Estimating the population survival function using additional information recorded over time: a filter based approach

TY - JOUR

T1 - Estimating the population survival function using additional information recorded over time: a filter based approach

AU - Martinussen, Torben

AU - Scheike, Thomas

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0303-6898

VL - 25

SP - 621

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

IS - 4

ER -