Testing quasi-independence of failure and truncation times via conditional kendall's tau

Emily C. Martin, Rebecca A. Betensky

Research output: Contribution to journalArticlepeer-review


Truncated survival data arise when the failure time is observed only if it falls within a subject-specific truncating set. Most analysis methods rely on the key assumption of quasi-independence, that is, factorization of the joint density of failure and truncation times into a product proportional to the individual densities in the observable region. Unlike independence of failure time and censoring time, quasi-independence can be tested. Tests of quasi-independence are available for one-sided truncation and for truncation that depends on a measured covariate, but not for more complex truncation schemes. Here tests of quasi-independenee based on a multivariate conditional Kendall's tau are proposed for doubly truncated data, bivariate left-truncated data, and other forms of truncated survival data that arise when initiating or terminating event times are interval-censored. Asymptotic properties under the null are derived. The tests are illustrated using several real datasets and evaluated via simulation.

Original languageEnglish (US)
Pages (from-to)484-492
Number of pages9
JournalJournal of the American Statistical Association
Issue number470
StatePublished - Jun 2005


  • Dependence
  • Truncated data
  • U-statistic

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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