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- Title
Estimating the Population Survival Function Using Additional Information Recorded Over Time: a Filter Based Approach.
- Authors
Martinussen, Torben; Scheike, Thomas H.
- Abstract
ABSTRACT. Survival studies often collect information about covariates. If these covariates are believed to contain information about the life-times, they may be considered when estimating the underlying life-time distribution. We propose a non-parametric estimator which uses the recorded information about the covariates. Various forms of incomplete data, e.g. right-censored data, are allowed. The estimator is the conditional mean of the true empirical survival function given the observed history, and it is derived using a general filtering formula. Feng & Kurtz (1994) showed that the estimator is the Kaplan-Meier estimator in the case of right-censoring when using the observed life-times and censoring-times as the observed history. We take the same approach as Feng & Kurtz (1994) but in addition we incorporate the recorded information about the covariates in the observed history. Two models are considered and in both cases the Kaplan-Meier estimator is a special case of the estimator. In a simulation study the estimator is compared with the Kaplan-Meier estimator in small samples.
- Subjects
ESTIMATION theory; SURVIVAL analysis (Biometry); PROBABILITY theory
- Publication
Scandinavian Journal of Statistics, 1998, Vol 25, Issue 4, p621
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/1467-9469.00125