Array-based schemes for group screening with test errors which incorporate a concentration effect

• Group screening for case identification with a concentration effect.
• Formulae for the expected numbers of tests, missed negatives and missed positives for the Dorfman, and, or and A2A2 schemes.
• Illustrative examples.
• Results extended to group factor screening.

Group screening is widely used as an efficient method for identifying samples or factors from a large population that are in some sense active. The focus in the present paper is on screening blood samples for infectious diseases when errors in testing are present. Specific attention is given to the introduction of a concentration effect, that is to settings in which the error in testing a group of blood samples depends on the number of samples in that group which are infected. Four array-based group screening schemes, the Dorfman, the and, the or and a modification of the and scheme, are considered and their performance appraised by deriving explicit formulae for the expected number of tests, the expected number of false negatives and the expected number of false positives. The results are illustrated by means of two examples. As an aside, relationships complementary to those derived in the context of blood screening are developed within the area of group factor screening.