Data-driven Algorithms for Dimension Reduction in Causal Inference: analyzing the effect of school achievements on acute complications of type 1 diabetes mellitus
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Abstract
In observational studies, the causal effect of a treatment may be confounded with
variables that are related to both the treatment and the outcome of interest. In order
to identify a causal effect, such studies often rely on the unconfoundedness assumption,
i.e., that all confounding variables are observed. The choice of covariates to control
for, which is primarily based on subject matter knowledge, may result in a large covariate
vector in the attempt to ensure that unconfoundedness holds. However, including redundant
covariates is suboptimal when the effect is estimated nonparametrically, e.g., due
to the curse of dimensionality. In this paper, data-driven algorithms for the selection
of sufficient covariate subsets are investigated. Under the assumption of unconfoundedness
we search for minimal subsets of the covariate vector. Based on the framework of sufficient
dimension reduction or kernel smoothing, the algorithms perform a backward elimination
procedure testing the significance of each covariate. Their performance is evaluated
in simulations and an application using data from the Swedish Childhood Diabetes Register
is also presented.