Statistica Sinica 25 (2015), 1065-1079
Abstract: We say that the signs of association measures among three variables {X,Y,Z} are transitive if a positive association measure between X and Y and a positive association measure between Y and Z imply a positive association measure between X and Z. We introduce four association measures with different stringencies, and discuss conditions for the transitivity of the signs of these association measures. When the variables follow exponential family distributions, the conditions become simpler and more interpretable. Applying our results to two data sets from an observational study and a randomized experiment, we demonstrate that the results can help us draw conclusions about the signs of the association measures between X and Z based only on separate studies about {X,Y } and {Y,Z}.
Key words and phrases: Association measure, causal inference, Prentice’s criterion, surrogate endpoint, Yule–Simpson Paradox.