Evaluating the treatment effects model for estimation of cross‐sectional associations between risk factors and cardiovascular biomarkers influenced by medication use

Abstract

In cross-sectional observational data, evaluation of biomarker-to-exposure associations is often complicated by nonrandom medication use. Traditional approaches often lead to biased estimates, consistent with known results involving confounding by indication. More sophisticated, yet easy to implement approaches such as inverse probability weighting and censored normal regression can address medication use in certain settings but have poor performance when medication use depends on off-medication biomarker values. More sophisticated approaches are necessary. Heckman's treatment effects model resembles the process that gives rise to cross-sectional data. In this study, we conduct a variety of simulation studies to illustrate why traditional approaches are inappropriate when medication use depends on underlying biomarker values. We illustrate how Heckman's model can accommodate this feature. We also apply the models to data from the Multi-Ethnic Study of Atherosclerosis. Inverse probability weighting and censored normal regression are sensitive to how strongly medication use is associated with untreated biomarker values (the untreated value acts as an unmeasured predictor of medication use in this context). Heckman's model can often adequately remove bias and is robust to certain forms of model misspecification but relies on knowing important predictors of medication use, even when they are independent of the biomarker. The advantages of Heckman's model can be negated if the effect of medication on biomarker values is proportionate to the underlying biomarker. If predictors of medication use are measured, data are cross-sectional, and effects are approximately additive, then Heckman's model is more accurate relative to alternative approaches.