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Causal diagrams
, 2008
"... Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probabil ..."
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Cited by 21 (2 self)
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Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probability models, enabling use of graph theory in probabilistic inference, and allowing easy deduction of independence conditions implied by the assumptions. They can also be used as a formal tool for causal inference, such as predicting the effects of external interventions. Given that the diagram is correct, one can see whether the causal effects of interest (target effects, or causal estimands) can be estimated from available data, or what additional observations are needed to validly estimate those effects. One can also see how to represent the effects as familiar standardized effect measures. The present article gives an overview of: (1) components of causal graph theory; (2) probability interpretations of graphical models; and (3) methodologic implications of the causal and probability structures encoded in the graph, such as sources of bias and the data needed for their control.
Adjustments and their Consequences – Collapsibility Analysis using Graphical Models
"... We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjus ..."
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Cited by 5 (1 self)
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We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association of two variables when that association is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a potential source of bias in estimating causal effects, and some additional special cases useful for casecontrol studies, cohort studies with loss, and trials with noncompliance (nonadherence).
MINIMAL SUFFICIENT CAUSATION AND DIRECTED ACYCLIC GRAPHS
, 2009
"... Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directe ..."
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Cited by 2 (1 self)
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Notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework. Doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs. This in turn provides a clear theoretical link between two major conceptualizations of causality: one counterfactualbased and the other based on a more mechanistic understanding of causation. The theory developed can be used to draw conclusions about the sign of the conditional covariances among variables.
Biologic Interaction and Their Identification
 COBRA PREPRINT SERIES YEAR 2006 PAPER 12
, 2006
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A Theory of Sufficient Cause Interactions
 COBRA PREPRINT SERIES YEAR 2006 PAPER 13
, 2006
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Adjustments and their Consequences— Collapsibility Analysis using Graphical Models
"... We review probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility or noninvariance under adjustment), whether that dependence is causal or purely predictive. We focus on disting ..."
Abstract
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We review probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility or noninvariance under adjustment), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association that is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a bias in estimating causal effects, and some additional special cases useful for casecontrol studies, cohort studies with loss, and trials with noncompliance (nonadherence). Key words: Bias; causality; causal models; collapsibility; compliance; confounding; graphical models; instrumental variables; mediation analysis; odds ratio. 1