A doubly robust estimator for continuous treatments in high dimensions

Generalized propensity score (GPS) methods have become popular for estimating causal relationships between a continuous treatment and an outcome in observational studies with rich covariate information. The presence of rich covariates enhances the plausibility of the unconfoundedness assumption. Nonetheless, it is also crucial to ensure the correct specification of both marginal and conditional treatment distributions, beyond the assumption of unconfoundedness.

We address limitations in existing GPS methods by extending balance-based approaches to high dimensions and introducing the Generalized Outcome-Adaptive LASSO and Doubly Robust Estimate (GOALDeR). This novel approach integrates a balance-based method that is robust to the misspecification of distributions required for GPS methods, a doubly robust estimator that is robust to the misspecification of models, and a variable selection technique for causal inference that ensures an unbiased and statistically efficient estimation.

Simulation studies showed that GOALDeR was able to generate nearly unbiased estimates when either the GPS model or the outcome model was correctly specified. Notably, GOALDeR demonstrated greater precision and accuracy compared to existing methods and was slightly affected by the covariate correlation structure and ratio of sample size to covariate dimension. Real data analysis revealed no statistically significant dose-response relationship between epigenetic age acceleration and Alzheimer's disease.

In this study, we proposed GOALDeR as an advanced GPS method for causal inference in high dimensions, and empirically demonstrated that GOALDeR is doubly robust, with improved accuracy and precision compared to existing methods. The R package is available at https://github.com/QianGao-SXMU/GOALDeR .