Properties of Monotonic Effects on Directed Acyclic Graphs
Download the Paper Forward to a colleague
Abstract:
Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. Counterexamples are provided to show that the results do not hold under less restrictive conditions. Monotonic effects are furthermore used to relate signed edges on a causal directed acyclic graph to qualitative effect modification. The theory is applied to an example concerning the direct effect of smoking on cardiovascular disease controlling for hypercholesterolemia. Monotonicity assumptions are used to construct a test for whether there is a variable that confounds the relationship between the mediator, hypercholesterolemia, and the outcome, cardiovascular disease.
Subject Area:
Statistical Theory and Methods
Suggested Citation:
Tyler J. VanderWeele and James M. Robins, "Properties of Monotonic Effects on Directed Acyclic Graphs" (April 2008). COBRA Preprint Series. Article 35.
http://biostats.bepress.com/cobra/ps/art35