Averaging causal estimators in high dimensions

Abstract

There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential estimators one could use in this setting. Each of these estimators has different operating characteristics, and it is unlikely that one estimator will outperform all others across all possible scenarios. Coupling this with the fact that an analyst can never know which approach is best for their particular data, we propose a synthetic estimator that averages over a set of candidate estimators. Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models. We show that these ideas carry over into the estimation of causal effects in high-dimensional scenarios. We show theoretically that averaging provides robustness against choosing a bad model, and show empirically via simulation that the averaging estimator performs quite well, and in most cases nearly as well as the best among all possible candidate estimators. Finally, we illustrate these ideas in an environmental wide association study and see that averaging provides the largest benefit in the more difficult scenarios that have large numbers of confounders.

Combining estimators in interlaboratory studies and meta‐analyses

“…The SU of the averaged estimator, calculated by Equation (6) or Equation (7), is conservative because all individual estimators may not be perfectly correlated. However, according to Antonelli and Cefalu, 23 conservative estimates of the variance (or SU) may lead to better interval coverage.…”

“…Furthermore, there may not be an estimator that is best in all cases, and the performance of an estimator may be highly dependent on the dataset. 23 Although the long-run performance of estimators can be evaluated through simulation studies, in practice it is difficult, if not impossible, to determine which estimator is best for a given dataset.…”

“…25 "Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models." 23 The aim of estimator averaging is to provide a new estimator, built as a linear combination of a set of individual estimators of the same quantity, that achieves better properties than each individual estimator. 25,26 A similar approach known as "model averaging" becomes an important tool to deal with model uncertainty.…”

“…27 Liang et al 28 stated, "The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process." Model averaging is used in many application areas in recent years, for example, estimating causal effects in high-dimensional scenarios 23 and estimating a high-dimensional covariance matrix with a network structure. 29 However, to the author's knowledge, estimator-averaging approaches have not been developed or used in interlaboratory studies or meta-analyses.…”

Improved inference for doubly robust estimators of heterogeneous treatment effects

“…Recent work has looked to extend these approaches to high-dimensional situations (Powers et al, 2018). Estimation of average treatment effects in high-dimensional scenarios has garnered substantial interest (Belloni et al, 2014;Farrell, 2015;Chernozhukov et al, 2018;Antonelli et al, 2018Antonelli et al, , 2019Antonelli and Cefalu, 2020;Ning et al, 2020;Tan, 2020b). When estimating average causal effects, adjusting for a high-dimensional set of covariates is a nuisance parameter, and the target of interest is a low-dimensional quantity.…”