Nonparametric estimation of conditional cumulative hazards for missing population marks

Dipankar Bandyopadhyay, Amalia Jácome Pumar

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A new function for the competing risks model, the conditional cumulative hazard function, is introduced, from which the conditional distribution of failure times of individuals failing due to cause j can be studied. The standard Nelson-Aalen estimator is not appropriate in this setting, as population membership (mark) information may be missing for some individuals owing to random right-censoring. We propose the use of imputed population marks for the censored individuals through fractional risk sets. Some asymptotic properties, including uniform strong consistency, are established. We study the practical performance of this estimator through simulation studies and apply it to a real data set for illustration.

Original languageEnglish (US)
Pages (from-to)75-91
Number of pages17
JournalAustralian and New Zealand Journal of Statistics
Issue number1
StatePublished - Mar 1 2010


  • Competing risks
  • Fractional risk set
  • Nelson-Aalen
  • Right-censoring

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