Graphical representations of Causal effects ● Visualizing casual relationships ● Relationship between variables ● Flow of time is inherent in DAGs ○ Time flow from left to right ○ L benign first even ■ Proceed to A ■ Preceding to Y ● Acyclic part of the name implies that there are no cycles ○ No variables can cause themselves ■ Not even through other variable Directed Acyclic Diagrams ● Statistical independence ○ ANy variable within the diagrams is independent of all other variables in diagrams ○ Value of one does not vary across strata of other variable ○ Marginal independence occurs when dealing with only two variable of interests ● Causation and association ○ Causation ■ Directed and unobservable ○ Association ■ Undirected and observable ○ Result form causal factors, need plausible explanation of causal pathway based on observed association. ● Collider BIas ○ Large source of bias ■ Can occur even if the two variables are statistically independent ■ Association between two variable changes when conditioning on third variable ■ Introduced through sample selection, stratification, covariate adjustment ■ Distinct from confounding, detrimental ● Include confounding Directed Acyclic Diagram ● Denote direct affect with a arrow ● Indirect denotion by series of arrows in one direction ● Intermediate variables are along the casual pathway ● Directed path corresponds to the assumption that variables do not affect each other ● Not necessary to include all variables ○ Need to include all key causal variables Ex) X and U does not have arrow within. Therefore… Does not affect each other Directed Acyclic Diagram Application to confounding ● Representation of Confounding with DAGSs ○ Arise from causes of Y associated with ut not affected by X ○ Biasing pathway or confounding pathway if ends n arrow to Y ● Representation of introduced confounding with DAGs ○ Conditioning confounding variables trying to adjust for surrogate markers that may be confounding variables ○ Collider bias can also be referred to selection bias if the variable conditioned on represents selection into the study sample ■ Only on this selection related variable