Estimation in emerging epidemics: biases and remedies

Abstract

When analysing new emerging infectious disease outbreaks, one typically has observational data over a limited period of time and several parameters to estimate, such as growth rate, the basic reproduction number R 0 , the case fatality rate and distributions of serial intervals, generation times, latency and incubation times and times between onset of symptoms, notification, death and recovery/discharge. These parameters form the basis for predicting a future outbreak, planning preventive measures and monitoring the progress of the disease outbreak. We study inference problems during the emerging phase of an outbreak, and point out potential sources of bias, with emphasis on: contact tracing backwards in time, replacing generation times by serial intervals, multiple potential infectors and censoring effects amplified by exponential growth. These biases directly affect the estimation of, for example, the generation time distribution and the case fatality rate, but can then propagate to other estimates such as R 0 and growth rate. We propose methods to remove or at least reduce bias using statistical modelling. We illustrate the theory by numerical examples and simulations.

Full text

Its licence does not allow us to show the full text. Read it at PubMed Central:

References 32

1. 1.

   Diekmann O, Heesterbeek H, Britton T 2013 Mathematical tools for understanding infectious disease dynamics. Princeton, NJ: Princeton University Press.

   Not in our library

2. 2.

   Trapman P, Ball F, Dhersin JS, Tran VC, Wallinga J, Britton T 2016 Inferring R0 in emerging epidemics: the effect of common population structure is small. J. R. Soc. Interface 13, 20160288 ()

   Not in our library10.1098/rsif.2016.0288

3. 3.

   WHO Ebola Response Team. 2014 Ebola virus disease in West Africa—the first 9 months of the epidemic and forward projections. N. Engl. J. Med. 371, 1481–1495. ()

   Not in our library10.1056/nejmoa1411100

4. 4.

   Anderson RM, May RM 1991 Infectious diseases of humans: dynamics and control. New York, NY: Wiley.

   Not in our library

5. 5.

   Kermack WO, McKendrick AG 1927 A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700–721. Reprinted as Bull. Math. Bio. (1991). 53, 33–55 ()

   Not in our library10.1098/rspa.1927.0118

6. 6.

   Jagers P 1975 Branching processes with biological applications. New York, NY: John Wiley & Sons.

   Not in our library

7. 7.

   Svensson Å 2015 The influence of assumptions on generation time distributions in epidemic models. Math. Biosci. 270, 81–89. ()

   Not in our library10.1016/j.mbs.2015.10.006

8. 8.

   Wallinga J, Lipsitch M 2007 How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. R. Soc. B 275, 599–604. ()

   Not in our library10.1098/rspb.2006.3754

9. 9.
   Real-time Estimates in Early Detection of SARS · 2006

   No notice
10. 10.

    Cauchemez S, Boëlle P-Y, Thomas G, Valleron A-J 2006 Estimating in real time the efficacy of measures to control emerging communicable diseases. Am. J. Epidemiol. 164, 591–597. ()

    Not in our library10.1093/aje/kwj274

11. 11.

    Mercer GN, Glass K, Becker NG 2011 Effective reproduction numbers are commonly overestimated early in a disease outbreak. Stat. Med. 30, 984–994. ()

    Not in our library10.1002/sim.4174

12. 12.

    Rebuli NP, Bean NG, Ross JV 2018 Estimating the basic reproductive number during the early stages of an emerging epidemic. Theor. Pop. Biol. 119, 26–36. ()

    Not in our library10.1016/j.tpb.2017.10.004

13. 13.

    Walker JN 2016 Inference methods for the first few hundred studies. MPh thesis, University of Adelaide, Australia. See http://hdl.handle.net/2440/99525.

    Not in our library

14. 14.

    Black AJ, Ross JV 2013 Estimating a Markovian epidemic model using household serial interval data from the early phase of an epidemic. PLoS ONE 8, e73420 ()

    Not in our library10.1371/journal.pone.0073420

15. 15.

    Black AJ, Geard N, McCaw JM, McVernon J, Ross JV 2017 Characterising pandemic severity and transmissibility from data collected during first few hundred studies. Epidemics 19, 61–73. ()

    Not in our library10.1016/j.epidem.2017.01.004

16. 16.

    Griffin JT, Garske T, Ghani AC, Clarke PS 2011 Joint estimation of the basic reproduction number and generation time parameters for infectious disease outbreaks. Biostatistics 12, 303–312. ()

    Not in our library10.1093/biostatistics/kxq058

17. 17.

    Svensson Å 2007 A note on generation times in epidemic models. Math. Biosci. 208, 300–311. ()

    Not in our library10.1016/j.mbs.2006.10.010

18. 18.

    Scalia Tomba G, Svensson Å, Asikainen T, Giesecke J 2010 Some model based considerations on observing generation times for communicable diseases. Math. Biosci. 223, 24–31. ()

    Not in our library10.1016/j.mbs.2009.10.004

19. 19.

    Champredon D, Dushoff J 2016 Intrinsic and realized generation intervals in infectious-disease transmission. Proc. R. Soc. B 282, 2015–2026. ()

    Not in our library10.1098/rspb.2015.2026

20. 20.

    Giesecke J, Scalia-Tomba G, Berglund O, Berntorp E, Schulman S, Stigendal L 1988 Incidence of symptoms and AIDS in 146 Swedish haemophiliacs and blood transfusion recipients infected with human immunodeficiency virus. Br. Med. J. 297, 99–102. ()

    Not in our library10.1136/bmj.297.6641.99

21. 21.

    Darby SC, Doll R, Rizza CR, Spooner RJD 1989 Seropositivity for HIV in U.K. haemophiliacs. Phil. Trans. R. Soc. Lond. B 325, 179–183. ()

    Not in our library10.1098/rstb.1989.0083

22. 22.

    Struthers CA, Farewell VT 1989 A mixture model for time to AIDS data with left truncation and an uncertain origin. Biometrika 76, 814–817. ()

    Not in our library10.1093/biomet/76.4.814

23. 23.

    De Gruttola V, Lagakos SW 1989 Analysis of doubly-censored survival data, with application to AIDS. Biometrics 45, 1–11. ()

    Not in our library10.2307/2532030

24. 24.

    Donnelly CA et al. 2003 Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. Lancet 361, 1761–1766. ()

    Not in our library10.1016/s0140-6736(03)13410-1

25. 25.

    McBryde ES, Gibson G, Pettitt AN, Zhang Y, Zhao B, McElwain DLS 2006 Bayesian modelling of an epidemic of severe acute respiratory syndrome. Bull. Math. Biol. 68, 889–917. ()

    Not in our library10.1007/s11538-005-9005-4

26. 26.
    When are pathogen genome sequences informative of transmission events? · 2018

    No notice
27. 27.

    Garske T et al. 2017 Heterogeneities in the case fatality ratio in the West African Ebola outbreak 2013–2016. Phil. Trans. R. Soc. B 372, 20160308 ()

    Not in our library10.1098/rstb.2016.0308

28. 28.

    Taïb Z 1992 Branching processes and neutral evolution. Lecture Notes in Biomathematics 93. Berlin, Germany: Springer.

    Not in our library

29. 29.

    Garske T, Legrand J, Donnelly CA, Ward H, Cauchemez S, Fraser C, Ferguson NM, Ghani AC 2009 Assessing the severity of the novel influenza A/H1N1 pandemic. Br. Med. J. 339, b2840 ()

    Not in our library10.1136/bmj.b2840

30. 30.

    Nishiura H, Klinkenberg D, Roberts M, Heesterbeek JA 2009 Early epidemiological assessment of the virulence of emerging infectious diseases: a case study of an influenza pandemic. PLoS ONE 4, e6852 ()

    Not in our library10.1371/journal.pone.0006852

31. 31.

    Kucharski AJ, Edmunds WJ 2014 Case fatality rate for Ebola virus disease in West Africa. Lancet 384, 1260 ()

    Not in our library10.1016/s0140-6736(14)61706-2

32. 32.

    Lau MSY, Dalziel BD, Funk S, McClelland A, Tiffany A, Riley S, Metcalf CJE, Grenfell BT 2017 Spatial and temporal dynamics of superspreading events in the 2014–2015 West Africa Ebola epidemic. Proc. Natl Acad. Sci. USA 114, 2337–2342. ()

    Not in our library10.1073/pnas.1614595114

Cited by papers we hold 3

• Epidemiology of Infections with SARS-CoV-2 Omicron BA.2 Variant, Hong Kong, January–March 2022 · 2022
  No notice
• The epidemicity index of recurrent SARS-CoV-2 infections · 2021
  Not checked
• Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data, March 2020 · 2020
  No notice

Reads

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.