Comparing methods to quantify experimental transmission of infectious agents. (English) Zbl 1129.92051
Summary: Transmission of an infectious agent can be quantified from experimental data using the transient-state (TS) algorithm. The TS algorithm is based on the stochastic SIR model and provides a time-dependent probability distribution over the number of infected individuals during an epidemic, with no need for the experiment to end in final-size (e.g., where no more infections can occur). Because of numerical limitations, the application of the TS algorithm is limited to populations with only a few individuals. We investigated the error of using the easily applicable, time-independent final-size (FS) algorithm knowing that the FS situation was not reached.
We conclude that the methods based on the FS algorithm: (i) underestimate \(R_{0}\), (ii) are liberal when testing \(H_{0}:R_{0}\geqslant \) 1 against \(H_{1}:R_{0}<\) 1, (iii) are conservative when testing \(H_{0}:R_{0}\leqslant \) 1 against \(H_{1}:R_0>1\), and (iv) are conservative when testing \(H_{0}:R_{\text{control}} = R_{\text{treatment}}\) against \(H_{1}:R_{\text{control}} > R_{\text{treatment}}\). Furthermore, a new method is presented to find a difference in transmission between two treatment groups (MaxDiff test). The MaxDiff test is compared to tests based on FS and TS algorithms. The TS test and the MaxDiff test were most powerful (approximately equally powerful) in finding a difference, whereas the FS test was less powerful (especially, when both \(R_{\text{control}}\) and \(R_{\text{treatment}}\) are \(>\)1).
We conclude that the methods based on the FS algorithm: (i) underestimate \(R_{0}\), (ii) are liberal when testing \(H_{0}:R_{0}\geqslant \) 1 against \(H_{1}:R_{0}<\) 1, (iii) are conservative when testing \(H_{0}:R_{0}\leqslant \) 1 against \(H_{1}:R_0>1\), and (iv) are conservative when testing \(H_{0}:R_{\text{control}} = R_{\text{treatment}}\) against \(H_{1}:R_{\text{control}} > R_{\text{treatment}}\). Furthermore, a new method is presented to find a difference in transmission between two treatment groups (MaxDiff test). The MaxDiff test is compared to tests based on FS and TS algorithms. The TS test and the MaxDiff test were most powerful (approximately equally powerful) in finding a difference, whereas the FS test was less powerful (especially, when both \(R_{\text{control}}\) and \(R_{\text{treatment}}\) are \(>\)1).
MSC:
| 92C60 | Medical epidemiology |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62N03 | Testing in survival analysis and censored data |
References:
| [1] | Greenwood, M.; Bradford Hill, A. T.; Wilson, W. W.C., Experimental Epidemiology (1936), HM Stationary Office: HM Stationary Office London, UK |
| [2] | Kermack, W. O.; McKendrick, A. G., Contributions to the mathematical theory of epidemics IV. Analysis of experimental epidemics of the virus disease mouse ectromelia, J. Hyg. (Cambridge), 37, 172 (1936) |
| [3] | Kermack, W. O.; McKendrick, A. G., Contributions to the mathematical theory of epidemics. V - analysis of experimental epidemics of mouse typhoid: a bacterial disease conferring incomplete immunity, J. Hyg. (Cambridge), 39 (1939) |
| [4] | Anderson, R. M.; May, R. M., Population biology of infectious diseases: part I, Nature, 280, 361 (1979) |
| [5] | De Jong, M. C.; Kimman, T. G., Experimental quantification of vaccine-induced reduction in virus transmission, Vaccine, 12, 761 (1994) |
| [6] | Bouma, A.; De Jong, M. C.M.; Kimman, T. G., Transmission of pseudorabies virus within pig populations is independent of the size of the population, Prev. Vet. Med., 23, 163 (1995) |
| [7] | Bouma, A.; De Jong, M. C.; Kimman, T. G., Transmission of two pseudorabies virus strains that differ in virulence and virus excretion in groups of vaccinated pigs, Am. J. Vet. Res., 57, 43 (1996) |
| [8] | Velthuis, A. G.J.; de Jong, M. C.M.; De Bree, J.; Nodelijk, G.; van Boven, M., Quantification of transmission in one-to-one experiments, Epidemiol. Infect., 128, 193 (2002) |
| [9] | Bouma, A.; De Jong, M. C.; Kimman, T. G., Comparison of two pseudorabies virus vaccines, that differ in capacity to reduce virus excretion after a challenge infection, in their capacity of reducing transmission of pseudorabies virus, Vet. Microbiol., 54, 113 (1997) |
| [10] | Bouma, A.; De Jong, M. C.; Kimman, T. G., The influence of maternal immunity on the transmission of pseudorabies virus and on the effectiveness of vaccination, Vaccine, 15, 287 (1997) |
