|Bias Correction for the Estimation of Proportions Using Group Testing
Graham Hepworth, Department of Mathematics and Statistics, University of Melbourne
Wednesday, April 18, 2012
4:00 p.m., room 237, Weber Bldg
Group testing (also known as pooled testing) occurs when units from a population are pooled together and tested as groups for the presence of an attribute, such as a disease. A positive result indicates the presence of at least one positive unit in the group. Our interest in group testing arose from an assessment of the prevalence of viruses in carnations grown in glasshouses. A sequential three-stage testing procedure was used, with progressively smaller group sizes at each stage. Such procedures reduce the probability of obtaining all positive groups, an outcome to be avoided if possible.
The MLE of the population prevalence is biased, and various adjustments have been proposed to correct for the bias. Analytical correction works well when all groups have the same number of units, or when the testing procedure is not sequential. It does not work so well for most sequential procedures because of the uneven bias patterns. For those situations we have developed a numerical method of correction which produces an almost unbiased estimator. It starts with the MLE and removes a substantial amount of the remaining bias with each iteration. The mean squared error properties of the numerically corrected estimator are at least as good as those of the MLE.
*This is a joint work with Ray Watson