Statistical Design for a Small Serial Dilution Series

We describe statistical plans for a serial dilution series designed to detect and estimate the number of viral particles in a solution. The design addresses a problem when a very limited number of aliquots are available for proliferation. A gamma prior distribution on the number of viral particles allows us to describe the marginal probability distribution of all experimental outcomes. We examine a design that minimizes the expected reciprocal information and compare this with the maximum entropy design. We argue that the maximum entropy design is more useful from the point of view of the laboratory technician. The problem and design are motivated by our study of the viability of human immunodeficiency virus in syringes and other equipment that might mediate blood-borne viral transmission.