An Introduction to Proximal Causal Learning

Unmeasured confounding is a threat to causal inference in observational studies. In recent years, use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a longstanding tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao et al. (2018) have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to nonparametrically identify the average treatment effect (ATE) from observational data subject to uncontrolled confounding. In this paper, we establish nonparametric identification of the ATE under weaker conditions in the case of categorical unmeasured confounding and negative control variables. We also provide a general semiparametric framework for obtaining inferences about the ATE while leveraging information about a possibly large number of measured …

In this paper we reviewed causal effect estimation from a Bayesian perspective in point-treatment and time-varying treatment settings. For the latter, we outlined how to estimate causal effects of both static and dynamic treatment regimes. Both parameteric and nonparametric settings were discussed. Along the way, we discussed the utility of priors both for providing interpretable shrinkage and also for conducting causal sensitivity analyses. Throughout, we emphasize that the ad-hoc procedures we often use correspond to strongly informative priors. Throughout, we have highlighted various BNP techniques used for causal estimation in the literature. We hope that these surveys will be useful literature overviews that can serve as a starting point for those who want to delve further into these methods.

Robins 1997 introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. In his work, identification of MSM parameters is established under a sequential randomization assumption (SRA), which rules out unmeasured confounding of treatment assignment over time. We consider sufficient conditions for identification of the parameters of a subclass, Marginal Structural Mean Models (MSMMs), when sequential randomization fails to hold due to unmeasured confounding, using instead a time-varying instrumental variable. Our identification conditions require that no unobserved confounder predicts compliance type for the time-varying treatment. We describe a simple weighted estimator and examine its finite-sample properties in a simulation study. We apply the proposed estimator to examine the effect of delivery hospital on neonatal survival probability …

The presence of confounding by high-dimensional variables complicates estimation of the average effect of a point treatment. On the one hand, it necessitates the use of variable selection strategies or more general data-adaptive high-dimensional statistical methods. On the other hand, the use of such techniques tends to result in biased estimators with a non-standard asymptotic behaviour. Double-robust estimators are vital for offering a resolution because they possess a so-called small bias property (Newey et al., 2004). This means that their bias vanishes faster than the bias in the nuisance parameter estimators when the relevant smoothing parameter goes to zero, making their performance less sensitive to smoothing (Chernozhukov et al., 2016). This property has been exploited to achieve valid (uniform) inference of the average causal effect when data-adaptive estimators of the propensity score and conditional outcome mean both converge to their respective truths at sufficiently fast …

In this paper we reviewed causal effect estimation from a Bayesian perspective in point-treatment and time-varying treatment settings. For the latter, we outlined how to estimate causal effects of both static and dynamic treatment regimes. Both parameteric and nonparametric settings were discussed. Along the way, we discussed the utility of priors both for providing interpretable shrinkage and also for conducting causal sensitivity analyses. Throughout, we emphasize that the ad-hoc procedures we often use correspond to strongly informative priors. Throughout, we have highlighted various BNP techniques used for causal estimation in the literature. We hope that these surveys will be useful literature overviews that can serve as a starting point for those who want to delve further into these methods.