Maximum Likelihood Estimators in Regression Models for Error‐prone Group Testing Data

Incorporating retesting outcomes for estimation of disease prevalence

Group testing has been widely used as a cost-effective strategy to screen for and estimate the prevalence of a rare disease. While it is well-recognized that retesting is necessary for identifying infected subjects, it is not required for estimating the prevalence. For a test without misclassification, gains in statistical efficiency are expected from incorporating retesting results in the estimation of the prevalence. However, when the test is subject to misclassification, it is not clear how much gain should be expected. There are a number of theoretical challenges in addressing this issue, including (1) enumerating the potential test results from retesting individual subjects in a group, (2) the dependence among these test results and the test result from testing at the group level, and (3) differential misclassification due to pooling of biospecimens. Overcoming some of these challenges, we show that retesting subjects in either positive or negative groups can substantially improve the efficiency of the estimation and that retesting positive groups yields higher efficiency than retesting a same number or proportion of negative groups.