We propose an instrumental variable framework for identifying and estimating causal effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution of the potential outcomes and unobservables determining treatment assignment. This representation allows us to introduce an identifying assumption, so-called constant local dependence, that restricts the local dependence of the copula with respect to the treatment propensity. We show that constant local dependence identifies treatment effects for the entire population and other subpopulations such as the treated. The identification results are constructive and lead to practical estimation and inference procedures based on distribution regression. An application to estimating the effect of sleep on well-being uncovers interesting patterns of heterogeneity.
Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This paper considers a flexible semi-parametric potential outcome model that allows for possibly invalid instruments. We propose new identifiability conditions to identify the causal parameters when the majority of the instrumental variables are valid. We devise a novel inference procedure for a new average structural function and the conditional average treatmen…
Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents a simple and general approach to construct a confidence interval that is robust to possib…
We apply causal forests to a dataset derived from the National Study of Learning Mindsets, and consider resulting practical and conceptual challenges. In particular, we discuss how causal forests use estimated propensity scores to be more robust to confounding, and how they handle data with clustered errors.
In observational studies, instrumental variables estimation is greatly utilized to identify causal effects. One of the key conditions for the instrumental variables estimator to be consistent is the exclusion restriction, which indicates that instruments affect the outcome of interest only via the exposure variable of interest. We propose a likelihood-free Bayesian approach to make consistent inferences about the causal effect when there are some invalid instruments in a way that they violate the exclusion restriction condition. Asymptotic properties of the proposed Bayes estimator, including …
Under a general structural equation framework for causal inference, we provide a definition of the causal effect of a variable X on another variable Y, and propose an approach to estimate this causal effect via the use of instrumental variables.
Uncovering the heterogeneity of causal effects of policies and business decisions at various levels of granularity provides substantial value to decision makers. This paper develops new estimation and inference procedures for multiple treatment models in a selection-on-observables framework by modifying the Causal Forest approach suggested by Wager and Athey (2018) in several dimensions. The new estimators have desirable theoretical, computational and practical properties for various aggregation levels of the causal effects. While an Empirical Monte Carlo study suggests that they outperform pr…
Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. Fi…
Inference for causal effects can benefit from the availability of an instrumental variable (IV) which, by definition, is associated with the given exposure, but not with the outcome of interest other than through a causal exposure effect. Estimation methods for instrumental variables are now well established for continuous outcomes, but much less so for dichotomous outcomes. In this article we review IV estimation of so-called conditional causal odds ratios which express the effect of an arbitrary exposure on a dichotomous outcome conditional on the exposure level, instrumental variable and me…
Estimating causal effects with propensity scores relies upon the availability of treated and untreated units observed at each value of the estimated propensity score. In settings with strong confounding, limited so-called "overlap" in propensity score distributions can undermine the empirical basis for estimating causal effects and yield erratic finite-sample performance of existing estimators. We propose a Bayesian procedure designed to estimate causal effects in settings where there is limited overlap in propensity score distributions. Our method relies on the posterior predictive treatment …
Background: Interpreting instrumental variable results often requires further assumptions in addition to the core assumptions of relevance, independence, and the exclusion restriction. Methods: We assess whether instrument-exposure additive homogeneity renders the Wald estimand equal to the average derivative effect (ADE) in the case of a binary instrument and a continuous exposure. Results: Instrument-exposure additive homogeneity is insufficient for ADE identification when the instrument is binary, the exposure is continuous and the effect of the exposure on the outcome is non-linear on the …
Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved confounders. In the case where relationships are linear, causal effects can be identified exactly from studying the regression of C on A and the regression of B on A, where A is the instrument. In the more general case, bounds have been developed in the literature for the causal effect of B on C, given observational data on the joint distribution of C, B and A. Using …
This paper considers inference of causal structure in a class of graphical models called "conditional DAGs". These are directed acyclic graph (DAG) models with two kinds of variables, primary and secondary. The secondary variables are used to aid in estimation of causal relationships between the primary variables. We give causal semantics for this model class and prove that, under certain assumptions, the direction of causal influence is identifiable from the joint observational distribution of the primary and secondary variables. A score-based approach is developed for estimation of causal st…
Instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice instruments are often continuous (e.g., measures of distance, or treatment preference). However, available methods for continuous instruments have important limitations: they either require restrictive parametric assumptions for identification, or else rely on modeling both the outcome and treatment process well (and require modeling effect modification by all adjustment covariates). In this work we develop the first semiparametric doubly robust estimators of the loc…
Researchers are often interested in analyzing conditional treatment effects. One variant of this is "causal moderation," which implies that intervention upon a third (moderator) variable would alter the treatment effect. This study considers the conditions under which causal moderation can be identified and presents a generalized framework for estimating causal moderation effects given randomized treatments and non-randomized moderators. As part of the estimation process, it allows researchers to implement their preferred method of covariate adjustment, including parametric and non-parametric …
Despite the major advances taken in causal modeling, causality is still an unfamiliar topic for many statisticians. In this paper, it is demonstrated from the beginning to the end how causal effects can be estimated from observational data assuming that the causal structure is known. To make the problem more challenging, the causal effects are highly nonlinear and the data are missing at random. The tools used in the estimation include causal models with design, causal calculus, multiple imputation and generalized additive models. The main message is that a trained statistician can estimate ca…
This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational data. We explain the key assumptions required to identify causal effects, and highlight the challenges associated with the use of observational data. We emphasize that experimental thinking is crucial in causal inference. The quality of the data (not necessarily the quantity), the study design, the degree to which the assumptions are met, and the rigor of th…
University of British Columbia（不列颠哥伦比亚大学）；Google（谷歌）；Columbia University（哥伦比亚大学）
Instrumental variable methods provide a powerful approach to estimating causal effects in the presence of unobserved confounding. But a key challenge when applying them is the reliance on untestable "exclusion" assumptions that rule out any relationship between the instrument variable and the response that is not mediated by the treatment. In this paper, we show how to perform consistent IV estimation despite violations of the exclusion assumption. In particular, we show that when one has multiple candidate instruments, only a majority of these candidates---or, more generally, the modal candid…
In observational study, the propensity score has the central role to estimate causal effects. Since the propensity score is usually unknown, estimating by appropriate procedures is an indispensable step. A point to note that a causal effect estimator might have some bias if a propensity score model was misspecified; valid model construction is important. To overcome the problem, a variety of interesting methods has been proposed. In this paper, we review four methods: using ordinary logistic regression approach; CBPS proposed by Imai and Ratkovic; boosted CART proposed by McCaffrey and colleag…
One of the basic aims in science is to unravel the chain of cause and effect of particular systems. Especially for large systems this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to resolve the causality question, but for many systems such interventions are impossible or too costly to obtain. Recently, Maathuis et al. (2010), following ideas from Spirtes et al. (2000), introduced a framework to estimate causal effects in large scale Gaussian systems. By describing the causal network as a directed acyclic graph it is a possible to estimate …
RCTs sometimes test interventions that aim to improve existing services targeted to a subset of individuals identified after randomization. Accordingly, the treatment could affect the composition of service recipients and the offered services. With such bias, intention-to-treat estimates using data on service recipients and nonrecipients may be difficult to interpret. This article develops causal estimands and inverse probability weighting (IPW) estimators for complier populations in these settings, using a generalized estimating equation approach that adjusts the standard errors for estimatio…
In many scientific fields such as biology, psychology and sociology, there is an increasing interest in estimating the causal effect of a matrix exposure on an outcome. Covariate balancing is crucial in causal inference and both exact balancing and approximate balancing methods have been proposed in the past decades. However, due to the large number of constraints, it is difficult to achieve exact balance or to select the threshold parameters for approximate balancing methods when the treatment is a matrix. To meet these challenges, we propose the weighted Euclidean balancing method, which app…
We propose the instrumental variable regime (IVR) method to estimate the causal effects of multiple sequential treatments. This method serves to address the problem of endogenous selections of sequential treatments. An IVR is a sequence of instrumental variables in which each IV instruments for an endogenous treatment variable. Our proposed method generalizes the LATE model in Imbens and Angrist (1994) from a single treatment to many treatments applied sequentially. More precisely, with the IVR this model allows for estimating the local average treatment regime effects (LATRE), possibly condit…
