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Scenarios for Example 2 |
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| Variables and parameters required for set-up |
Formulas and values of parameters |
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| Stratification/Proxy Z (with J strata) |
Environmental exposure E and Gene proxy SG |
| J = 4 |
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| Z = 1: E- SG-, Z = 2: E- SG+, Z = 3: E+ SG-, Z = 4: E+ SG+ |
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| 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)] |
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| 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+ |
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| Disease Model (Odds Ratios ψk) |
ψ1 = 1, ψ2 = 3, ψ3 = 2, ψ4 = ψ2 × ψ3 × ORI = 30 |
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| 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 |
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| Z = 2: π021 = (1 - PE)(1 - Sp)(1-PG)/Pr(SG+), |
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| π022 = 1 - π021, π023 = π024 = 0 |
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| Z = 3: π031 = π032 = 0, π033 = PE Sp(1-PG)/Pr(SG-), |
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| π034 = 1 - π033 |
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| Z = 4: π041 = = π042 = 0, π043 = PE (1 - Sp)(1-PG)/Pr(SG+), |
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| π044 = 1 - π043 |
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*Se = sensitivity; Sp = specificity | |
Wild et al. Epidemiologic Perspectives & Innovations 2008 5:4 doi:10.1186/1742-5573-5-4 |
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