Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.

Data-driven decision making relies on estimating the effect of interventions, i.e. causal effect estimation . For example, a doctor must decide which medicine she will give her patient, ideally the one with the greatest effect on positive outcomes.

Recent text-based causal methods attempt to mitigate confounding bias by estimating proxies of confounding variables that are partially or imperfectly measured from unstructured text data. These approaches, however, assume analysts have supervised labels of the confounders given text for a subset of instances, a constraint that is sometimes infeasible due to data privacy or annotation costs. In this work, we address settings in which an important confounding variable is completely unobserved. We propose a new causal inference method that uses two instances of pre-treatment text data, infers two proxies using two zero-shot models on the separate instances, and applies these proxies in the proximal g-formula. We prove, under certain assumptions about the instances of text and accuracy of the zero-shot predictions, that our method of inferring text-based proxies satisfies identification conditions of the proximal g-formula while other seemingly reasonable proposals do not.

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.

In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and missing-not-at-random data with shadow variables, we are interested in inference on a continuous linear functional (e.g., average causal effects) of nuisance function (e.g., NPIV regression) defined by conditional moment restrictions. These nuisance functions are generally weakly identified, in that the conditional moment restrictions can be severely ill-posed as well as admit multiple solutions. This is sometimes resolved by imposing strong conditions that imply the function can be estimated at rates that make inference on the functional possible. In this paper, we study a novel condition for the functional to be strongly identified even when the nuisance function is not; that is, the functional is amenable to asymptotically-normal estimation at $\sqrt{n}$-rates. The condition implies the existence of debiasing nuisance functions, and we propose penalized minimax estimators for both the primary and debiasing nuisance functions. The proposed nuisance estimators can accommodate flexible function classes, and importantly they can converge to fixed limits determined by the penalization regardless of the identifiability of the nuisances. We use the penalized nuisance estimators to form a debiased estimator for the functional of interest and prove its asymptotic normality under generic high-level conditions, which provide for asymptotically valid confidence intervals. We also illustrate our method in a novel partially linear proximal causal inference problem and a partially linear instrumental variable regression problem.

Proximal causal inference was recently proposed as a framework to identify causal effects from observational data in the presence of hidden confounders for which proxies are available. In this paper, we extend the proximal causal approach to settings where identification of causal effects hinges upon a set of mediators which unfortunately are not directly observed, however proxies of the hidden mediators are measured. Specifically, we establish (i) a new hidden front-door criterion which extends the classical front-door result to allow for hidden mediators for which proxies are available; (ii) We extend causal mediation analysis to identify direct and indirect causal effects under unconfoundedness conditions in a setting where the mediator in view is hidden, but error prone proxies of the latter are available. We view (i) and (ii) as important steps towards the practical application of front-door criteria and mediation analysis as mediators are almost always error prone and thus, the most one can hope for in practice is that our measurements are at best proxies of mediating mechanisms. Finally, we show that identification of certain causal effects remains possible even in settings where challenges in (i) and (ii) might co-exist.

Unobserved confounding is a fundamental obstacle to establishing valid causal conclusions from observational data. Two complementary types of approaches have been developed to address this obstacle. An extensive line of work (Wright, 1928; Angrist and Krueger, 2001; Kuroki and Pearl, 2014) is based on taking advantage of fortuitous external aids (such as the presence of an instrumental variable or other proxy), along with additional assumptions to ensure identification. A recent line of work of proximal causal inference (Miao et al., 2018a; Tchetgen Tchetgen et al., 2020) has aimed to provide a novel approach to using proxies to deal with unobserved confounding without relying on stringent parametric assumptions. On the other hand, a complete characterization of identifiability of a large class of causal parameters in arbitrary causal models with hidden variables has been developed using the language of graphical models, resulting in the ID algorithm and related extensions (Tian and Pearl, 2002; Shpitser and Pearl, 2006a,b; Huang and Valtorta, 2006; Shpitser and Sherman, 2018). Celebrated special cases of this approach, such as the frontdoor model (Pearl, 1995), are able to obtain non-parametric identification in seemingly counter-intuitive situations when a treatment and an outcome share an arbitrarily complicated unobserved common cause. In this paper we aim to develop a synthesis of the proximaland graphicalapproachesto identification in causal inference to yield the most general identification algorithm in multivariate systems currently known - the proximal ID algorithm. In addition to being able to obtain non-parametric identification in all cases where the ID algorithm succeeds, our approach allows us to systematically exploit proxies to adjust for the presence of unobserved confounders that would have otherwise prevented identification. In addition, we outline a class of estimation strategies for causal parameters identified by our method in an important special case.