Resources for Causal Reasoning in Health Services Research

Conditional probability

the quotient of the joint probability of two events in the same space and the marginal probability of one of the events

Confounding

association between two variables due to a third variable

Consistency assumption

for a given individual, the observed outcome equals the potential outcome, as a function of intervention, when the intervention is set to the observed level

Counterfactual reasoning

comparing potential outcomes of alternative interventions with observed outcomes in a thought experiment

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

Direct effect

the expected change in outcome in response to changing exposure while holding all other variables fixed

Directed acyclic graph (DAG)

a graph in which nodes represent variables and arrows represent influence between the variables they connect without loops; an arrow drawn from variable X to variable Y represents a dependency of Y on X, and no dependency of X on Y