Table 1:

Predictors employed when comparing individual-specimen analyses, pooled-specimen analyses with naïve standardization after equal-volume pooling, and pooled-specimen analyses with standardization based on either the just-add-water or unequal-volumes protocols.

Standard- ization	Causal Scenarios	Individual-specimen analysesa		Pooled-specimen analysesb
				Naïve standardization		Proposed methods
		Exposure Variable, S	Covariates, X	Exposure Variable, SP	Covariates, XP	Exposure Variable, SP	Covariates, XP
Creatinine (covariate-adjusted)	A	$\frac{Z}{R}$	none	$K\frac{\sum Z_j}{\sum C_j}$	none	$\sum \frac{Z_j}{R_j}$	none
	B, B’, C, C’	$\frac{Z}{R}$	X	$K\frac{\sum Z_j}{\sum C_j}$	$\sum X_j$	$\sum \frac{Z_j}{R_j}$	$\sum X_j$
Total Lipid (traditional)	D	$\frac{Z}{C}$	none	$K\frac{\sum Z_j}{\sum C_j}$	none	$\sum \frac{Z_j}{C_j}$	none
	E, E’, F, F’	$\frac{Z}{C}$	X	$K\frac{\sum Z_j}{\sum C_j}$	$\sum X_j$	$\sum \frac{Z_j}{C_j}$	$\sum X_j$

Note: Causal scenarios are defined in Figures 1 and 2 (scenarios with primes (‘) eliminate the causal arrow from X to D in the corresponding un-primed scenarios); notation is defined in the text.

^a

Equation fitted in analyses of individual specimens:

$$\frac{\mathrm{Pr}[\mathit{case}\mid S,X]}{\mathrm{Pr}[\mathit{control}\mid S,X]}=\mathit{exp}\{\mu +\beta S+\alpha X\}$$

^b

Equation fitted in analyses of pooled specimens:

$$\frac{\mathrm{Pr}[\mathrm{case}\mathrm{set}\mid K,S_P,X_p]}{\mathrm{Pr}[\mathrm{control}\mathrm{set}\mid K,S_P,X_p]}=\mathit{exp}\{{\mu }^{\ast }K+\beta S_P+\alpha X_p+\ln (r_K)\}$$