Semi-parametric estimation of biomarker age trends with endogenous medication use in longitudinal data

TL;DR

This paper introduces a semi-parametric method extending treatment effects models to longitudinal data, enabling unbiased estimation of biomarker age trends despite endogenous medication use and unmeasured confounders.

Contribution

It generalizes the treatment effects model to handle clustered longitudinal data without specifying correlation structures, addressing endogenous treatment bias in biomarker trend estimation.

Findings

Method successfully applied to MESA data to reveal LDL trends by age and gender.

Approach reduces bias caused by endogenous medication use in longitudinal biomarker studies.

Demonstrates robustness of semi-parametric inference without specifying correlation structures.

Abstract

In cohort studies, non-random medication use can pose barriers to estimation of the natural history trend in a mean biomarker value (namely, the association between a predictor of interest and a biomarker outcome that would be observed in the absence of biomarker-specific treatment). Common causes of treatment and outcomes are often unmeasured, obscuring our ability to easily account for medication use with commonly invoked assumptions such as ignorability. Further, absent some variable satisfying the exclusion restriction, use of instrumental variable approaches may be difficult to justify. Heckman's hybrid model with structural shift (sometimes referred to less specifically as the treatment effects model) can be used to correct endogeneity bias via a homogeneity assumption (i.e., that average treatment effects do not vary across covariates) and parametric specification of a joint model for the outcome and treatment. In recent work, we relaxed the homogeneity assumption by allowing observed covariates to serve as treatment effect modifiers. While this method has been shown to be reasonably robust in settings of cross-sectional data, application of this methodology to settings of longitudinal data remains unexplored. We demonstrate how the assumptions of the treatment effects model can be extended to accommodate clustered data arising from longitudinal studies. Our proposed approach is semi-parametric in nature in that valid inference can be obtained without the need to specify the longitudinal correlation structure. As an illustrative example, we use data from the Multi-Ethnic Study of Atherosclerosis to evaluate trends in low-density lipoprotein by age and gender. We confirm that our generalization of the treatment effects model can serve as a useful tool to uncover natural history trends in longitudinal data that are obscured by endogenous treatment.