  Choosing an optimal strategy for hierarchical group testing is an important
problem for practitioners who are interested in disease screening with limited
resources. For example, when screening for infectious diseases in large
populations, it is important to use algorithms that minimize the cost of
potentially expensive assays. Black et al. (2015) described this as an
intractable problem unless the number of individuals to screen is small. They
proposed an approximation to an optimal strategy that is difficult to implement
for large population sizes. In this article, we develop an optimal design with
respect to the expected total number of tests that can be obtained using a
novel dynamic programming algorithm. We show that this algorithm is
substantially more efficient than the approach proposed by Black et al. (2015).
In addition, we compare the two designs for imperfect tests. R code is provided
for the practitioner.
