Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data

By Zhiqiang Tan. 2018

101 citations recorded by the source corpus.

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building and fitting iteratively can be difficult to implement, depending on ad hoc choices of what variables are included. In addition, uncertainty from the iterative process of model selection is complicated and often ignored in subsequent inference about treatment effects. We develop new methods and theory to obtain not only doubly robust point estimators for average treatment effects, which remain consistent if either the propensity score model or the outcome regression model is correctly specified, but also model-assisted confidence intervals, which are valid when the propensity score model is correctly specified but the outcome regression model may be misspecified. With a linear outcome model, the confidence intervals are doubly robust, that is, being also valid when the outcome model is correctly specified but the propensity score model may be misspecified. Our methods involve regularized calibrated estimators with Lasso penalties, but carefully chosen loss functions, for fitting propensity score and outcome regression models. We provide high-dimensional analysis to establish the desired properties of our methods under comparable conditions to previous results, which give valid confidence intervals when both the propensity score and outcome regression are correctly specified. We present a simulation study and an empirical application which confirm the advantages of the proposed methods compared with related methods based on regularized maximum likelihood estimation.

Subfields: Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, methodology): “Other methods for causal inference under relaxed assumptions may be useful here, such as extensions to doubly robust estimation (Tan, 2018) and inverse weighting (Ma and Wang, 2018).”
A unifying approach for doubly-robust $\ell_1$ regularized estimation of causal contrasts (2019, methodology): “Because the estimators are not computed using the special loss as in Avagyan and Vansteelandt (2017), Tan (2018) and Ning et al. (2018), the resulting estimators of the counterfactual means do not have the model DR property.”
Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score. (2018, methodology): “Second, our theory holds for generalized linear models, whereas Tan (2018)’s method is not 440 applicable if the propensity score model is misspecified.”
Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data (2017, methodology): “Our implementation in the R (R Development Core Team, 2020) package RCAL (Tan, 2019b) employs the simple surrogate function CAL, Q3(γ ; γ̃ ) and then a variation of the active set algorithm of Osborne et al. (2000), which enjoys a finite termination property.”
Locally Robust Semiparametric Estimation (2016, methodology): “Orthogonality was used to estimate unknown components of doubly robust moment functions for the average treatment effect by Vermeulen and Vansteelandt (2015), Tan (2020), and Avagyan and Vansteelandt (2021) in order to obtain standard errors that are robust to misspecification.”
Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments (2019, unknown): “Tan (2020) develops doubly robust inference for the average binary treatment effect by carefully chosen loss functions to estimate the nuisance functions.”