Nonparametric Regression Analysis for Group Testing Data

• Published in: Journal of the American Statistical Association Vol. 106; no. 494; pp. 640 - 650
• Main Authors: Delaigle, Aurore, Meister, Alexander
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2011; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Bandwidth selection; Bandwidths; Binary regression; Consistent estimators; Data analysis; Diagnostic tests; Disease models; Dorfman screening; Estimation; Estimation bias; Estimation methods; Estimators; Exact sciences and technology; General topics; Group size; Kernel estimator; Local polynomial estimator; Mathematics; Medical research; Medical sciences; Medical statistics; Methodology; Modeling; Multivariate analysis; Nonparametric inference; Parameter estimation; Polynomials; Pooled data; Prevalence; Probability; Probability and statistics; Regression analysis; Sample size; Sampling; Sciences and techniques of general use; Simulation; Statistics; Survey data; Theory and Methods; Biometrics; Polynomial; Dorfman screening; Prevalence; Bandwith selection; Non parametric estimation; Numerical method; Conditional probability; Multivariate analysis; Covariate; Kernel estimator; Stochastic method; Statistical test; Medical science; Consistent estimator; Smoothing parameter; Local polynomial estimator; Sample survey; Speed; Discriminant analysis; Data analysis; Bandwidth selection; Nutrition; Grouped data; Asymptotic behavior; Nonparametric regression; Kernel estimation; Pooled data; Statistical estimation; Regression analysis; Binary regression; Statistical method; Statistical regression; Numerical analysis; Sampling theory; Simulation; Observation data
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2011.tm10520

Group testing is a procedure used to reduce the cost and increase the speed of large screening studies in which infection or contamination of individuals is detected by a test carried out on a sample of, for example, blood, urine, or water. Instead of testing the sample of each individual, the method involves pooling samples of groups of several individuals and testing 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 selecting an important smoothing parameter, and we suggest a way to do this 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.