When testing donated blood for infectious diseases, each sample can either be te

Question

When testing donated blood for infectious diseases, each sample can either be tested individually or in groups of b samples. When pooled samples are tested, a negative test indicates that all of the donors contributing to the group are disease-free. On the other hand, if a group test is positive, then each donor contributing to the group must be individually tested to determine which are infected. If there are D donors and the prevalence of the disease in the population is p, find conditions on p, b and D such that the expected number of tests performed using groups is less than the number required without grouping. For convenience, you may assume that D is an integer multiple of b.

Explanation / Answer

D is the total number of donors

b = number of samples

p = prevalence of disease

.

The first condition must be that p is very small, which makes the entire population to be less likely to be checked indivdually

Second condition: D is very large that makes it difficult to follow the individual tests and hence increases its number

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