Title: Optimal group testing designs for estimating prevalence with uncertain testing errors,
Abstract: We construct optimal designs for group testing experiments where the goal is
to estimate the prevalence of a trait by using a test with uncertain
sensitivity and specificity. Using optimal design theory for approximate
designs, we show that the most efficient design for simultaneously estimating
the prevalence, sensitivity and specificity requires three different group
sizes with equal frequencies. However, if estimating prevalence as accurately
as possible is the only focus, the optimal strategy is to have three group
sizes with unequal frequencies. On the basis of a chlamydia study in the
U.S.A., we compare performances of competing designs and provide insights into
how the unknown sensitivity and specificity of the test affect the performance
of the prevalence estimator. We demonstrate that the locally D- and Ds-optimal
designs proposed have high efficiencies even when the prespecified values of
the parameters are moderately misspecified.