Table 3

Scenarios for Example 2

Variables and parameters required for set-up
Formulas and values of parameters

Stratification/Proxy Z (with J strata)
Environmental exposure E and Gene proxy SG

J = 4

Z = 1: E- SG-, Z = 2: E- SG+, Z = 3: E+ SG-, Z = 4: E+ SG+

Phase One prevalence among controls (τ0j):
τ01 = Pr(E-)Pr(SG-) = (1 - PE)[(1-Se)PG+Sp(1-PG)]
PE = 20%
τ02 = Pr(E-)Pr(SG+) = (1 - PE)[SePG+(1-Sp).(1-PG)]
PG = 1%
τ03 = Pr(E+)Pr(SG-) = PE[(1-Se)PG+Sp(1-PG)]

τ04 = Pr(E+)Pr(SG+) = PE[SePG+(1-Sp).(1-PG)]

Risk factor X (with K outcomes)
Exposure to E and exposure to G: K = 4

X = 1: E- G-, X = 2: E- G+, X = 3: E+ G-, X = 4: E+ G+

Disease Model (Odds Ratios ψk)
ψ1 = 1, ψ2 = 3, ψ3 = 2, ψ4 = ψ2 × ψ3 × ORI = 30

Phase Two prevalence of X among controls by stratum (π0jk)
Z = 1: π011 = (1 -PE)Sp(1-PG)/Pr(SG-),

π012 = 1 - π011, π013 = π014 = 0

Z = 2: π021 = (1 - PE)(1 - Sp)(1-PG)/Pr(SG+),

π022 = 1 - π021, π023 = π024 = 0

Z = 3: π031 = π032 = 0, π033 = PE Sp(1-PG)/Pr(SG-),

π034 = 1 - π033

Z = 4: π041 = = π042 = 0, π043 = PE (1 - Sp)(1-PG)/Pr(SG+),

π044 = 1 - π043

*Se = sensitivity; Sp = specificity

Wild et al. Epidemiologic Perspectives & Innovations 2008 5:4   doi:10.1186/1742-5573-5-4