  Covariate-specific treatment effects (CSTEs) represent heterogeneous
treatment effects across subpopulations defined by certain selected covariates.
In this article, we consider marginal structural models where CSTEs are
linearly represented using a set of basis functions of the selected covariates.
We develop a new approach in high-dimensional settings to obtain not only
doubly robust point estimators of CSTEs, but also model-assisted confidence
intervals, which are valid when a propensity score model is correctly specified
but an outcome regression model may be misspecified. With a linear outcome
model and subpopulations defined by discrete covariates, both point estimators
and confidence intervals are doubly robust for CSTEs. In contrast, confidence
intervals from existing high-dimensional methods are valid only when both the
propensity score and outcome models are correctly specified. We establish
asymptotic properties of the proposed point estimators and the associated
confidence intervals. We present simulation studies and empirical applications
which demonstrate the advantages of the proposed method compared with competing
ones.
