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a detection limit, the explanatory variable is observable only in an aggregated form and the existing techniques are no longer valid.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.

Nonparametric adaptive estimation for grouped data

“…However, theoretical optimality properties for the adaptive procedure have only been shown under quite restrictive assumptions on the characteristic function. Meister (2007) also proposed a generalization of the estimation procedure to the skewed case and a modified version of this estimator is used by Delaigle and Zhou (2015). However, this estimator has the disadvantage that it is not given in a closed form, making the practical calculation difficult to handle.…”

“…Recently, Delaigle and Zhou (2015) studied the nonparametric estimation of the probability of contamination given a covariate X, when only aggregated observations of this covariate are available. From an applied point of view, grouped data are encountered in many fields, especially related to the study of infection diseases.…”

Group testing regression models with dilution submodels

“…Other extensions could include using submodels which are specified nonparametrically, eg, h (·,·, λ ) monotone in λ , or using Bayesian methods if prior information on the dilution effect is available. Finally, it should be possible to utilize our dilution submodel approach with other group testing regression methods, such as those which incorporate random effects, covariate measurement error, and aggregated covariates …”

“…Finally, it should be possible to utilize our dilution submodel approach with other group testing regression methods, such as those which incorporate random effects, 36 covariate measurement error, 37 and aggregated covariates. 38…”

Determination of Varying Group Sizes for Pooling Procedure

“…Note that only group-level status is observed, e.g., positive or negative. This problem has been studied in parametric context through the framework of binary regression models [29–31], and also in semiparametric [32, 33] or nonparametric context [34, 35]. However, aforementioned work mostly uses a single group size that is determined in advance.…”