Distributionally Robust Group Testing with Correlation Information

Group testing is an efficient method of conducting massive tests using limited resources. We consider a group testing problem with the aim of deriving an optimal partition policy that minimizes the systematic objective, which is the weighted sum of the expected false-negative classifications, the false-positive classifications, and the number of total tests. Our model takes into account the correlation of subjects' infection, which makes the joint probability distribution of infections difficult to characterize precisely. To address this issue, we use a distributionally robust optimization approach. Specifically, we assume that only the rate of prevalence and pairwise correlations are known. In this case, we show that in an optimal grouping decision, all groups are the same size, which can be identified by an efficient algorithm. We further extend our study to the case where correlation only partially exists in the whole population. We focus on a two-cluster case and compare two representative grouping decisions to give managerial insights. We find that grouping subjects together who are all positively correlated is only more efficient when the rate of prevalence is low, and the correlation coefficient is high. Numerically, we compare our model with the classical model that assumes independent infection. The result shows that incorporating correlation in group testing increases the optimal group size and decreases the number of total tests