Design and Analysis of Multistage Group Testing Surveys with Application to Detecting and Estimating Prevalence of Transgenic Corn in Mexico

Group testing is a cost efficient technique first proposed by Dorfman (1943) to detect soldiers with syphilis during World War II. It is a cost efficient technique since in place of performing a diagnostic test on each individual, the blood of s individuals is pooled and a diagnostic test is applied to each pool. Assuming a perfect diagnostic test, if a pool tests positive, at least one of the s individuals in the pool is positive, while if a pool tests negative, all s individuals in a pool are free of the disease. When a pool tests positive, the blood of each individual is re-tested to identify the individuals with syphilis. However, If the purpose of the analysis is only to estimate prevalence, it is not necessary to re-test the members of a positive group (Remund et al., 2001; Hernandez-Suarez et al., 2008). When a positive individual is rare this method produces a significant saving of time and resources, with reported reductions in the number of required diagnostic tests of more than 80% (Remund et al., 2001).;Group testing has been used to estimate the prevalence of diseases or to classify individual animals, plants or humans (Dodd et al., 2002; Remlinger et al., 2006; Verstraeten et al., 1998; Peck, 2006; Hernandez-Suarez et al., 2008) and has motivated the development of sampling methods and regression models for group testing data. In the case of sampling methods for group testing, only methods for sample size determination under simple random sampling (SRS) have been developed. Group testing regression models have been well developed under SRS and under two stage sampling. However, under two stage sampling these models assume that the sample of clusters (primary sampling units) and individuals (secondary sampling units) are taken under SRS. However, in many applications this assumption is violated since the primary sampling units are selected with probability proportional to size (PPS) as opposed to SRS. An additional problem is that PPS sampling can produce an informative sampling process, where the response variable is correlated with the probability of selection even after conditioning on the model covariates (Pfeffermann, et al., 2006). Informative sampling can produce substantial biases when using traditional estimation methods in either group testing or non-group testing applications.;One recent application of group testing used to estimate the prevalence of rare traits under a complex survey structure was described in Pineyro-Nelson, et al. (2009). They used group testing to estimate the presence of transgenic corn in Mexico. However, due to the lack of an appropriate methodology they analyzed the data ignoring the complex sampling structure with the likely consequences of producing inefficient and possible biased estimates. For this reason, the present work develops sampling designs and regression group testing methods for complex surveys and these methods are used to estimate the prevalence of transgenic corn in Mexico.