Nonparametric regression analysis for group testing data

Group testing is a procedure employed to reduce the cost and increase the speed of large screening studies where infection or contamination of individuals is detected by a test carried out on a sample of, for example, blood, urine, water, etc. Instead of testing the sample of each individual, the method consists in pooling samples of groups of several individuals, and test those pooled samples. We construct a nonparametric procedure for estimating the conditional probability of contamination given an explanatory variable, when the observations are pooled data of this type. We investigate asymptotic theoretical properties of the estimator and establish its consistency. The procedure requires the selection of an important smoothing parameter, and we suggest a way for choosing it automatically from the data. We illustrate the numerical performance of the method on some simulated examples and on data from the National Health and Nutrition Examination Survey. We discuss extensions of the procedure to cases where the test is imprecise and the covariates are observed inaccurately, and to the multivariate setting. Supplemental materials including proofs, R codes and additional simulation results are available from the online JASA website.