Recovering Natural History: Modeling Cardiovascular Biomarkers in the Presence of Endogenous Medication Use

Thesis (Ph.D.)--University of Washington, 2016-08

In the modern era, cardiovascular biomarkers are often measured in the presence of medication use, whereby the observed value is different than the underlying untreated value for participants on medication. However, for certain problems, the natural history of the biomarker that would have occurred in the absence of medication use is of greater interest than the observed value. In observational data, medication use is nonrandom in that participants on medication tend to have higher underlying biomarker values than participants off medication. That is to say that medication use is endogenous. When faced with endogenous medication use, traditional methods such as adjustment for medication use in linear regression models are inappropriate. The goal of this dissertation is to develop methods to estimate associations between predictors of interest and biomarker outcomes in the presence of endogenous medication use. First, we focus on methods for use in a cross-sectional setting. Heckman's treatment effects model, as suggested by its name, has historically been used to estimate the effect of medication use on a continuous outcome. In this research, we take a definitive departure from the historical use of the model, in that we utilize the Heckman framework in order to estimate associations between exposures and underlying (off-medication) outcomes, regarding the effect of medication on the biomarker as a nuisance rather than a parameter of interest. We show that the treatment effects model is fairly robust to departures from several of its main assumptions. One assumption to which the treatment effects model is particularly sensitive, however, is the assumption of uniform treatment effects. In particular, the expected effect of medication use on the biomarker is presumed to be constant across participants (an assumption that is often thought to be unrealistic in practice). We extend the treatment effects model to allow effect modification, or "subgroup-specific" treatment effects. The second major aim of this dissertation pertains to developing methodology to address endogenous medication use when repeated measures are available on subjects over time. Very little work has been done to address the challenges of endogenous medication use in longitudinal data. For certain types of probit analyses, existing methods invoke standard results on M-estimation theory to construct asymptotically valid estimates of marginal parameters. As cardiovascular biomarkers of interest show strong within-subject correlation over time, there is much efficiency to be gained by modeling that correlation. We seek to understand situations in which accounting for correlation can be advantageous (e.g., in the setting of deterministic covariates), and elucidate efficiency gains with specification of a working covariance. These two objectives primarily target bias reduction for the challenge of addressing endogenous medication use in estimating biomarker associations. Improving estimation of these associations can help us better understand underlying biological mechanisms of disease and better motivate future clinical research.