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A Weibull multi‐state model for the dependence of progression‐free survival and overall survival
Author(s) -
Li Yimei,
Zhang Qiang
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6501
Subject(s) - weibull distribution , statistics , goodness of fit , survival analysis , covariate , survival function , mathematics , econometrics
In oncology clinical trials, overall survival, time to progression, and progression‐free survival are three commonly used endpoints. Empirical correlations among them have been published for different cancers, but statistical models describing the dependence structures are limited. Recently, Fleischer et al. proposed a statistical model that is mathematically tractable and shows some flexibility to describe the dependencies in a realistic way, based on the assumption of exponential distributions. This paper aims to extend their model to the more flexible Weibull distribution. We derived theoretical correlations among different survival outcomes, as well as the distribution of overall survival induced by the model. Model parameters were estimated by the maximum likelihood method and the goodness of fit was assessed by plotting estimated versus observed survival curves for overall survival. We applied the method to three cancer clinical trials. In the non‐small‐cell lung cancer trial, both the exponential and the Weibull models provided an adequate fit to the data, and the estimated correlations were very similar under both models. In the prostate cancer trial and the laryngeal cancer trial, the Weibull model exhibited advantages over the exponential model and yielded larger estimated correlations. Simulations suggested that the proposed Weibull model is robust for data generated from a range of distributions. Copyright © 2015 John Wiley & Sons, Ltd.