Empirical and kernel estimation of covariate distribution conditional on survival time

Xiaochun Li, Ronghui Xu

Research output: Contribution to journalArticle


In biomedical research there is often interest in describing covariate distributions given different survival groups. This is not immediately available due to censoring. In this paper we develop an empirical estimate of the conditional covariate distribution under the proportional hazards regression model. We show that it converges weakly to a Gaussian process and provide its variance estimate. We then apply kernel smoothing to obtain an estimate of the corresponding density function. The density estimate is consistent and has the same rate of convergence as the classical kernel density estimator. We have developed an R package to implement our methodology, which is demonstrated through the Mayo Clinic primary biliary cirrhosis data.

Original languageEnglish (US)
Pages (from-to)3629-3643
Number of pages15
JournalComputational Statistics and Data Analysis
Issue number12
StatePublished - Aug 2006
Externally publishedYes


  • Censoring
  • Conditional distribution
  • Covariate
  • Smoothing
  • Survival

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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