Fig. 1

Causal diagram for hypercapnic respiratory failure. Directed acyclic graph illustrating assumed causal relationships between pre-specified exposure variables and the outcome of hypercapnic respiratory failure. In this case, obstructive lung disease has been selected as the exposure (green-shaded variable). Green arrows represent causal paths. Blue-shaded variables represent ancestors of the outcome and red-shaded variables represent ancestors of both the exposure and outcome. Red arrows represent biasing paths. Based on this diagram, the minimum adjustment set of variables to estimate the total effect of obstructive lung disease on hypercapnic respiratory failure are: age, smoking