Abstract
We develop an adjusted Product Limit estimator for estimating survival probabilities in the presence of ties that incorporates censored individuals using the proportion of failing for uncensored individuals. We also develop a variance estimator of the adjusted Product Limit estimator for calculating confidence intervals. Simulation studies are carried out to assess the performance of the developed estimator in comparison to the performance of Kaplan-Meier and modified Kaplan-Meier estimators. Some simulation results are presented and one real data is used for illustration. The results indicate that the proposed estimator out performs the other estimators in estimating survival probabilities in presence of ties.
Highlights
Survival analysis is the phrase used to describe the analysis of data that correspond to time from a well-defined time origin until the occurrence of some particular event of interest or end point as in [1]
In this article we propose an adjusted Product Limit estimator (APLE) that incorporates censored individuals in the presence of ties using the proportion of failing for uncensored individuals
We developed an adjusted PL estimator and a variance estimator for the developed estimator for calculating confidence intervals
Summary
Survival analysis is the phrase used to describe the analysis of data that correspond to time from a well-defined time origin until the occurrence of some particular event of interest or end point as in [1]. The major limitation of PL estimator is that it ignores censored individuals incase ties between event and censoring times are observed. Because of this limitation, modified Kaplan-Meier (MKM) estimator discussed in [5] was suggested based on the arithmetic mean of the censored individuals and the survival probability for reduced sample size, considering this probability to be a single observation. KM estimator overestimate survival probabilities [6,7,8] and this might be due to ignoring censored individuals in the presence of ties Due to these drawbacks, in this article we propose an adjusted Product Limit estimator (APLE) that incorporates censored individuals in the presence of ties using the proportion of failing for uncensored individuals.
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