A generalized Kaplan-Meier estimator. (English) Zbl 0543.62033

Robertson, James B.; Uppuluri, V. R. R.

Ann. Stat. 12, 366-371 (1984).

A class of nonparametric maximum likelihood estimators of the survival function based on incomplete or right-censored data is derived in the general situation that the time to death and the time to loss (censoring) are not necessarily independent. This is the competing risks problem with two causes of failure.
It is shown that in the special case of independent causes, the Kaplan- Meier product-limit estimator is obtained as a member of this class of estimators. Also, a ”weight matrix” is introduced as a possible way to study various dependent models.

Reviewer: W.J.Padgett

MSC:

62G05	Nonparametric estimation
62N05	Reliability and life testing

Keywords:

incomplete data; maximum likelihood estimators; survival function; right- censored data; competing risks; Kaplan-Meier product-limit estimator; weight matrix