Optimal group testing with heterogeneous risks

We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436-440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.