Bayesian parameter inference for dynamic infectious disease modelling: Rotavirus in Germany

Statistics in Medicine

Volumn 33, Issue 9, 2014, Pages 1580-1599

  Weidemann, Felix ^a   Dehnert, Manuel ^a,c   Koch, Judith ^a   Wichmann, Ole ^a   Höhle, Michael ^a,b  

^a ROBERT KOCH INSTITUTE   (Germany)

^b STOCKHOLM UNIVERSITY   (Sweden)

^c UNIVERSITY OF APPLIED SCIENCES WEIHENSTEPHAN TRIESDORF   (Germany)

Author keywords

Bayesian inference; Disease transmission; Model averaging; Ordinary differential equations; Residual autocorrelation; Rotavirus

Indexed keywords

ARTICLE; ASYMPTOMATIC INFECTION; BAYES THEOREM; BAYESIAN PARAMETER INFERENCE; DISEASE MODEL; EPIDEMIOLOGICAL DATA; GERMANY; INCIDENCE; PREDICTION; ROTAVIRUS INFECTION; VIRUS TRANSMISSION; ADOLESCENT; ADULT; AGED; CALIBRATION; CHILD; EPIDEMIOLOGY; HUMAN; INFANT; ISOLATION AND PURIFICATION; MIDDLE AGED; PRESCHOOL CHILD; PROCEDURES; ROTAVIRUS; ROTAVIRUS INFECTIONS; STATISTICAL MODEL; STATISTICS; TRANSMISSION; VERY ELDERLY; YOUNG ADULT;

ADOLESCENT; ADULT; AGED; AGED, 80 AND OVER; BAYES THEOREM; CALIBRATION; CHILD; CHILD, PRESCHOOL; GERMANY; HUMANS; INCIDENCE; INFANT; MIDDLE AGED; MODELS, STATISTICAL; ROTAVIRUS; ROTAVIRUS INFECTIONS; STATISTICS AS TOPIC; YOUNG ADULT;

EID: 84898056841     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6041     Document Type: Article

References (48)

