Abstract
We consider the problem of combining multiple biomarkers to improve the diagnostic accuracy of detecting a disease when only group-tested data on the disease status are available. There are several challenges in addressing this problem, including unavailable individual disease statuses, differential misclassification depending on group size and number of diseased individuals in the group, and extensive computation due to a large number of possible combinations of multiple biomarkers. To tackle these issues, we propose a pairwise model fitting approach to estimating the distribution of the optimal linear combination of biomarkers and its diagnostic accuracy under the assumption of a multivariate normal distribution. The approach is evaluated in simulation studies and applied to data on chlamydia detection and COVID-19 diagnosis.