Debiased estimation of proportions in group testing

Abstract

In the assessment of disease, estimation of the proportion of infected units in a population can sometimes be facilitated by pooling units into groups for testing. Such group testing was used in a study of virus infection levels in carnation plants grown in glasshouses. In group testing problems, the maximum likelihood estimator is a biased estimator of the population proportion. We investigate the bias of the maximum likelihood estimator when testing groups of different size, using fixed and sequential procedures. The possibility of obtaining all positive groups contributes substantially to the bias. Analytical methods are shown to correct the bias for fixed procedures satisfactorily. For sequential procedures, with their uneven bias patterns, we propose a numerical method of correction which produces an almost unbiased estimator. © 2009 Royal Statistical Society.