Nonparametric analysis of bivariate gap time with competing risks

Chiung-Yu Huang, Chenguang Wang, Mei Cheng Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This article considers nonparametric methods for studying recurrent disease and death with competing risks. We first point out that comparisons based on the well-known cumulative incidence function can be confounded by different prevalence rates of the competing events, and that comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease. We then propose nonparametric estimators for the conditional cumulative incidence function as well as the conditional bivariate cumulative incidence function for the bivariate gap times, that is, the time to disease recurrence and the residual lifetime after recurrence. To quantify the association between the two gap times in the competing risks setting, a modified Kendall's tau statistic is proposed. The proposed estimators for the conditional bivariate cumulative incidence distribution and the association measure account for the induced dependent censoring for the second gap time. Uniform consistency and weak convergence of the proposed estimators are established. Hypothesis testing procedures for two-sample comparisons are discussed. Numerical simulation studies with practical sample sizes are conducted to evaluate the performance of the proposed nonparametric estimators and tests. An application to data from a pancreatic cancer study is presented to illustrate the methods developed in this article.

Original languageEnglish (US)
Pages (from-to)780-790
Number of pages11
Issue number3
StatePublished - Sep 1 2016


  • Bivariate gap time
  • Induced dependent censoring
  • Kendall's tau
  • Permutation tests
  • Survival analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


Dive into the research topics of 'Nonparametric analysis of bivariate gap time with competing risks'. Together they form a unique fingerprint.

Cite this