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An accurate multiclass classification strategy is crucial to interpretingantibody tests. However, traditional methods based on confidence intervals orreceiver operating characteristics lack clear extensions to settings with morethan two classes. We address this problem by developing a multiclassclassification based on probabilistic modeling and optimal decision theory thatminimizes the convex combination of false classification rates. Theclassification process is challenging when the relative fraction of thepopulation in each class, or generalized prevalence, is unknown. Thus, we alsodevelop a method for estimating the generalized prevalence of test data that isindependent of classification. We validate our approach on serological datawith severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) na\"ive,previously infected, and vaccinated classes. Synthetic data are used todemonstrate that (i) prevalence estimates are unbiased and converge to truevalues and (ii) our procedure applies to arbitrary measurement dimensions. Incontrast to the binary problem, the multiclass setting offers wide-reachingutility as the most general framework and provides new insight into prevalenceestimation best practices.

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