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Semiparametric modelling and estimation of covariate‐adjusted dependence between bivariate recurrent events

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  • Jing Ning
  • Chunyan Cai
  • Yong Chen
  • Xuelin Huang
  • Mei‐Cheng Wang

Abstract

A time‐dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one‐sample settings. However, the one‐sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate‐adjusted rate ratio, a measure of covariate‐adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo‐partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.

Suggested Citation

  • Jing Ning & Chunyan Cai & Yong Chen & Xuelin Huang & Mei‐Cheng Wang, 2020. "Semiparametric modelling and estimation of covariate‐adjusted dependence between bivariate recurrent events," Biometrics, The International Biometric Society, vol. 76(4), pages 1229-1239, December.
  • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1229-1239
    DOI: 10.1111/biom.13229
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    References listed on IDEAS

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    1. Wang M-C. & Qin J. & Chiang C-T., 2001. "Analyzing Recurrent Event Data With Informative Censoring," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1057-1065, September.
    2. Chin‐Tsang Chiang & Mei‐Cheng Wang & Chiung‐Yu Huang, 2005. "Kernel Estimation of Rate Function for Recurrent Event Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 77-91, March.
    3. Sun, Liuquan & Zhu, Liang & Sun, Jianguo, 2009. "Regression analysis of multivariate recurrent event data with time-varying covariate effects," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2214-2223, November.
    4. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    5. Jing Ning & Yong Chen & Chunyan Cai & Xuelin Huang & Mei-Cheng Wang, 2015. "On the dependence structure of bivariate recurrent event processes: inference and estimation," Biometrika, Biometrika Trust, vol. 102(2), pages 345-358.
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