Correcting for Bias in Estimating Proportions Using Group Testing

• Activity Number: 282
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Graham Hepworth*+ and Ray Watson
• Companies: The University of Melbourne and The University of Melbourne
• Keywords: group testing ; estimation of proportions ; bias correction ; sequential procedure

Abstract

Group testing was used in a series of studies in Australia in which the aim was to estimate virus infection levels in ornamental plant populations. A feature of some of the studies was a sequential testing procedure involving two or three different group sizes. The MLE arising from group testing is a biased estimator of the proportion of infected plants in the population, and various adjustments have been proposed to correct it. We investigated the bias when there are groups of different size, using both fixed and sequential procedures. Analytical methods provide satisfactory bias correction for fixed procedures. For sequential procedures, with their uneven bias patterns, we propose a numerical method of correction which produces an almost unbiased estimator. It starts with the MLE and progressively modifies it, based on its expectation in the neighborhood of the estimate.