Figure 1.

Examples of causal directed acyclic graph that encodes a priori domain knowledge and causal structural hypothesis. (A) Birth-weight paradox. There is no direct arrow from maternal smoking (exposure) to infant mortality (outcome), representing no causal effect. However, association/prediction-mode machine learning algorithm would automatically adjust for variables that are associated both with smoking and mortality (e.g., low birth-weight). Graphically, a rectangle placed around the low-birth weight variable represents adjustment. However, this adjustment for the collider (a node on which two directed arrows “collide”; Table 1) opens the flow of association from exposure → collider → covariates (e.g., structural anomaly) → outcome, which leads to a spurious (non-causal) association. (B) Simple example of causal diagram, consisting of exposure (biologic agent), outcome (asthma control), and covariates (e.g., baseline severity of illness). The presence of edge from a variable to another represents our knowledge on the presence of a direct effect. (C) Example of confounding. While there is no causal effect (i.e., no direct arrow from exposure to outcome), there is an association between these variables through the paths involving a common-cause covariate (i.e., a confounder), leading to a non-causal association between the exposure and outcome (i.e., confounding; Table 1). (D) Example of de-confounding. This confounding can be addressed by adjusting for the confounder by blocking the back-door path. Graphically, a rectangle placed around the confounder blocks the association flow through the back-door path. (E) Example of mediation. The causal relation between the exposure (systemic antibiotic use), mediator (airway microbiome), and outcome (asthma development). The confounders (e.g., acute respiratory infections) between the exposure, mediator, and outcome should be adjusted. The indirect (or mediation) effect is represented by the path which passes through the mediator. The direct effect is represented by the path which does not pass (the broken line; Table 1). (F) Example of mendelian randomization. Genetic variants that are strongly associated with the exposure of interest (mental illnesses) function as the instrument variable. Note that there is no association (or path) between the genetic variants and unmeasured confounders (i.e., independent condition) and that the genetic variants affect the outcome only through their effect on the exposure (i.e., exclusion restriction condition; Table 3).