Quantification of transmission in one-to-one experiments

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 <e1>R</e1><inf>0</inf>, is liberal when testing <e1>H0</e1>∶<e1>R</e1><inf>0</inf>1 against <e1>H1</e1>∶<e1>R</e1><inf>0</inf>&lt;1, is conservative when testing <e1>H0</e1>∶<e1>R</e1><inf>0</inf>1 against <e1>H1</e1>∶<e1>R</e1><inf>0</inf>>1 and calculates the same probability as the TS algorithm when testing <e1>H0</e1>∶<e1>R</e1><inf>0-control</inf> = <e1>R</e1><inf>0-treatment</inf> against <e1>H1</e1>∶<e1>R</e1><inf>0-control</inf>><e1>R</e1><inf>0-treatment</inf>. 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).