This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321--334, (1998b) Encyclopedia of Biostatistics 6 4372--4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372--4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.
We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic statistical causality (DT), which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as "assisted decision-making", and aims to understand when, and how, I can make use of external data, typically observational, to help me solve a decision problem by taking advantage of assumed relationships between the data and my problem. The relationships embodied in any representation of a causal problem require deeper justification, which is necessarily conte…
We present an overview of the decision-theoretic framework of statistical causality, which is well-suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and is related to and contrasted with other current formulations, such as structural equation models and potential responses. Topics and applications covered include confounding, the effect of treatment on the treated, instrumental variables, and dynamic treatment strategies.
Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data collection have yielded near continuous-time measurements, from e.g. physiological monitors, wearable digital devices, and environmental sensors. Statistical methodology for estimating the causal effect of a time-varying treatment, measured discretely in time, is well developed. But discrete-time methods like the g-formula, structural nested models, and marg…
The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and, in particular, the Decision Theoretic framework for statistical causality, which uses the language and calculus of conditi…
Amazon（亚马逊）；Massachusetts Institute of Technology（麻省理工学院）
We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero if, and only if, the causal effect is identifiable via covariate adjustment. We show that under some restrictions on the structural equations, the causal bias can be estimated efficiently and allows for causal regularization of predictive probabilistic models. We demonstrate the effectiveness of our method for causal bias quantification in various settings wh…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any structure beyond an arbitrarily-indexed family of probability models. The formalism is simple but can incorporate a variety of causal modelling frameworks, including 'structural causal models', but also models expressed in terms of, e.g., differential equations. We focus primarily on the structural/graphical causal modelling literature, however. Secondly, w…
Estimating causal effects of continuous-time dynamic treatments with unmeasured confounders
Key Laboratory of Advanced Theory and Application in Statistics and Data Science -MOE, School of Statistics, East China Normal University（华东师范大学统计学院统计学与数据科学前沿理论及应用教育部重点实验室）
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…
Amazon.com, Inc.（亚马逊公司）；Wharton School of the University of Pennsylvania（宾夕法尼亚大学沃顿商学院）
We study the problem of observational causal inference with continuous treatments in the framework of inverse propensity-score weighting. To obtain stable weights, we design a new algorithm based on entropy balancing that learns weights to directly maximize causal inference accuracy using end-to-end optimization. In the process of optimization, these weights are automatically tuned to the specific dataset and causal inference algorithm being used. We provide a theoretical analysis demonstrating consistency of our approach. Using synthetic and real-world data, we show that our algorithm estimat…
One of the main tasks of causal inference is estimating well-defined causal parameters. One of the main causal parameters is the average causal effect (ACE) - the expected value of the individual level causal effects in the target population. For binary treatments, the individual level causal effect is defined as contrast between potential outcomes. For continuous outcomes, however, there are many such contrasts in finite samples, thus hampering their use as a useful summary of the causal relationship. Here, we proposed a generalized version of the ACE, where individual level causal effects ar…
The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since was devel…
Motivated by Breiman's rousing 2001 paper on the "two cultures" in statistics, we consider the role that different modeling approaches play in causal inference. We discuss the relationship between model complexity and causal (mis)interpretation, the relative merits of plug-in versus targeted estimation, issues that arise in tuning flexible estimators of causal effects, and some outstanding cultural divisions in causal inference.
