Fitting and testing the Marshall–Olkin extended Weibull model with randomly censored data

Abstract

The random censorship model (RCM) is commonly used in biomedical science for modeling life distributions. The popular non-parametric Kaplan–Meier estimator and some semiparametric models such as Cox proportional hazard models are extensively discussed in the literature. In this paper, we propose to fit the RCM with the assumption that the actual life distribution and the censoring distribution have a proportional odds relationship. The parametric model is defined using Marshall–Olkin's extended Weibull distribution. We utilize the maximum-likelihood procedure to estimate model parameters, the survival distribution, the mean residual life function, and the hazard rate as well. The proportional odds assumption is also justified by the newly proposed bootstrap Komogorov–Smirnov type goodness-of-fit test. A simulation study on the MLE of model parameters and the median survival time is carried out to assess the finite sample performance of the model. Finally, we implement the proposed model on two real-life data sets.

Keywords:

• The random censorship model
• proportional odds
• extended Weibull distribution
• quantile survival time
• hazard rate
• bootstrap confidence intervals
• Kaplan–Meier estimator
• bootstrap Komogorov–Smirnov test

AMS 2000 Subject Classifications:

• Primary: 62N01
• Secondary: 62N02
• 62N03
• 62P20

Acknowledgements

The authors wish to express their gratitude to the two anonymous reviewers whose constructive comments helped in restructuring the introduction and simulation sections. The research of the first author is supported by the Natural Science Foundation of the City of Ningbo (2011A610166), China.