Principal stratification has recently become a popular tool to address certain causal inference questions, particularly in dealing with post-randomization factors in randomized trials. Here, we analyze the conceptual basis for this framework and invite response to clarify the value of principal stratification in estimating causal effects of interest.

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## Scholarly Works (66 results)

This paper summarizes recent advances in causal inference and underscores the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and uniﬁes other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the eﬀects of potential interventions, (also called “causal eﬀects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of eﬀects”) and (3) queries about direct and indirect eﬀects (also known as “mediation”). Finally, the paper deﬁnes the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

Recent advances in causal inference have given rise to a general and easy-to-use estimator for assessing the extent to which the effect of one variable on another is mdiated by a third. This estimator, called Mediation Formula, is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediated-effect” and show how to estimate the two components in nonlinear systems with continuous and categorical variables.

Abstract: This review presents empirical researchers with recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and uniﬁes other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the eﬀects of potential interventions, (also called “causal eﬀects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of eﬀects”) and (3) queries about direct and indirect eﬀects (also known as “mediation”). Finally, the paper deﬁnes the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

Mediation analysis aims to uncover causal pathways along which changes are transmitted from stimulus to response. Recent advances in causal inference have given rise to a general and easy-to-use estimator for assessing the extent to which the effect of one variable on another is mediated by a third, thus setting a causally-sound standard for mediation analysis of empirical data. This estimator, called Mediation Formula, is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediated-effect” and show how to estimate the two components in systems with categorical variables, including logistic, probit, and nonparametric regressions.