  In diagnostic testing, establishing an indeterminate class is an effective
way to identify samples that cannot be accurately classified. However, such
approaches also make testing less efficient and must be balanced against
overall assay performance. We address this problem by reformulating data
classification in terms of a constrained optimization problem that (i)
minimizes the probability of labeling samples as indeterminate while (ii)
ensuring that the remaining ones are classified with an average target accuracy
X. We show that the solution to this problem is expressed in terms of a bathtub
principle that holds out those samples with the lowest local accuracy up to an
X-dependent threshold. To illustrate the usefulness of this analysis, we apply
it to a multiplex, saliva-based SARS-CoV-2 antibody assay and demonstrate up to
a 30 % reduction in the number of indeterminate samples relative to more
traditional approaches.
