Regression models for group testing: identifiability and asymptotics

Abstract

Group testing has been widely used in epidemiology and related fields to estimate prevalence of rare diseases. Parametric binary regression models are used in group testing to estimate the covariate adjusted prevalence. Unlike the standard binary regression model (viz., logistic, complementary log–log, etc.), the regression model for group testing data connects the maximum of a group of independent binary responses to its covariate values. Recently, in group testing literature, it has been extensively used for estimating covariate adjusted prevalence of a disease making the tacit assumptions that (i) the regression model is identifiable, and (ii) the standard asymptotic theory is valid for the maximum likelihood estimators of the regression parameters. Verifying these assumptions is found to be non-trivial theoretical issues. In this paper, we give theoretical proofs of these assumptions under a set of simple sufficient conditions, thus, providing a theoretical justification for likelihood based inference on the regression parameters. We also provide an outline of the proof extending the asymptotic theory to the data obtained by Dorfman retesting, where all subjects in a positive group are retested.