Lipid-Standardized Model for Serum PCB Levels

The lipid-standardized model is one way to account for the effect of serum lipids on serum PCB levels. This model is used frequently and is conceptually similar to use of the body mass index (BMI; weight in kilograms divided by the squared height in meters) to adjust weight for height in measuring adiposity.
The power, m in Equation 2 is a factor that generalizes the relation of PCBs and serum lipids. Due to measurement error in the quantification of lipids, use of Equation 2 when Figure 1A holds can result in biased estimates. If Figure 1B holds, estimates will be affected by a scaling issue, as the beta coefficient is that for the log of the ratio of PCB to lipids. If the true relations follow Figure 1 (C or D), then use of Equation 2 will adjust, albeit incompletely, for the exposure of interest, as in both Figure 1C and D, PCBs determine the variance of serum lipids. Figure 1C depicts a causal relation between both PCBs and serum lipids with the outcome, and a noncausal association between PCBs and serum lipids resulting from a common ancestor, A. Use of the standardization model will be valid for this situation only if the standardization completely accounts for the association between PCB and serum lipids. Otherwise, use of this model will result in biased estimates.
Figure 1F is modeled similarly to Figure 1D in that the relation between PCBs and lipids is due to a common cause, A. In this scenario, the standardized model again suffers from a scale issue. All other models will produce unbiased estimates, but precision of the estimate may vary depending on several factors, including measurement error. The potential error associated with the measurement of serum lipids can exceed that for the analyte itself (Needham and Wang 2002 (link)) and is an important source of bias.
Figure 1G represents two possible circumstances in which serum PCBs are causally related or correlated with the true exposure/outcome association. If the relation between serum and adipose concentration levels of PCBs is governed by serum lipid levels, then standardization may allow use of one as a proxy for the other.