Stage I Notation E True exposure status with E=1 if exposed and E=0 if non-exposed X Screening test of the exposure status with X=1 if positive and X=0 if negative t Probability of a positive screening test = Pr[X=1] M Total sample size of the Stage I study PPV Positive predictive value of the screening test= Pr[E=1 | X=1] NPV Negative predictive value of the screening test = Pr[E=0 | X=0] C1 Cost per person in Stage I study Stage II Notation fx1 Sampling fraction of those testing positive at Stage I fx0 Sampling fraction of those testing negative at Stage I rSF Sampling fraction ratio  fx1: fx0 N Total sample size of Stage II study with N0 and N1 in the two exposure groups w Sampling weight for the exposure group in Stage II study C2 Cost per person in Stage II study fx1 Sampling fraction of those testing positive at Stage I

Table 1: Notation for Stage I and Stage II Studies.