The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

Structural equation modeling (SEM) has dominated causal analysis in the social and behavioral sciences since the 1960s. Currently, many SEM practitioners are having difficulty articulating the causal content of SEM and are seeking foundational answers.

Counterfactual quantities representing path-specific effects arise in cases where we are interested in computing the effect of one variable on another only along certain causal paths in the graph (in other words by excluding a set of edges from consideration). A recent paper [7] details a method by which such an exclusion can be specified formally by fixing the value of the parent node of each excluded edge. In this paper we derive simple, graphical conditions for experimental identifiability of path-specific effects, namely, conditions under which path-specific effects can be estimated consistently from data obtained from controlled experiments. 1

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This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.

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Common strategies to decide whether a variable is a confounder that should be adjusted for in the analysis rely mostly on statistical criteria. The authors present findings from the Slone Epidemiology Unit Birth Defects Study, 1992–1997, a case-control study on folic acid supplementation and risk of neural tube defects. When statistical strategies for confounding evaluation are used, the adjusted odds ratio is 0.80 (95 % confidence interval: 0.62, 1.21). However, the consideration of a priori causal knowledge suggests that the crude odds ratio of 0.65 (95 % confidence interval: 0.46, 0.94) should be used because the adjusted odds ratio is invalid. Causal diagrams are used to encode qualitative a priori subject matter knowledge.

A key notion that has received much attention in epidemiology over the past few years has been that not all disease determinants can be conceptualized as individual-level attributes, hence the need to consider features of the groups to which individuals belong when studying the causes of ill health. This has led epidemiologists and public health researchers to rethink the ideas on ecologic studies and ecologic variables traditionally espoused in epidemiology (1–6). This reconceptualization of ecologic or group-level variables has been manifested, for example, in recent interest and debate on the possible health effects of group-level constructs, such as income inequality (7, 8), social capital (9, 10), and neighborhood characteristics (11–14). In this context, the advent of the statistical technique of multilevel models has been viewed as especially promising because of

Summary. This paper considers the problem of estimating the average con-trolled direct effect (ACDE) of a treatment on an outcome, in the presence of unmeasured confounders between an intermediate variable and the outcome. Such confounders render the direct effect unidentifiable even in cases where the total effect is unconfounded (hence identifiable). Kaufman et al. (2005) applied a linear programming software to find the minimum and maximum possible values of the ACDE for specific numerical data. In this paper, we apply the symbolic Balke-Pearl (1997) linear programming method to derive closed-form formulas for the upper and lower bounds on the ACDE under various assumptions of monotonicity. These universal bounds enable clini-cal experimenters to assess the direct effect of treatment from observed data with minimum computational effort, and they further shed light on the sign of the direct effect and the accuracy of the assessments.

Consider the query: Does a binary treatment X have a causal effect on a response Y through a causal pathway that does not involve the intermediate variable M? This query is often rephrased as: Does X have a direct causal effect on Y not through M? Direct effects have been formally defined in three different ways: the controlled direct effects (CDE), the natural direct effects (i.e. pure and total direct effects- PDE and TDE), and the principal stratum direct effects (PSDE). In this issue of the journal, Hafeman and VanderWeele (H&V) 7 provide novel minimal or near minimal conditions for identification of the CDE, PDE and TDE but do not consider the PSDE. In this commentary, we review inference for direct effects and the results of H&V. We also review the close relationship between the direct effects literature and the literature on instrumental variables and Mendelian randomization. 1 Formal Definitions To proceed, we review the formal definitions of the three types of direct effects. We first consider a study with baseline covariates C, a dichotomous treatment X