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Causal Diagrams For Empirical Research
"... The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subjectmatter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if ..."
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Cited by 247 (37 self)
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The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subjectmatter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained. Key words: Causal inference, graph models, interventions treatment effect 1 Introduction The tools introduced in this paper are aimed at helping researchers communicate qualitative assumptions about causeeffect relationships, elucidate the ramifications of such assumptions, and derive causal inferences from a combination...
Marginal structural models and causal inference in epidemiology
 Epidemiology
, 2000
"... In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist timedependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal mo ..."
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Cited by 106 (2 self)
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In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist timedependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverseprobabilityoftreatment weighted estimators. (Epidemiology 2000;11:550–560)
Covariance adjustment in randomized experiments and observational studies
 Statistical Science
"... Abstract. By slightly reframing the concept of covariance adjustment in randomized experiments, a method of exact permutation inference is derived that is entirely free of distributional assumptions and uses the random assignment of treatments as the “reasoned basis for inference.” This method of ex ..."
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Cited by 49 (9 self)
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Abstract. By slightly reframing the concept of covariance adjustment in randomized experiments, a method of exact permutation inference is derived that is entirely free of distributional assumptions and uses the random assignment of treatments as the “reasoned basis for inference.” This method of exact permutation inference may be used with many forms of covariance adjustment, including robust regression and locally weighted smoothers. The method is then generalized to observational studies where treatments were not randomly assigned, so that sensitivity to hidden biases must be examined. Adjustments using an instrumental variable are also discussed. The methods are illustrated using data from two observational studies.
2007): “Defining and estimating intervention effects for groups that will develop an auxiliary outcome
 Statistical Science
"... Abstract. It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropri ..."
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Cited by 20 (1 self)
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Abstract. It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropriately adjusts for variables affected by treatment and so is biased. We consider several appropriate ways to formalize the effects: principal stratification, stratification on a single potential auxiliary variable, stratification on an observed auxiliary variable and stratification on expected levels of auxiliary variables. We then outline identifying assumptions for each type of estimand. We evaluate the utility of these estimands and estimation procedures for decision making and understanding causal processes, contrasting them with the concepts of direct and indirect effects. We motivate our development with examples from nephrology and cancer screening, and use simulated data and real data on cancer screening to illustrate the estimation methods. Key words and phrases: Causality, direct effects, interaction, effect modification, bias, principal stratification.
Methods for Conducting Sensitivity Analysis of Trials with Potentially Nonignorable Competing Causes of Censoring
"... : We consider inference for the treatmentarm mean difference of an outcome that would have been measured at the end of a randomized followup study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatmentarm mean difference ..."
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Cited by 18 (4 self)
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: We consider inference for the treatmentarm mean difference of an outcome that would have been measured at the end of a randomized followup study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatmentarm mean difference is not identified unless unverifiable assumptions are made. We describe identifying assumptions that are tantamount to postulating relationships between the components of a patternmixture model, but can also be interpreted as imposing restrictions on the causespecific censoring probabilities of a selection model. We then argue that although sufficient for identification, these assumptions are insufficient for inference due to the curse of dimensionality. We propose reducing dimensionality by specifying semiparametric causespecific selection models. These models are useful for conducting a sensitivity analysis to examine how inference for the treatmentarm mean difference changes as one v...
Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality
"... We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with ..."
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Cited by 15 (2 self)
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We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on the set of treatment variables. The nodes on the SWIG are the corresponding counterfactual random variables. We illustrate the theory with a number of examples. Our graphical theory of SWIGs may be used to infer the counterfactual independence relations implied by the counterfactual models developed in Robins (1986, 1987). Moreover, in the absence of hidden variables, the joint distribution of the counterfactuals is identified; the identifying formula is the extended gcomputation formula introduced in (Robins et al., 2004). Although Robins (1986, 1987) did not use DAGs we translate his algebraic results to facilitate understanding of this prior work. An attractive feature of Robins ’ approach is that it largely avoids making counterfactual independence assumptions that are experimentally untestable. As an important illustration we revisit the critique of Robins ’ gcomputation given in (Pearl, 2009, Ch. 11.3.7); we use SWIGs to show that all of Pearl’s claims are either erroneous or based on misconceptions. We also show that simple extensions of the formalism may be used to accommodate dynamic regimes, and to formulate nonparametric structural equation models in which assumptions relating to the absence of direct effects are formulated at the population level. Finally, we show that our graphical theory also naturally arises in the context of an expanded causal Bayesian network in which we are able to observe the natural state of a Potential outcomes are extensively used within Statistics, Political Science, Economics, and Epidemiology for reasoning about causation. Directed acyclic graphs (DAGs) are another formalism used to represent causal systems also
STATISTICAL MODELING OF CAUSAL EFFECTS IN CONTINUOUS TIME 1
, 2008
"... This article studies the estimation of the causal effect of a timevarying treatment on timetoanevent or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to timedependent patient characteristics. The treatment effect cannot b ..."
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Cited by 12 (0 self)
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This article studies the estimation of the causal effect of a timevarying treatment on timetoanevent or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to timedependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these timedependent patient characteristics, as they may themselves be indications of the treatment effect. This timedependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321–334, (1998b) Encyclopedia of Biostatistics 6 4372–4389] has proposed the socalled structural nested models to estimate treatment effects in the presence of timedependent 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. 1. Introduction. Causality