1. O'Neill PD. Introduction and snapshot review: relating infectious disease transmission models to data. Statistics in Medicine 2010; 29(20):2069-2077.
2. Tate JE, Burton AH, Boschi-Pinto C, Steele AD, Duque J, Parashar UD. 2008 estimate of worldwide rotavirus-associated mortality in children younger than 5 years before the introduction of universal rotavirus vaccination programmes: a systematic review and meta-analysis. The Lancet Infectious Diseases 2012; 12(2):136-141.
3. Pitzer VE, Viboud C, Simonsen L, Steiner C, Panozzo CA, Alonso WJ, Miller MA, Glass RI, Glasser JW, Parashar UD, Grenfell BT. Demographic variability, vaccination, and the spatiotemporal dynamics of rotavirus epidemics. Science 2009; 325(5938):290-294. DOI: 10.1126/science.1172330.
4. Atkins KE, Shim E, Pitzer VE, Galvani AP. Impact of rotavirus vaccination on epidemiological dynamics in England and Wales. Vaccine 2012; 30(3):552-564. DOI: 10.1016/j.vaccine.2011.11.064.
5. Atchison C, Lopman B, Edmunds WJ. Modelling the seasonality of rotavirus disease and the impact of vaccination in England and Wales. Vaccine 2010; 28(18):3118-3126. DOI: 10.1016/j.vaccine.2010.02.060.
6. VanEffelterre T, M. Soriano-Gabarró M, Debrus S, ClaireNewbern E, Gray J. A mathematical model of the indirect effects of rotavirus vaccination. Epidemiology and Infection 2010; 138(6):884-897. DOI: 10.1017/S0950268809991245.
7. Shim E, Banks C, Castillo-Chavez HT. Seasonality of rotavirus infection with its vaccination. AMS Contemporary Mathematics Book Series 2006; 410: 327-348.
8. Freiesleben de Blasio B, Kasymbekova K, Flem E. Dynamic model of rotavirus transmission and the impact of rotavirus vaccination in Kyrgyzstan. Vaccine 2010; 28(50):7923-7932. DOI: 10.1016/j.vaccine.2010.09.070.
9. Shim E, Castillo-Chavez C. The epidemiological impact of rotavirus vaccination in the United States and Mexico. Mathematical and Statistical Estimation Approaches in Epidemiology 2009: 303-323.
10. Shim E, Galvani AP. Impact of transmission dynamics on the cost-effectiveness of rotavirus vaccination. Vaccine 2009; 27(30):4025-4030. DOI: 10.1016/j.vaccine.2009.04.030.
11. Pitzer VE, Viboud C, Lopman BA, Patel MM, Parashar UD, Grenfell BT. Influence of birth rates and transmission rates on the global seasonality of rotavirus incidence. Journal of the Royal Society Interface 2011; 8(64):1584-1593. DOI: 10.1098/rsif.2011.0062.
12. Brookhart MA, Hubbard AE, vander Laan MJ, Colford JM, Eisenberg JNS. Statistical estimation of parameters in a disease transmission model: analysis of a Cryptosporidium outbreak. Statistics in Medicine 2002; 21(23):3627-3638.
13. Whitaker HJ, Farrington CP. Estimation of infectious disease parameters from serological survey data: the impact of regular epidemics. Statistics in Medicine 2004; 23(15):2429-2443.
14. Elderd BD, Dukic VM, Dwyer G. Uncertainty in predictions of disease spread and public health responses to bioterrorism and emerging diseases. PNAS 2006; 103(42):15693-15697. DOI: 10.1073/pnas.0600816103.
15. Birrell PJ, Ketsetzis G, Gay NJ, Cooper BS, Presanis AM, Harris RJ, Charlett A, Zhang XS, White PJ, Pebody RG, DeAngelis D. Bayesian modeling to unmask and predict influenza A/H1N1pdm dynamics in London. PNAS 2011; 108(45):18238-18243. DOI: 10.1073/pnas.1103002108.
16. Dorigatti I, Cauchemez S, Pugliese A, Ferguson NM. A new approach to characterising infectious disease transmission dynamics from sentinel surveillance: application to the Italian 2009-2010 A/H1N1 influenza pandemic. Epidemics 2012; 4(1):9-21. DOI: 10.1016/j.epidem.2011.11.001.
17. Coelho FC, Codeço CT, Gomes MGM. A Bayesian framework for parameter estimation in dynamical models. PLoS ONE 05 2011; 6(5):e19616.
18. Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface 2009; 6(31):187-202. DOI: 10.1098/rsif.2008.0172.
19. He D, Ionides EL, King AA. Plug-and-play inference for disease dynamics: measles in large and small populations as a case study. Journal of the Royal Society Interface 2010; 7(43):271-283. DOI: 10.1098/rsif.2009.0151.
20. Held L, Höhle M, Hofmann M. A statistical framework for the analysis of multivariate infectious disease surveillance counts. Statistical Modelling 2005; 5(3):187-199. DOI: 10.1191/1471082X05st098oa.
21. Paul M, Held L, Toschke AM. Multivariate modelling of infectious disease surveillance data. Statistics in Medicine 2008; 27(29):6250-6267.
22. Koch J, Wiese-Posselt M. Epidemiology of rotavirus infections in children<5 years of age: Germany, 2001-2008. Pediatric Infectious Disease Journal 2011; 30(2):112-117.
