Table 3.

Statistical models for each analytic method, as applied to biomarkers measured in serum.

Method	logit[Pr(BC)] =
1. Unadjusted	α + β × EPz + δ × W
2. Standardized	α + β × ratioz + δ × W
3. Covariate-adjusted standardization	α + β × Cratioz + δ × W
4. Covariate adjustment	α + β × EPz + λ × SLL + δ × W
5. 2-stage model	α + β × EPz + θ × R + δ × W; SLL = α + β × EPz + R
6. Standardization plus covariate adjustment	α + β × ratioz + λ × SLL + δ × W
7. Covariate-adjusted standardization plus covariate adjustment	α + β × Cratioz + λ × SLL + δ × W
Abbreviations: Cratio, $E_P/\mathsf{(}\mathrm{SLL}/\widehat{\mathsf{SLL}}\mathsf{)}$; EP, proxy exposure level; EPz, proxy exposure z-score; ratioz, z-score for EP:SLL ratio; SLL, serum lipid level; $\widehat{\mathsf{SLL}}$, predicted SLL. SLL predicted based on X2 in all scenarios. W not included in scenario D. In scenarios E and F, W = X2.