Informative Dorfman screening

Abstract

Since the early 1940s, group testing (pooled testing) has been used to reduce costs in a variety of applications, including infectious disease screening, drug discovery, and genetics. In such applications, the goal is often to classify individuals as positive or negative using initial group testing results and the subsequent process of decoding of positive pools. Many decoding algorithms have been proposed, but most fail to acknowledge, and to further exploit, the heterogeneous nature of the individuals being screened. In this article, we use individuals' risk probabilities to formulate new informative decoding algorithms that implement Dorfman retesting in a heterogeneous population. We introduce the concept of "thresholding" to classify individuals as "high" or "low risk," so that separate, risk-specific algorithms may be used, while simultaneously identifying pool sizes that minimize the expected number of tests. When compared to competing algorithms which treat the population as homogeneous, we show that significant gains in testing efficiency can be realized with virtually no loss in screening accuracy. An important additional benefit is that our new procedures are easy to implement. We apply our methods to chlamydia and gonorrhea data collected recently in Nebraska as part of the Infertility Prevention Project.

Figure 1

Comparison of Dorfman algorithms. Expected per-individual efficiency, with M = 10 and N = 1000, for p = 0.01, 0.05, 0.10, 0.20, and 0.30. The optimal pool size for D has been used. A more comprehensive comparison among D, OD, TOD, PSOD, and H is in Web Appendix C.

Figure 2

Comparison of Dorfman algorithms (OD, TOD, and PSOD) with A when M = 10 and N = 1000. Top: OD versus A; Middle: TOD versus A; Bottom: PSOD versus A. Regions in dark grey denote those where the Dorfman procedures are more efficient. The optimal (square) array size for A has been used for each (p, S_e, S_p) configuration.