Most large cohort studies collect measures on a wide variety of constructs to allow a broad range of research hypotheses to be tested, but few research designs make use of the correlation structure of all of these data in aggregate. In this project, we aim to leverage this common feature of large cohort studies to approximate the effect of unmeasured confounding variables. Principal component analysis (PCA) is a common data reduction technique that aims to explain the maximum amount of variance in a set of variables using as few variables as possible. Under complementary assumptions about (1) the proportion of confounding data that is measured and (2) the correlation structure of the measured and unmeasured confounding data, PCA of measured data may provide some insight into the effects of measured and unmeasured confounders in aggregate. Specifically, the principal components (PCs) are assumed to be constructed from observed confounders that act as proxies for the correlated error structure in the model driven by both measured and unmeasured factors. Under these assumptions, inclusion of the PCs of measured confounders as covariates may
