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Relative Mean Squared Error and Cost Considerations in Choosing Group Size for Group Testing to Estimate Infection Rates and Probabilities of Disease Transmission. William H. Swallow, Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203; Phytopathology 77:1376-1381. Accepted for publication 31 March 1987. Copyright 1987 The American Phytopathological Society. DOI: 10.1094/Phyto-77-1376.

Virus-vector research often has the goal of estimating some probability p, which may be an infection rate or a probability of disease transmission by a single vector. Statisticians have recommended group testing (multiple-vector-transfer designs) over single-vector-transfer designs for doing this efficiently. In group testing, vectors or other units are tested in groups, rather than individually. The statistical argument for group testing has been based on the superior properties of optimal (meaning minimum mean squared error) group-testing designs. However, in application, the optimal design cannot be used or even identified, because to do so requires knowing beforehand the unknown p, the very probability one is preparing to estimate. As a workable alternative, using group testing with a group size (vectors per test plant, pool size per test) presumed to be smaller than the optimal group size (for minimizing mean squared error with a fixed number of tests or test plants) has been recommended as a safe way to realize at least some (unknown) fraction of the benefits of the optimal group-testing design. A method for choosing that smaller group size has been suggested in earlier work. This paper provides more detailed information on the extent of benefits one can actually hope to realize with group testing using smaller-than-optimal group sizes. It shows that often a large fraction of the benefits of the optimal design can be attained with a much smaller group size. It further illustrates how, when costs are taken into account, using a smaller group size may actually be more cost effective than using the group size that is optimal for minimizing mean squared error.

Additional keywords: aphid vectors, estimating plant resistance, insect vectors, maximum likelihood estimation, virus transmission.