In this paper, we deal with the problem of estimating the intervention effect in the statistical causal analysis using the structural equation model and the causal diagram. The intervention effect is defined as a causal effect on the response variable $Y$ when the causal variable $X$ is fixed to a certain value by an external operation and is defined based on the causal diagram. The intervention effect is defined as a function of the probability distributions in the causal diagram, however, generally these probability distributions are unknown, so it is required to estimate them from data. In …
Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy balancing method to multiple dimensions to balance the covariates. Both parametric and nonparametric methods are proposed to estimate the causal effect of multivariate continuous treatments and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method is better than other methods in various c…
Arizona State University（亚利桑那州立大学）；Oregon State University（俄勒冈州立大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Yonsei University（延世大学）
Continuous-time dynamics models, such as neural ordinary differential equations, have enabled the modeling of underlying dynamics in time-series data and accurate forecasting. However, parameterization of dynamics using a neural network makes it difficult for humans to identify causal structures in the data. In consequence, this opaqueness hinders the use of these models in the domains where capturing causal relationships carries the same importance as accurate predictions, e.g., tsunami forecasting. In this paper, we address this challenge by proposing a mechanism for mining causal structures…
Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. However, situations in which continuous and discrete variables coexist in the same problem are common in practice. Most existing causal discovery methods either ignore the discrete data and apply a continuous-valued algorithm or discretize all the continuous data and then apply a dis…
Causality is a subject of philosophical debate and a central scientific issue with a long history. In the statistical domain, the study of cause and effect based on the notion of `fairness' in comparisons dates back several hundred years, and yet statistical concepts and developments that form the area of causal inference are only decades old. In this paper, we review core tenets and methods of causal inference and key developments in the history of the field. We highlight connections with traditional `associational' statistical methods, including estimating equations and semiparametric theory…
This paper presents a topological learning-theoretic perspective on causal inference by introducing a series of topologies defined on general spaces of structural causal models (SCMs). As an illustration of the framework we prove a topological causal hierarchy theorem, showing that substantive assumption-free causal inference is possible only in a meager set of SCMs. Thanks to a known correspondence between open sets in the weak topology and statistically verifiable hypotheses, our results show that inductive assumptions sufficient to license valid causal inferences are statistically unverifia…
Université Libre de Bruxelles（布鲁塞尔自由大学）；Interuniversity Institute of Bioinformatics in Brussels（布鲁塞尔大学生物信息学研究所）
The relationship between statistical dependency and causality lies at the heart of all statistical approaches to causal inference. Recent results in the ChaLearn cause-effect pair challenge have shown that causal directionality can be inferred with good accuracy also in Markov indistinguishable configurations thanks to data driven approaches. This paper proposes a supervised machine learning approach to infer the existence of a directed causal link between two variables in multivariate settings with $n>2$ variables. The approach relies on the asymmetry of some conditional (in)dependence relati…
In semicompeting risks problems, nonterminal time-to-event outcomes such as time to hospital readmission are subject to truncation by death. These settings are often modeled with illness-death models for the hazards of the terminal and nonterminal events, but evaluating causal treatment effects with hazard models is problematic due to conditioning on survival (a post-treatment outcome) that is embedded in the definition of a hazard. Extending an existing survivor average causal effect (SACE) estimand, we frame the evaluation of treatment effects in the context of semicompeting risks with princ…
Two-stage Estimation for Causal Inference Involving a Semi-continuous Exposure
University of Waterloo（滑铁卢大学）；Ankara University（安卡拉大学）；Columbia University（哥伦比亚大学）；Wayne State University（韦恩州立大学）；University of Technology Sydney（悉尼科技大学）
Mendelian randomization uses genetic variants to make causal inferences about a modifiable exposure. Subject to a genetic variant satisfying the instrumental variable assumptions, an association between the variant and outcome implies a causal effect of the exposure on the outcome. Complications arise with a binary exposure that is a dichotomization of a continuous risk factor (for example, hypertension is a dichotomization of blood pressure). This can lead to violation of the exclusion restriction assumption: the genetic variant can influence the outcome via the continuous risk factor even if…
In addition to efficient statistical estimators of a treatment's effect, successful application of causal inference requires specifying assumptions about the mechanisms underlying observed data and testing whether they are valid, and to what extent. However, most libraries for causal inference focus only on the task of providing powerful statistical estimators. We describe DoWhy, an open-source Python library that is built with causal assumptions as its first-class citizens, based on the formal framework of causal graphs to specify and test causal assumptions. DoWhy presents an API for the fou…
University of Amsterdam（阿姆斯特丹大学）；Radboud University Nijmegen（奈梅亨拉德堡德大学）
We propose a method for learning cyclic causal models from a combination of observational and interventional equilibrium data. Novel aspects of the proposed method are its ability to work with continuous data (without assuming linearity) and to deal with feedback loops. Within the context of biochemical reactions, we also propose a novel way of modeling interventions that modify the activity of compounds instead of their abundance. For computational reasons, we approximate the nonlinear causal mechanisms by (coupled) local linearizations, one for each experimental condition. We apply the metho…
Toyota Technological Institute-Chicago（芝加哥丰田理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. We derive general conditions under which the given family of inference methods consistently infers the causal direction in a nonparametric setting.
The generalized propensity score (GPS) is an extension of the propensity score for use with quantitative or continuous exposures (e.g., dose of medication or years of education). Current GPS methods allow estimation of the dose-response relationship between a single continuous exposure and an outcome. However, in many real-world settings, there are multiple exposures occurring simultaneously that could be causally related to the outcome. We propose a multivariate GPS method (mvGPS) that allows estimation of a dose-response surface that relates the joint distribution of multiple continuous expo…
Multidata Causal Discovery for Statistical Hurricane Intensity Forecasting
Faculty of Geosciences and Environment, Expertise Center for Climate Extremes, University of Lausanne（洛桑大学地球科学与环境学院、气候极端事件专业中心）；Cooperative Institute for Research in the Atmosphere, Colorado State University（科罗拉多州立大学大气合作研究所）；Department of Computer Science, University of Potsdam（波茨坦大学计算机科学系）
We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus lea…
