Group testing regression models with dilution submodels

Abstract

Group testing, where specimens are tested initially in pools, is widely used to screen individuals for sexually transmitted diseases. However, a common problem encountered in practice is that group testing can increase the number of false negative test results. This occurs primarily when positive individual specimens within a pool are diluted by negative ones, resulting in positive pools testing negatively. If the goal is to estimate a population-level regression model relating individual disease status to observed covariates, severe bias can result if an adjustment for dilution is not made. Recognizing this as a critical issue, recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution. In this paper, we have the same overall goal but take a different approach. We augment existing group testing regression models (that assume no dilution) with a parametric dilution submodel for pool-level sensitivity and estimate all parameters using maximum likelihood. An advantage of our approach is that it does not rely on external biomarker test data, which may not be available in surveillance studies. Furthermore, unlike previous approaches, our framework allows one to formally test whether dilution is present based on the observed group testing data. We use simulation to illustrate the performance of our estimation and inference methods, and we apply these methods to 2 infectious disease data sets.

Keywords: binary regression; dilution effect; likelihood ratio test; maximum likelihood; pooled testing; sensitivity.

Figure 1

Irish HBV data. Estimated regression functions for the model in (9), averaged over B = 500 implementations of DT for different master pool sizes c_j = c. Master pools were created by random assignment. The covariate x is the standardized value of age. In each subfigure, the estimated individual data regression function is shown for comparison.