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Quantification of transmission in one-to-one experiments

Published online by Cambridge University Press:  25 April 2002

A. G. J. VELTHUIS ,
M. C. M. DE JONG ,
J. DE BREE ,
G. NODELIJK  and
M. VAN BOVEN
A. G. J. VELTHUIS
Affiliation:
Quantitative Veterinary Epidemiology, Institute for Animal Science and Health, Edelhertweg, Lelystad, The Netherlands Quantitative Veterinary Epidemiology, Wageningen Institute of Animal Science, Wageningen University, Marijkeweg, Wageningen, The Netherlands Farm Management Group, Wageningen University, Hollandseweg, Wageningen, The Netherlands
M. C. M. DE JONG
Affiliation:
Quantitative Veterinary Epidemiology, Institute for Animal Science and Health, Edelhertweg, Lelystad, The Netherlands Quantitative Veterinary Epidemiology, Wageningen Institute of Animal Science, Wageningen University, Marijkeweg, Wageningen, The Netherlands
J. DE BREE
Affiliation:
Quantitative Veterinary Epidemiology, Institute for Animal Science and Health, Edelhertweg, Lelystad, The Netherlands
G. NODELIJK
Affiliation:
Quantitative Veterinary Epidemiology, Institute for Animal Science and Health, Edelhertweg, Lelystad, The Netherlands
M. VAN BOVEN
Affiliation:
Quantitative Veterinary Epidemiology, Institute for Animal Science and Health, Edelhertweg, Lelystad, The Netherlands
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Abstract

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We study the statistical inference from data on transmission obtained from one-to-one experiments, and compare two algorithms by which the reproduction ratio can be quantified. The first algorithm, the transient state (TS) algorithm, takes the time course of the epidemic into account. The second algorithm, the final size (FS) algorithm, does not take time into account but is based on the assumption that the epidemic process has ended before the experiment is stopped. The FS algorithm is a limiting case of the TS algorithm for the situation where time tends to infinity. So far quantification of transmission has relied almost exclusively on the FS algorithm, even if the TS algorithm would have been more appropriate. Its practical use, however, is limited to experiments with only a few animals. Here, we quantify the error made when the FS algorithm is applied to data of one-to-one experiments not having reached the final size. We conclude that given the chosen tests, the FS algorithm underestimates the reproduction ratio R0, is liberal when testing H0[ratio ]R0[ges ]1 against H1[ratio ]R0<1, is conservative when testing H0[ratio ]R0[les ]1 against H1[ratio ]R0>1 and calculates the same probability as the TS algorithm when testing H0[ratio ]R0-control = R0-treatment against H1[ratio ]R0-control>R0-treatment. We show how the power of the test depends on the duration of the experiments and on the number of replicates. The methods are illustrated by an application to porcine reproductive and respiratory syndrome virus (PRRSV).

Type
Research Article
Information
Epidemiology & Infection , Volume 128 , Issue 2 , April 2002 , pp. 193 - 204
Copyright
© 2002 Cambridge University Press