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Excerpt from Pooled Testing for Hiv Screening: Capturing the Dilution Effect In the first years of the aids epidemic, numerous instances of aids infection caused by blood transfusion were reported to the Center for Disease Control. The incidence indi cated that the blood supply is a virtually frictionless pathway for spreading the epidemic, and the extent of the epidemic dictated that screening at the individual level should be adopted. As a consequence, all infected blood donors would be identified and a measurably safer blood supply would be attained. Nevertheless, the cost for such a screening program is substantial, and many developing countries, particularly in Africa where the epidemic is spreading rapidly, are struggling to fight the disease on limited budgets. Pooled testing is one potential way to reduce the monetary cost without compromising the accuracy of the tests. The rationale behind pooled testing is simple and intuitive: suppose we can pool the sera from ten (for example) individuals and test the pool using a single test. If the seroprevalence of hiv, which is the fraction of the population that is infected, is low enough, then there is a high probability that all ten individuals in the pool are hiv negative; in this case, we would learn from a single test what otherwise would be learned from ten individual tests. If, on the other hand, the test outcome is positive, then additional tests (either pooled or individual) would need to be carried out. However, pooled testing has a possible shortcoming, the dilution efiect: there is a serious concern that if the pool size is too large, then any hiv positive sera will be sufficiently diluted so as to become undetectable by the test. These false negatives can be extremely costly, particularly when pooled testing is employed to protect the blood supply. Moreover, infected individuals exhibiting an unusually low level of antibody concentration are less likely to be detected when screened in pools. Co