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In diagnostic testing, establishing an indeterminate class is an effectiveway to identify samples that cannot be accurately classified. However, suchapproaches also make testing less efficient and must be balanced againstoverall assay performance. We address this problem by reformulating dataclassification 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 accuracyX. We show that the solution to this problem is expressed in terms of a bathtubprinciple that holds out those samples with the lowest local accuracy up to anX-dependent threshold. To illustrate the usefulness of this analysis, we applyit to a multiplex, saliva-based SARS-CoV-2 antibody assay and demonstrate up toa 30 % reduction in the number of indeterminate samples relative to moretraditional approaches.

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays