Evaluation of a Frequentist Hierarchical Model to Estimate Prevalence when sampling from a large geographic area using Pool Screening.

We present a frequentist Bernoulli-Beta hierarchical model to relax the constant prevalence assumption underlying the traditional prevalence estimation approach based on pooled data. This assumption is called into question when sampling from a large geographic area. Pool screening is a method that combines individual items into pools. Each pool will either test positive (at least one of the items is positive) or negative (all items are negative). Pool screening is commonly applied to the study of tropical diseases where pools consist of vectors (e.g. black flies) that can transmit the disease. The goal is to estimate the proportion of infected vectors. Intermediate estimators (model parameters) and estimators of ultimate interest (pertaining to prevalence) are evaluated by standard measures of merit, such as bias, variance and mean squared error making extensive use of expansions. Using the hierarchical model an investigator can determine the probability of the prevalence being below a prespecified threshold value, a value at which no reemergence of the disease is expected. An investigation into the least biased choice of the α parameter in the Beta (α, β) prevalence distribution leads to the choice of α = 1.