This note deals with a class of variables that, if conditioned on, tends to amplify confounding bias in the analysis of causal effects. This class, independently discovered by Bhattacharya and Vogt (2007) and Wooldridge (2009), includes instrumental variables and variables that have greater influence on treatment selection than on the outcome. We offer a simple derivation and an intuitive explanation of this phenomenon and then extend the analysis to non linear models. We show that: 1. the bias-amplifying potential of instrumental variables extends over to nonlinear models, though not as sweepingly as in linear models; 2. in non-linear models, conditioning on instrumental variables may introduce new bias where none existed before; 3. in both linear and non-linear models, instrumental variables have no effect on selection-induced bias.

We provide a formal definition of the notion of “transportability,” or “external validity,” which we view as a license to transfer causal information learned in experimental studies to a different environment, in which only observational studies can be conducted. We introduce a formal representation called “selection diagrams” for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we derive procedures for deciding whether causal effects in the target environment can be inferred from experimental findings in a different environment. When the answer is affirmative, the procedures identify the set of experimental and observational studies that need be conducted to license the transport. We further demonstrate how transportability analysis can guide the transfer of knowledge among non-experimental studies to minimize re-measurement cost and improve prediction power. We further provide a causally principled definition of “surrogate endpoint” and show that the theory of transportability can assist the identification of valid surrogates in a complex network of cause-effect relationships.

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.

The usefulness of graphical models in reasoning and decision making stems from facilitating four main computational features: (1) modular representation of probabilities, (2) systematic construction methods, (3) explicit encoding of independencies, and (4) efficient inference procedures. This note explains why the original introduction of influence diagrams, lacking formal underpinning of these features, has had only mild influence on automated reasoning research, and how Bayesian belief networks, which were formulated and defined directly by these features, became the focus of graphical modeling research.

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.