchez, A., Zaki, S. R., Swanepoel, R., Tomori, O., Nichol, S. T., Peters, C., Muyembe-Tamfum, J., and Ksiazek, T. G. (1999), "The reemergence of Ebola Hemorrhagic Fever, Democratic Republic of Congo, 1995," The Journal of Infectious Diseases, 179, 76-86. (Pubitemid 29091374)
37. Krishnarajah, I., Cook, A., Marion, G., and Gibson, G. (2005), "Novel moment closure approximations in stochastic epidemics," Bulletin of Mathematical Biology, 67, 855-873. (Pubitemid 40707615)
38. Lekone, P. E. and Finkensẗadt, B. F. (2006), "Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study," Biometrics, 62, 1170-1177.
39. Liu, J. S. (2001), Monte Carlo Strategies in Scientific Computing, Springer- Verlag.
40. Marjoram, P., Molitor, J., Plagnol, V., and Tavaŕe, S. (2003), "Markov Chain Monte Carlo without likelihoods," Proceedings of the National Academy of Sciences USA, 100, 15324-15328. (Pubitemid 38020988)
41. Moral, P. D., Doucet, A., and Jasra, A. (2006), "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society, Series B, 68, 411-436.
42. Moser, M. R., Bender, T. R., Margolis, H. S., Noble, G. R., Kendal, A. P., and Ritter, D. G. (1979), "An outbreak of influenza aboard a commercial airliner," Am J Epidemiol, 110, 1-6.
43. Okware, S. I., Omaswa, F. G., Zaramba, S., Opio, A., Lutwama, J. J., Kamugisha, J., Rwaguma, E. B., Kagwa, P., and Lamunu, M. (2002), "An outbreak of Ebola in Uganda," Trop Med Int Health, 7, 1068-1075.
44. O'Neill, P. D. (2002), "A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods," Math Biosci, 180, 103-114. (Pubitemid 35304348)
45. O'Neill, P., Balding, D., Becker, N., Eerola, M., and Mollison, D. (2000), "Analyses of infectious disease data from household outbreaks by Markov Chain Monte Carlo methods," Applied Statistics, 49, 517-542.
46. O'Neill, P. D. and Roberts, G. O. (1999), "Bayesian inference for partially observed stochastic epidemics," Journal of the Royal Statistical Society. Series A (General), 162, 121-129.
47. Plagnol, V. and Tavaŕe, S. (2002), "Approximate Bayesian computation and MCMC," in Monte Carlo and Quasi-Monte Carlo Methods 2002, ed. Niederreiter, H., Springer-Verlag, 99-114.
48. Pritchard, J. K., Seielstad, M. T., Perez-Lezaun, A., and Feldman, M. W. (1999), "Population growth of human Y chromosomes: a study of Y chromosome microsatellites," Molecular Biology and Evolution, 16, 1791-1798.
49. R Development Core Team (2008), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.
50. Renshaw, E. (1993), Modelling Biological Populations in Space and Time, Cambridge University Press.
51. Riley, S., Fraser, C., Donnelly, C. A., Ghani, A. C., Abu-Raddad, L. J., Hedley, A. J., Leung, G. M., Ho, L.-M., Lam, T.-H., Thach, T. Q., Chau, P., Chan, K.-P., Lo, S.-V., Leung, P.-Y., Tsang, T., Ho, W., Lee, K.-H., Lau, E. M., Ferguson, N. M., and Anderson, R. M. (2003), "Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions," Science, 300, 1961-1966. (Pubitemid 36734606)
52. Ross, J., Taimre, T., and Pollett, P. (2006), "On parameter estimation in population models," Theoretical Population Biology, 70, 498-510.
53. Sisson, S., Fan, Y., and Tanaka, M. M. (2007a), "Sequential Monte Carlo without likelihoods," Proceedings of the National Academy of Sciences USA, 104, 1760-1765. (Pubitemid 46239852)
54. Sisson, S., Fan, Y., and Tanaka, M. M. (2007b), "A note on backward kernel choice for sequential Monte Carlo without likelihoods," http://web.maths.unsw.edu.au/~scott/papers/paper-smcabc-optimal.pdf.
55. Streftaris, G. and Gibson, G. J. (2004), " Bayesian inference for stochastic epidemics in closed populations," Statistical Modelling, 4, 63-75.
56. Tallmon, D. A., Luikart, G., and Beaumont, M. A. (2004), "Comparative evolution of a new effective population size estimator based on Approximate Bayesian Computation," Genetics, 167, 977-988. (Pubitemid 38931882)
57. Tanaka, M. M., Francis, A. R., Luciani, F., and Sisson, S. (2006), "Using Approximate Bayesian Computation to estimate tuberculosis transmission parameters from genotype data," Genetics, 173, 1511-1520. (Pubitemid 44127654)
58. Tavaŕe, S., Balding, D. J., Griffiths, R., and Donnelly, P. (1997), "Inferring coalescence times from DNA sequence data," Genetics, 145, 505-518. (Pubitemid 27068401)
59. Tavaŕe, S., Marshall, C. R., Will, O., Soligo, C., and Martin, R. D. (2002), "Using the fossil record to estimate the age of the last common ancestor of extant primates," Nature, 416, 726-729. (Pubitemid 34429146)
60. Tildesley, M. J., Savill, N. J., Shaw, D. J., Deardon, R., Brooks, S. P., Woolhouse, M. E., Grenfell, B. T., and Keeling, M. J. (2006), "Optimal reactive vaccination strategies for a foot-and-mouth outbreak in the UK," Nature, 440, 83-86. (Pubitemid 43336271)
61. Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Strumpf, M. P. (2009), "Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems," Journal of the Royal Society Interface, 6, 187-202.
62. Vynnycky, E., Trindall, A., and Mangtani, P. (2007), "Estimates of the reproduction number of Spanish influenza using morbidity data," Int J Epidem, 38, 881-889. (Pubitemid 47394158)
63. World Health Organisation (WHO) (2008), "Ebola haemorrhagic fever," http://www.who.int/mediacentre/factsheets/fs103/en/index.html.