Estimating the causal effects of an intervention in the presence of confounding is a frequently occurring problem in applications such as medicine. The task is challenging since there may be multiple confounding factors, some of which may be missing, and inferences must be made from high-dimensional, noisy measurements. In this paper, we propose a decision-theoretic approach to estimate the causal effects of interventions where a subset of the covariates is unavailable for some patients during testing. Our approach uses the information bottleneck principle to perform a discrete, low-dimensiona…
Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can r…
Instrumental variables have been widely used for estimating the causal effect between exposure and outcome. Conventional estimation methods require complete knowledge about all the instruments' validity; a valid instrument must not have a direct effect on the outcome and not be related to unmeasured confounders. Often, this is impractical as highlighted by Mendelian randomization studies where genetic markers are used as instruments and complete knowledge about instruments' validity is equivalent to complete knowledge about the involved genes' functions. In this paper, we propose a method for …
Background: Instrumental variables (IVs) can be used to provide evidence as to whether a treatment X has a causal effect on an outcome Y. Even if the instrument Z satisfies the three core IV assumptions of relevance, independence and the exclusion restriction, further assumptions are required to identify the average causal effect (ACE) of X on Y. Sufficient assumptions for this include: homogeneity in the causal effect of X on Y; homogeneity in the association of Z with X; and no effect modification (NEM). Methods: We describe the NO Simultaneous Heterogeneity (NOSH) assumption, which requires…
One of the most common mistakes made when performing data analysis is attributing causal meaning to regression coefficients. Formally, a causal effect can only be computed if it is identifiable from a combination of observational data and structural knowledge about the domain under investigation (Pearl, 2000, Ch. 5). Building on the literature of instrumental variables (IVs), a plethora of methods has been developed to identify causal effects in linear systems. Almost invariably, however, the most powerful such methods rely on exponential-time procedures. In this paper, we investigate graphica…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that the methods based on the independence of cause and mechanism, indirectly contain traces of …
The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a z…
The purpose of this work is to improve the efficiency in estimating the average causal effect (ACE) on the survival scale where right-censoring exists and high-dimensional covariate information is available. We propose new estimators using regularized survival regression and survival random forests (SRF) to make the adjustment for the high dimensional covariates to improve efficiency. We study the behavior of the adjusted estimator under mild assumptions and show theoretical guarantees that the proposed estimators are more efficient than the unadjusted ones asymptotically when using SRF for ad…
Randomized clinical trials (RCTs) are ideal for estimating causal effects, because the distributions of background covariates are similar in expectation across treatment groups. When estimating causal effects using observational data, matching is a commonly used method to replicate the covariate balance achieved in a RCT. Matching algorithms have a rich history dating back to the mid-1900s, but have been used mostly to estimate causal effects between two treatment groups. When there are more than two treatments, estimating causal effects requires additional assumptions and techniques. We propo…
The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such regression methods are tuned via smoothing parameters which regulates the amount of degrees of freedom used in the fit. In this paper we propose data-driven methods for selecting smoothing parameters when the targeted parameter is an average causal effect. For this purpose, we propose to estimate the exact expression of the mean squared error of the estimators. As…
The most widely discussed methods for estimating the Average Causal Effect/Average Treatment Effect are those for intervention in discrete binary variables whose value represents intervention/non-intervention groups. On the other hand, methods for intervening in continuous variables independent of data generating models have not been developed. In this study, we give a method for estimating the average causal effect for intervention in continuous variables that can be applied to data of any generating models as long as the causal effect is identifiable. The proposing method is independent of m…
Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in a survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments, we find our approach to perform well relative to a number of baselines.
The instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable. A valid instrumental variable is a variable that is independent of unmeasured confounders and affects the treatment but does not have a direct effect on the outcome beyond its effect on the treatment. Two commonly used estimators for using an instrumental variable to estimate a treatment effect are the two stage least squares estimator and the control function estimator. For linear causal effect models, these two estimators are equivalent, bu…
Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustme…
Point processes are probabilistic tools for modeling event data. While there exists a fast-growing literature studying the relationships between point processes, it remains unexplored how such relationships connect to causal effects. In the presence of unmeasured confounders, parameters from point process models do not necessarily have causal interpretations. We propose an instrumental variable method for causal inference with point process treatment and outcome. We define causal quantities based on potential outcomes and establish nonparametric identification results with a binary instrumenta…
