Towards optimal doubly robust estimation of heterogeneous causal effects

By Edward H. Kennedy. 2020

504 citations recorded by the source corpus.

Heterogeneous effect estimation plays a crucial role in causal inference, with applications across medicine and social science. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but there are important theoretical gaps in understanding if and when such methods are optimal. This is especially true when the CATE has nontrivial structure (e.g., smoothness or sparsity). Our work contributes in several main ways. First, we study a two-stage doubly robust CATE estimator and give a generic model-free error bound, which, despite its generality, yields sharper results than those in the current literature. We apply the bound to derive error rates in nonparametric models with smoothness or sparsity, and give sufficient conditions for oracle efficiency. Underlying our error bound is a general oracle inequality for regression with estimated or imputed outcomes, which is of independent interest; this is the second main contribution. The third contribution is aimed at understanding the fundamental statistical limits of CATE estimation. To that end, we propose and study a local polynomial adaptation of double-residual regression. We show that this estimator can be oracle efficient under even weaker conditions, if used with a specialized form of sample splitting and careful choices of tuning parameters. These are the weakest conditions currently found in the literature, and we conjecture that they are minimal in a minimax sense. We go on to give error bounds in the non-trivial regime where oracle rates cannot be achieved. Some finite-sample properties are explored with simulations.

Subfields: Statistics and Probability

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Citations in the corpus

Local Linear Forests (2018, methodology): “From the perspective, we can see local linear causal forests as an adapted R-learner method; note that Nie and Wager [2017] and Kennedy [2020] give quasi-oracle and double-robustness properties of R-learner estimates.”
Semiparametric doubly robust targeted double machine learning: a review (2022, background): “…et al., 2021, Kim et al., 2018, Robins and Rotnitzky, 2001, Westling and Carone, 2020], heterogeneous effect estimation [Foster and Syrgkanis, 2019, Kennedy, 2020, Kennedy et al., 2022, Nie and Wager, 2021, Semenova and Chernozhukov, 2017], etc. Interestingly, although these quantities take…”
Causal machine learning for predicting treatment outcomes (2024, unknown): “23,27,49,53,54,61,98,99).”
Conformal inference of counterfactuals and individual treatment effects (2020, background): “Under the strong ignorability assumption, a standard argument shows that Thus, the estimation problem reduces to that of estimating certain conditional expectations (e.g. Foster & Syrgkanis, 2019; Kennedy, 2020; Nie & Wager, 2017).”
The Balancing Act in Causal Inference (2021, background): “…δm, the AIPW estimator has nearly the same asymptotic behavior.16 Work like this, which brings us closer to understanding what is needed for straightforward inference than arguments based on maximal imbalance or the error rate product, is an important area of ongoing research (e.g. Kennedy, 2020).”