Causal mediation analysis with double machine learning

Abstract

This paper combines causal mediation analysis with double machine learning to control for observed confounders in a data-driven way under a selection-on-observables assumption in a highdimensional setting. We consider the average indirect effect of a binary treatment operating through an intermediate variable (or mediator) on the causal path between the treatment and the outcome, as well as the unmediated direct effect. Estimation is based on efficient score functions, which possess a multiple robustness property w.r.t. misspecifications of the outcome, mediator, and treatment models. This property is key for selecting these models by double machine learning, which is combined with data splitting to prevent overfitting in the estimation of the effects of interest. We demonstrate that the direct and indirect effect estimators are asymptotically normal and root-n consistent under specific regularity conditions and investigate the finite sample properties of the suggested methods in a simulation study when considering lasso as machine learner. We also provide an empirical application to the U.S. National Longitudinal Survey of Youth, assessing the indirect effect of health insurance coverage on general health operating via routine checkups as mediator, as well as the direct effect. We find a moderate short term effect of health insurance coverage on general health which is, however, not mediated by routine checkups.

Kernel Methods for Multistage Causal Inference: Mediation Analysis and Dynamic Treatment Effects

“…In our case, we combine generalized kernel ridge regressions to estimate nonparametric quantities without explicit density estimation. We use doubly robust moment functions from [59,72] and prove new, sufficiently fast nonparametric rates to verify abstract rate conditions from [10,20,6]. Similarly, one could relate our analysis with the rate conditions of [74].…”

“…The semiparametric procedure combines our new nonparametric estimator from Algorithm 1 with the multiply robust moment function from Lemma 1 and sample splitting. The meta algorithm of using the multiply robust moment function and sample splitting (without specifying the nonparametric subroutines) is sometimes called DML for mediation analysis [10,20]. 1.…”

A Finite Sample Theorem for Longitudinal Causal Inference with Machine Learning: Long Term, Dynamic, and Mediated Effects

“…For dynamic and mediated effects, the theorem subsumes existing work on certain special cases while also providing new results for additional cases. In particular, asymptotic results for unconfounded dynamic [17,18] and mediated effects [36] for the full population exist (albeit without variance estimation guarantees for the latter). I provide a finite sample guarantee that encompasses semiparametric effects for the full population as well as nonparametric, heterogeneous effects for subpopulations.…”

“…Proximal mediation analysis does not have existing inference guarantees for machine learning. The traditional mediation analysis does have such guarantees [36], however previous work is asymptotic and excludes consistency of asymptotic variance estimation (which is critical for the construction of confidence intervals). By contrast, I study the proximal setting and elucidate which conditions are required for consistent variance estimation (and hence valid confidence intervals).…”

“…Note that this procedure does not require higher order sample splitting, unlike [27,36,13,17,18]. Higher order sample splitting leads to smaller effective sample sizes for machine learning estimators, which can significantly depreciate coverage in practice.…”