Statistical Survival Analysis with Stochastic Ordering
Date
2020-05
Authors
Hardt, Marie
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Hofmann, Heike
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Abstract
Survival analysis is an area of great interest in many fields, including medicine and engineering. When performing a survival analysis, we are interested in determining the probability that someone or something will continue to survive, given that it has survived up to a particular point. The Kaplan-Meier estimator is the method of choice for calculating survival probabilities, but it does not take into account the added information provided by stochastic ordering in the data, where we know that members of one group are more likely to survive longer than members of the other group. Alternative estimators to the Kaplan-Meier estimator have been proposed by many authors, including Rojo (2004) and Rojo and Jiang (2013). We discuss these alternative estimators and examine a previously proposed solution to prevent violations of the nonincreasing property of survival functions that sometimes occur with the Rojo-Jiang estimator. We also propose a new way to prevent such violations in the Rojo-Jiang estimator.
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