Probability estimation in group screening designs with put errors in decisions

Abstract

Sometimes due to confidentiality purposes, the objective is to estimate the proportion P of individuals that posses a certain characteristic, such as a blood disease or an antibody, without necessarily identifying the individuals. In such a case, testing blood samples from k individuals may result in an estimator of P with substantial lower mean square error than traditional estimator. The mean square error varies with k and P , and we show a method for choosing the optimal value of k . Practical considerations as applied to determining proportions of people with a disease are discussed. Substantial cost savings may result when the prevalence of a disease is low.