Nonparametric methods for group testing data, taking dilution into account

Abstract

Group testing methods are used widely to assess the presence of a contaminant, based on measurements of the concentration of a biomarker, for example to test the presence of a disease in pooled blood samples. The test would be perfect if it produced a positive result whenever the contaminant was present, and a negative result otherwise. However, in practice the test is always at least somewhat imperfect, for example because it is sensitive to the proportion of contaminated items in the group, rather than to the sheer existence of one or more contaminated items. We develop a nonparametric method for accommodating this dilution effect. Our approach allows us to estimate, under minimal assumpti..