Classification under uncertainty: data analysis for diagnostic antibody testing

Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant classification errors. We present a novel method that leverages optimal decision theory to address this problem. As a preliminary step, we develop an analysis that uses an assumed prevalence and conditional probability models of diagnostic measurement outcomes to define optimal (in the sense of minimizing rates of false positives and false negatives) classification domains. Critically, we demonstrate how this strategy can be generalized to a setting in which the prevalence is unknown by either (i) defining a third class of hold-out samples that require further testing or (ii) using an adaptive algorithm to estimate prevalence prior to defining classification domains. We also provide examples for a recently published SARS-CoV-2 serology test and discuss how measurement uncertainty (e.g. associated with instrumentation) can be incorporated into the analysis. We find that our new strategy decreases classification error by up to a decade relative to more traditional methods based on confidence intervals. Moreover, it establishes a theoretical foundation for generalizing techniques such as receiver operating characteristics by connecting them to the broader field of optimization.