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

arXiv: https://arxiv.org/abs/2202.00494 · HTML: https://mlsanity.com/paper/2202.00494/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Analysis of Diagnostics (Part I): Prevalence, Uncertainty Quantification, and Machine Learning](https://mlsanity.com/paper/2309.00645/) (2023)
- [Analysis of Diagnostics (Part II): Prevalence, Linear Independence, and Unsupervised Learning](https://mlsanity.com/paper/2408.16035/) (2024)
- [Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing](https://mlsanity.com/paper/2508.01065/) (2025)

## Abstract (arXiv)

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.