Robustness of Group Testing in the Estimation of Proportions

Abstract

In binomial group testing, unlike one-at-a-time testing, the test unit consists of a group of individuals, and each group is declared to be defective or nondefective. A defective group is one that is presumed to include one or more defective (e.g., infected, positive) individuals and a nondefective group to contain only nondefective individuals. The usual binomial model considers the individuals being grouped as independent and identically distributed Bernoulli random variables. Under the binomial model and presuming that groups are tested and classified without error, it has been shown that, when the proportion of defective individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives. We discuss the robustness of group testing for estimating proportions when the underlying assumptions of (i) no testing errors and (ii) independent individuals are violated. To evaluate the effect of these model violations, two dilution-effect models and a serial correlation model are considered. Group testing proved to be quite robust to serial correlation. In the presence of a dilution effect, smaller group sizes should be used, but most of the benefits of group testing can still be realized.

Optimality of group testing in the presence of misclassification

“…This strategy and its variations developed later, often referred to as group testing or pooled testing, have received substantial attention for efficient identification of an event or estimation of the probability that the event occurs; see Sobel & Groll (1959), Sobel & Elashoff (1975), Le (1981), Gastwirth & Hammick (1989), Chen & Swallow (1990), Farrington (1992), Gastwirth & Johnson (1994), Hughes-Oliver & Swallow (1994), Litvak et al (1994), Tu et al (1995), Barcellos et al (1997), Brookmeyer (1999), Hung & Swallow (1999), Hughes-Oliver & Rosenberger (2000) and Tebbs & Swallow (2003). An attractive feature of group testing is that retesting on individuals is not necessary if one is only interested in estimation of the probability of a positive test.…”

More Powerful Likelihood Ratio Tests for Isotonic Binomial Proportions

“…For example, tests currently used in HIV screening are reported to have negligible loss in both sensitivity and specificity for group sizes up to 15 (Emmanuel et al, 1988;Cahoon-Young et al, 1989;Kline et al, 1989;Monzon et al, 1992;Tu et al, 1995). If, in fact, testing errors do exist but are rare, group testing with small-sized pools is often still efficient when the prevalence is small (Chen and Swallow, 1995;Hung and Swallow, 1999).…”

Cost Considerations in Choosing Group Size for Group Testing in the Seed Potato Certification Program

“…A defective group is one that includes one or more defective individuals. The purpose of group testing is either to identify the defective units in the groups tested or to estimate the proportion of defective units in the population (Hung and Swallow, 1999). The former is regarded a classification problem and the latter as an estimation problem.…”