Minimizing uncertainty in prevalence estimates

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 is an element of Gamma subset of 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 Gamma. 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.