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

TL;DR

This paper introduces an optimal decision framework for diagnostic tests that balances minimizing indeterminate results with maintaining accuracy, demonstrated on saliva-based SARS-CoV-2 antibody assays.

Contribution

It formulates a constrained optimization approach for diagnostic classification that reduces indeterminate samples while preserving accuracy, with a novel solution based on a bathtub principle.

Findings

Up to 30% reduction in indeterminate samples.

Application to saliva-based SARS-CoV-2 antibody testing.

Theoretical formulation of the classification problem.

Abstract

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.