| [11] | Bouma, A.; De Jong, M. D.; Kimman, T. G., The influence of maternal immunity on the development of the in vitro lymphocyte proliferation response against pseudorabies virus in pigs, Res. Vet. Sci., 64, 167 (1998) |
| [12] | Bouma, A.; De Smit, A. J.; De Jong, M. C.M.; De Kluijver, E. P.; Moormann, R. J.M., Determination of the onset of the herd-immunity induced by the E2 sub-unit vaccine against classical swine fever virus, Vaccine, 18, 1374 (2000) |
| [13] | Velthuis, A. G.J.; De Jong, M. C.M.; Kamp, E. M.; Stockhofe, N.; Verheijden, J. H.M., Design and analysis of an Actinobacillus pleuropneumoniae transmission experiment, Prev. Vet. Med., 60, 53 (2003) |
| [14] | Velthuis, A. G.J.; De Jong, M. C.M.; Stockhofe, N.; Vermeulen, T. M.M.; Kamp, E. M., Transmission of Actinobacillus pleuropneumoniae in pigs is characterized by variation in infectivity, Epidemiol. Infect., 129, 203 (2002) |
| [15] | Wit, J. J.d.; de Jong, M. C.M.; Pijpers, A.; Verheijden, J. H.M.; de Wit, J. J.; De Jong, M. C.M., Transmission of infectious bronchitis virus within vaccinated and unvaccinated groups of chickens, Avian Pathol., 27, 464 (1998) |
| [16] | Laevens, H.; Koenen, F.; Deluyker, H.; Berkvens, D.; de Kruif, A., An experimental infection with classical swine fever virus in weaner pigs. I. Transmission of the virus, course of the disease, and antibody response, Vet. Q, 20, 41 (1998) |
| [17] | Mars, M. H.; de Jong, M. C.; van Oirschot, J. T., A gE-negative bovine herpesvirus 1 vaccine strain is not reexcreted nor transmitted in an experimental cattle population after corticosteroid treatments, Vaccine, 18, 1975 (2000) |
| [18] | Mars, M. H.; de Jong, M. C.M.; van Maanen, C.; Hage, J. J.; van Oirschot, J. T., Airborne transmission of bovine herpesvirus 1 infections in calves under field conditions, Vet. Microbiol., 76, 1 (2000) |
| [19] | Mars, M. H.; de Jong, M. C.M.; van Oirschot, J. T., A gE-negative BHV1 vaccine virus strain cannot perpetuate in cattle populations, Vaccine, 18, 2120 (2000) |
| [20] | Nodelijk, G.; de Jong, M. C.M.; van Leengoed, L., A quantitative assessment of the effectiveness of PRRSV vaccination in pigs under experimental conditions, Vaccine, 19, 3636 (2001) |
| [21] | Van Nes, A.; De Jong, M. C.; Schoevers, E. J.; Van Oirschot, J. T.; Verheijden, J. H., Pseudorabies virus is transmitted among vaccinated conventional pigs, but not among vaccinated SPF pigs, Vet. Microbiol., 80, 303 (2001) |
| [22] | Dewulf, J.; Leavens, H.; Koenen, F.; Mintiens, K.; de Kruif, A., An E2 sub-unit marker vaccine does not prevent horizontal or vertical transmission of classical swine fever virus, Vaccine, 20, 86 (2001) |
| [23] | Klinkenberg, D.; De Bree, J.; Laevens, H.; De Jong, M. C.M., Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments, Epidemiol. Infect., 128, 293 (2002) |
| [24] | Maurice, H.; Nielen, M.; Stegeman, J. A.; Vanderhallen, H.; Koenen, F., Transmission of Encephalomyocarditis virus (EMCV) among pigs experimentally quantified, Vet. Microbiol., 88, 301 (2002) |
| [25] | Bartlett, M. S., Some evolutionary stochastic processes, J. R. Stat. Soc. Ser. B, 11, 211 (1949) · Zbl 0037.08503 |
| [26] | Bailey, N. T.J., General epidemics, (Bailey, N. T.J., The Mathematical Theory of Infectious Diseases and its Applications (1975), Hafner: Hafner New York), 81 · Zbl 0134.38002 |
| [27] | Diekmann, O.; Heesterbeek, J. A.; Metz, J. A., On the definition and the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28, 365 (1990) · Zbl 0726.92018 |
| [28] | Velthuis, A. G.J.; Bouma, A.; Katsma, W. E.A.; Nodelijk, G.; De Jong, M. C.M., Design and analysis of small-scale transmission experiments with animals, Epidemiol. Infect., 135, 202 (2007) |
| [29] | Karlin, S.; Taylor, H. M., A first course in stochastic processes (1975), Academic: Academic New York · Zbl 0315.60016 |
| [30] | Billard, L.; Zhao, Z., The stochastic general epidemic revisited and a generalization, IMAJ Math. Appl. Med. Biol., 67 (1993) · Zbl 0774.92015 |
| [31] | Daley, D. J.; Gani, J., Stochastic models in continuous time, (Daley, D. J.; Gani, J., Epidemic Modelling: An Introduction (1999), Cambridge University: Cambridge University Cambridge), 56 · Zbl 0922.92022 |
| [32] | Gilks, W. R.; Richardson, S.; Spiegelhalter, D. J., Markov Chain Monte Carlo in Practice (1996), Chapman & Hall: Chapman & Hall London · Zbl 0832.00018 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
