# Collapsibility of some association measures and survival models

Collapsibility of some association measures and survival models Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables Y and X equals the marginal measure of association. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient conditions for the average collapsibility of the association measures are obtained. Some interesting counterexamples are constructed and applications to linear, Poisson, logistic and negative binomial regression models are discussed. An extension to the case of multivariate covariate W is also analyzed. Finally, we discuss the collapsibility conditions of some dependence measures for survival models and illustrate them for the case of linear transformation models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of the Institute of Statistical Mathematics Springer Journals

# Collapsibility of some association measures and survival models

, Volume 69 (5) – Aug 18, 2016
22 pages

/lp/springer_journal/collapsibility-of-some-association-measures-and-survival-models-0GsEptv9Hv
Publisher
Springer Japan
Subject
Statistics; Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance
ISSN
0020-3157
eISSN
1572-9052
D.O.I.
10.1007/s10463-016-0580-y
Publisher site
See Article on Publisher Site

### Abstract

Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables Y and X equals the marginal measure of association. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient conditions for the average collapsibility of the association measures are obtained. Some interesting counterexamples are constructed and applications to linear, Poisson, logistic and negative binomial regression models are discussed. An extension to the case of multivariate covariate W is also analyzed. Finally, we discuss the collapsibility conditions of some dependence measures for survival models and illustrate them for the case of linear transformation models.

### Journal

Annals of the Institute of Statistical MathematicsSpringer Journals

Published: Aug 18, 2016

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