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Estimating the Population Survival Function Using Additional Information Recorded Over Time: a Filter Based Approach
Author(s) -
Martinussen Torben,
Scheike Thomas H.
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00125
Subject(s) - estimator , covariate , mathematics , statistics , survival function , censoring (clinical trials) , kaplan–meier estimator , survival analysis , econometrics , efficient estimator , consistent estimator , population , minimum variance unbiased estimator , demography , sociology
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.