Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes

TL;DR

This paper introduces a probabilistic multiclass classification method optimized for diagnostic tests with more than two classes, along with an independent prevalence estimation technique, validated on SARS-CoV-2 serological data.

Contribution

It develops a novel multiclass classification approach based on decision theory and a prevalence estimation method that is independent of classification, applicable to arbitrary measurement dimensions.

Findings

Prevalence estimates are unbiased and converge to true values.

The method applies to arbitrary measurement dimensions.

Validated on SARS-CoV-2 serological data.

Abstract

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two classes. We address this problem by developing a multiclass classification based on probabilistic modeling and optimal decision theory that minimizes the convex combination of false classification rates. The classification process is challenging when the relative fraction of the population in each class, or generalized prevalence, is unknown. Thus, we also develop a method for estimating the generalized prevalence of test data that is independent of classification. We validate our approach on serological data with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) na\"ive, previously infected, and vaccinated classes. Synthetic data are used to demonstrate that (i) prevalence estimates are unbiased and converge to true values and (ii) our procedure applies to arbitrary measurement dimensions. In contrast to the binary problem, the multiclass setting offers wide-reaching utility as the most general framework and provides new insight into prevalence estimation best practices.