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Collapsibility of some association measures and survival models

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  • P. Vellaisamy

    (Indian Institute of Technology Bombay)

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.

Suggested Citation

  • P. Vellaisamy, 2017. "Collapsibility of some association measures and survival models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1155-1176, October.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0580-y
    DOI: 10.1007/s10463-016-0580-y
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    References listed on IDEAS

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    1. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2009. "Simpson's Paradox in Survival Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 463-480, September.
    2. Zongming Ma & Xianchao Xie & Zhi Geng, 2006. "Collapsibility of distribution dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 127-133, February.
    3. A. N. Pettitt, 1984. "Proportional Odds Models for Survival Data and Estimates Using Ranks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 169-175, June.
    4. P. Vellaisamy & V. Vijay, 2007. "Some collapsibility results for n-dimensional contingency tables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 557-576, September.
    5. D. R. Cox & Nanny Wermuth, 2003. "A general condition for avoiding effect reversal after marginalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 937-941, November.
    6. P. Vellaisamy, 2012. "Average Collapsibility of Distribution Dependence and Quantile Regression Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 153-165, March.
    7. D. R. Cox, 2003. "Conditional and marginal association for binary random variables," Biometrika, Biometrika Trust, vol. 90(4), pages 982-984, December.
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