23. Dudareva S, Koch J, Ander Heiden M, Oberle D, Keller-Stanislawski B, Wichmann O. Impact of rotavirus vaccination in regions with low and moderate vaccine uptake in Germany. Human Vaccines & Immunotherapeutics 2012; 8(10):1407-1415. DOI: 10.4161/hv.21593.
24. Rosner B, Stark K, Werber D. Epidemiology of reported Yersinia enterocolitica infections in Germany, 2001-2008. BMC Public Health 2010; 10(1):337-344.
25. Federal Bureau of Statistics, GENESIS Online Database. https://www-genesis.destatis.de/genesis/online, Accessed: 2013-09-01.
26. Fischer TK, Valentiner-Branth P, Steinsland H, Perch M, Santos G, Aaby P, Mølbak K, Sommerfelt H. Protective immunity after natural rotavirus infection: a community cohort study of newborn children in Guinea-Bissau, West Africa. The Journal of Infectious Disease 2002; 186(5):593-597. DOI: 10.1086/342294.
27. Moulton LH, Staat MA, Santosham M, Ward RL. The protective effectiveness of natural rotavirus infection in an American Indian population. The Journal of Infectious Disease 1998; 178(6):1562-1566. DOI: 10.1086/314504.
28. Azzalini A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 1985; 12: 171-178.
29. Anderson EJ, Weber SG. Rotavirus infection in adults. The Lancet Infectious Diseases 2004; 4(2):91-99. DOI: 10.1016/S1473-3099(04)00928-4.
30. Pickering LK, Bartlett AV III, Reves RR, Morrow A. Asymptomatic excretion of rotavirus before and after rotavirus diarrhea in children in day care centers. The Journal of Pediatrics 1988; 112(3):361-365. DOI: 10.1016/S0022-3476(88)80313-5.
31. Wilde J, Yolken R, Willoughby R, Eiden J. Improved detection of rotavirus shedding by polymerase chain reaction. The Lancet 1991; 337(8737):323-326. DOI: 10.1016/0140-6736(91)90945-L.
32. Clark HF, Marcello A, Lawley D, Reilly M, DiNubile M. Unexpectedly high burden of rotavirus gastroenteritis in very young infants. BMC Pediatrics 2010; 10(1):40-46.
33. Clemens J, Rao M, Ahmed F, Ward R, Huda S, Chakraborty J, Yunus M, Khan MR, Ali M, Kay B, van Loon F, Sack D. Breast-feeding and the risk of life-threatening rotavirus diarrhea: prevention or postponement? Pediatrics 1993; 92(5):680-685.
34. Pickering LK, Morrow AL, Herrera I, O'Ryan M, Estes MK, Guilliams SE, Jackson L, Carter-Campbell S, Matson DO. Effect of maternal rotavirus immunization on milk and serum antibody titers. Journal of Infectious Diseases 1995; 172(3):723-728. DOI: 10.1093/infdis/172.3.723.
35. Ward RL, Bernstein DI, Shukla R, McNeal MM, Sherwood JR, Young EC, Schiff GM. Protection of adults rechallenged with a human rotavirus. Journal of Infectious Diseases 1990; 161(3):440-445. DOI: 10.1093/infdis/161.3.440.
36. Soriano-Gabarró M, Mrukowicz J, Vesikari T, Verstraeten T. Burden of rotavirus disease in european union countries. The Pediatric Infectious Disease Journal 2006; 25(1):7-11.
37. F. RaúlVelásquez DOM, Ruiz-Palacios GM. Rotavirus infection in infants as protection against subsequent infections. Vaccine 1996; 335(14):1022-1028.
38. Mrukowicz JZ, Thompson J, Reed GW, Tollefson SJ, Kobayashi M, Araki K, Wright PF. Epidemiology of rotavirus in infants and protection against symptomatic illness afforded by primary infection and vaccination. Vaccine 1999; 17(7-8):745-753.
39. Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M. Bayesian Statistics 8. Oxford University Press: Oxford, 2007.
40. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes 3rd Edition. Cambridge University Press: New York, 2007.
41. Thiébaux HJ, Zwiers FW. The interpretation and estimation of effective sample size. Journal of Applied Meteorology May 1984; 23: 800-811. DOI: 10.1175/1520-0450(1984)0232.0.CO;2.
42. McMillan H, Freer J, Pappenberger F, Krueger T, Clark M. Impacts of uncertain river flow data on rainfall-runoff model calibration and discharge predictions. Hydrological Processes 2010; 24(10):1270-1284.
43. Raftery AE. Approximate Bayes factors and accounting for model uncertainty in generalised linear models. Biometrika 1996; 83(2):251-266. DOI: 10.1093/biomet/83.2.251.
44. Mossong J, Hens N, Jit M, Beutels P, Auranen K, Mikolajczyk R, Massari M, Salmaso S, Tomba GS, Wallinga J, Heijne J, Sadkowska-Todys M, Rosinska M, Edmunds WJ. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Medicine 2008; 5: e74.
45. Friel N, Pettitt AN. Marginal likelihood estimation via power posteriors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2008; 70(3):589-607.
46. Hardin JW, Hilbe JM. Generalized Linear Models and Extensions. Stata Press: College Station, Texas, 2007.
47. Abramowitz M, Stegun I. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications: New York, 1964.
48. Brockwell PJ, Davis RA. Time Series: Theory and Methods. Springer: New York, 1991.