Topics in Heterogeneous Group Testing

DISS_abstract\u3e Since the early 1940s, group testing has been widely used to reduce costs in a variety of applications, including infectious disease screening, drug discovery, and genetics. Statistical research in group testing generally splits into two areas: classification and estimation. Following this bifurcated structure, this dissertation consists of three research problems which address methods of classification and estimation in a heterogeneous population. The goal of classification is to identify all positives among those individuals screened 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 dissertation, we use individuals\u27 risk probabilities to formulate group testing algorithms which implement Dorfman retesting and array testing in a heterogeneous population. When compared to competing algorithms which treat the population as homogeneous, we show that significant gains in testing efficiency can be realized when using our informative retesting methods. In addition, with the recent development of pooled binary response regression models, the estimation problem has been extended to acknowledge population heterogeneity. Unfortunately, all existing group testing regression approaches have assumed that testing error rates for pooled specimens are known and are independent of the pool sizes used. In this dissertation, we remove this potentially unrealistic modeling assumption. We also show that when pool responses are in fact subjected to a dilution effect, existing regression methods can lead to inaccurate inference, especially when larger pool sizes are used