Estimating Confidence Intervals and Sampling Proportions in Two-Stage Prevalence Designs

In response to Abbott and Volberg's (in press) rejoinder to my epidemiologic note on verification bias and estimation of prevalence rates (Gambino, in press), I provide the formulas for computing confidence intervals for the results of second-stage verification. In addition, I provide the appropriate equation for determining confidence intervals when prevalence is near zero or one. Finally, we present formulas for determining the most efficient sample sizes needed to minimize second-stage variance estimates. These allow the investigator working under a fixed budget to determine the relative value of sampling negative screens to test for false negatives. We close with an observation on the interpretability of evidence.