Resources for Causal Reasoning in Health Services Research

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Glossary of Terms

Interventional probability
Definition
Interventional probability

the probability of outcome of a deliberately set intervention; a truncated form of factorization of the joint probability function in which the conditional probability for intervened variables is replaced with 1, and all other conditional probabilities are considered at set values of the intervened variables

Conditional independence
Definition
Conditional independence

equivalence of the joint distribution of two variables to the product of distributions of each variable, given value of a third variable

Marginal structural models
Definition
Marginal structural models

link the expected value of a counterfactual outcome to covariates; unlike in regression models, the expected value is not conditional on the covariates

d-separation
Definition
d-separation

variables X and Y are said to be d-separated, if all paths from X to Y are blocked. A path may be blocked by a set of variables S, if the path contains at least one arrow-emitting variable that is in S or if the path contains at least one collider that is not in S and has no descendent in S. A collider is defined as a variable on a path such that the path enters and leaves via arrow heads. X and Y are, therefore, d-separated conditional on S, if S blocks all paths between X and Y. X and Y are marginally independent when S contains the null set

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