Minimizing Uncertainty in Prevalence Estimates

Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to estimating prevalence are biased and have uncontrolled uncertainty. Here, we construct a new, unbiased, minimum variance estimator for prevalence. Recent result show that prevalence can be estimated from counting arguments that compare the fraction of samples in an arbitrary subset of the measurement space to what is expected from conditional probability models of the diagnostic test. The variance of this estimator depends on both the choice of subset and the fraction of samples falling in it. We employ a bathtub principle to recast variance minimization as a one-dimensional optimization problem. Using symmetry properties, we show that the resulting objective function is well-behaved and can be numerically minimized.