Nonparametric and Parametric Estimators of Prevalence From Group Testing Data With Aggregated Covariates

Abstract

Group testing is a technique employed in large screening studies involving infectious disease, where individuals in the study are grouped before being observed. Parametric and nonparametric estimators of conditional prevalence have been developed in the group testing literature, in the case where the binary variable indicating the disease status is available only for the group, but the explanatory variable is observed for each individual. However, for reasons such as the high cost of assays, the confidentiality of the patients, or the impossibility of measuring a concentration under a detection limit, the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid. We develop consistent parametric and nonparametric estimators of the conditional prevalence in this complex problem. We establish theoretical properties of our estimators and illustrate their practical performance on simulated and real data. We extend our techniques to the case where the group status is measured imperfectly, and to the setting where the covariate is aggregated and the individual status is available. Supplementary materials for this article are available online.

• Averaged biomarker
• Binary outcome
• Group testing
• Local polynomial
• Nonparametric regression
• Pooled data

Additional information

Notes on contributors

Aurore Delaigle

Aurore Delaigle, School of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia, and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights, Parkville, VIC, 3010, Australia (E-mail: [email protected]). Wen-Xin Zhou, School of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia, and Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). This research was supported by a grant and a fellowship from the Australian Research Council. The NHANES data are available from the NHANES website of the Centers for Disease Control and Prevention, National Center for Health Statistics, Hyattsville, MD: http://wwwn.cdc.gov/nchs/nhanes/search/nhanes99_00.aspx.

Wen-Xin Zhou

Aurore Delaigle, School of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia, and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights, Parkville, VIC, 3010, Australia (E-mail: [email protected]). Wen-Xin Zhou, School of Mathematics and Statistics, University of Melbourne, VIC, 3010, Australia, and Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). This research was supported by a grant and a fellowship from the Australian Research Council. The NHANES data are available from the NHANES website of the Centers for Disease Control and Prevention, National Center for Health Statistics, Hyattsville, MD: http://wwwn.cdc.gov/nchs/nhanes/search/nhanes99_00.aspx.