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Estimating prevalence q , the fraction of a population with a specific medical condition, is fundamental to epidemiology. Traditional methods address this task by using a diagnostic test outcome r ∈ Γ ⊂ R n to classify and count samples, but such approaches suffer from bias and uncontrolled uncertainty. Recently we showed that unbiased prevalence estimates can be constructed in terms of measures of conditional probability distributions on arbitrary sets D ± that partition Γ. In this work, we minimize the variance of this estimator by optimizing the partition itself. In particular, we employ a bathtub principle to recast optimization over the D ± in terms of a one-dimensional problem depending only on the total probability mass in these sets. Using symmetry, we show that the resulting objective function is well behaved and can be numerically optimized. [ABSTRACT FROM AUTHOR]

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-type 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. • New theory of diagnostic classification with holdout classes. • Fundamental connection between local and global accuracy of diagnostic assay. • New mathematical concept of "set-derivatives". [ABSTRACT FROM AUTHOR]