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Proportional cross-ratio model

Author

Listed:
  • Tianle Hu

    (Eli Lilly and Company)

  • Bin Nan

    (University of California - Irvine)

  • Xihong Lin

    (Harvard School of Public Health)

Abstract

Cross-ratio is an important local measure of the strength of dependence among correlated failure times. If a covariate is available, it may be of scientific interest to understand how the cross-ratio varies with the covariate as well as time components. Motivated by the Tremin study, where the dependence between age at a marker event reflecting early lengthening of menstrual cycles and age at menopause may be affected by age at menarche, we propose a proportional cross-ratio model through a baseline cross-ratio function and a multiplicative covariate effect. Assuming a parametric model for the baseline cross-ratio, we generalize the pseudo-partial likelihood approach of Hu et al. (Biometrika 98:341–354, 2011) to the joint estimation of the baseline cross-ratio and the covariate effect. We show that the proposed parameter estimator is consistent and asymptotically normal. The performance of the proposed technique in finite samples is examined using simulation studies. In addition, the proposed method is applied to the Tremin study for the dependence between age at a marker event and age at menopause adjusting for age at menarche. The method is also applied to the Australian twin data for the estimation of zygosity effect on cross-ratio for age at appendicitis between twin pairs.

Suggested Citation

  • Tianle Hu & Bin Nan & Xihong Lin, 2019. "Proportional cross-ratio model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 480-506, July.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:3:d:10.1007_s10985-018-9451-6
    DOI: 10.1007/s10985-018-9451-6
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    References listed on IDEAS

    as
    1. Tianle Hu & Bin Nan & Xihong Lin & James M. Robins, 2011. "Time-dependent cross ratio estimation for bivariate failure times," Biometrika, Biometrika Trust, vol. 98(2), pages 341-354.
    2. Nan, Bin & Lin, Xihong & Lisabeth, Lynda D. & Harlow, Sioban D., 2006. "Piecewise Constant Cross-Ratio Estimation for Association of Age at a Marker Event and Age at Menopause," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 65-77, March.
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