Back To Index Previous Article Next Article Full Text

Statistica Sinica 25 (2015), 1065-1079

QUALITATIVE EVALUATION OF ASSOCIATIONS
BY THE TRANSITIVITY OF THE ASSOCIATION SIGNS
Zhichao Jiang1, Peng Ding2 and Zhi Geng1
1Peking University and 2Harvard University

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.

Back To Index Previous Article Next Article Full Text