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Formulating accurate and robust classification strategies is a key challengeof developing diagnostic and antibody tests. Methods that do not explicitlyaccount for disease prevalence and uncertainty therein can lead to significantclassification errors. We present a novel method that leverages optimaldecision theory to address this problem. As a preliminary step, we develop ananalysis that uses an assumed prevalence and conditional probability models ofdiagnostic measurement outcomes to define optimal (in the sense of minimizingrates of false positives and false negatives) classification domains.Critically, we demonstrate how this strategy can be generalized to a setting inwhich the prevalence is unknown by either: (i) defining a third class ofhold-out samples that require further testing; or (ii) using an adaptivealgorithm to estimate prevalence prior to defining classification domains. Wealso provide examples for a recently published SARS-CoV-2 serology test anddiscuss how measurement uncertainty (e.g. associated with instrumentation) canbe incorporated into the analysis. We find that our new strategy decreasesclassification error by up to a decade relative to more traditional methodsbased on confidence intervals. Moreover, it establishes a theoreticalfoundation for generalizing techniques such as receiver operatingcharacteristics (ROC) by connecting them to the broader field of optimization.

Classification Under Uncertainty: Data Analysis for Diagnostic Antibody Testing