An Adaptive Group-testing Procedure for Estimating Proportions

Group-testing procedures begin by testing units in groups or batches rather than one at a time. This scheme benefits from the possibility that a single measurement/response may simultaneously indicate the satisfactory state of several individual units. Indeed, the savings afforded by group-testing procedures can be substantial, provided a good choice of the group size is made. Unfortunately, careful choice of the group size for estimating the proportion of defectives/infected in a population requires some a priori knowledge of that proportion, which is not always available. This paper describes an adaptive group-testing estimation scheme that is not as sensitive to having good a priori information about the proportion (p) to be estimated as is the currentlyused group-testing estimation scheme. The comparison between the two procedures is based on asymptotic and small-sample relative efficiency. In large samples (~ 100), the adaptive estimator is at least comparable to the nonadaptive estimator, and can be much more efficient than the nonadaptive estimator. In small samples, the adaptive estimator is the more efficient when the a priori value for p is less than the true value (possibly thousands of times as efficient as the nonadaptive estimator), with the cost being a slight loss in efficiency when the priori value is equal to p (and hence no adaptation is needed) or larger. Thus, the adaptive estimator is recommended with the restriction that adaptations (adjustments in group size as data are collected) are based on at least ten measurements/responses to provide adequate information