Abstract
In the modern era, cardiovascular biomarkers are often measured in the presence of medication use, such that the observed biomarker value for the treated participants is different than their underlying natural history value. However, for certain predictors (e.g. age, gender, and genetic exposures) the observed biomarker value is not of primary interest. Rather, we are interested in estimating the association between these predictors and the natural history of the biomarker that would have occurred in the absence of treatment. Nonrandom medication use obscures our ability to estimate this association in cross-sectional observational data. Structural equation methodology (e.g. the treatment effects model), while historically used to estimate treatment effects, has been previously shown to be a reasonable way to correct endogeneity bias when estimating natural biomarker associations. However, the assumption that the effects of medication use on the biomarker are uniform across participants on medication is generally not thought to be reasonable. We derive an extension of the treatment effects model to accommodate effect modification. Based on several simulation studies and an application to data from the Multi-Ethnic Study of Atherosclerosis, we show that our extension substantially improves bias in estimating associations of interest, particularly when effect modifiers are associated with the biomarker or with medication use, without a meaningful cost of efficiency.