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Title: A general framework for parametric survival analysis
Authors: Crowther, Michael J.
Lambert, P. C.
First Published: 14-Sep-2014
Publisher: Wiley
Citation: Statistics in Medicine, 2014, 33 (30), pp. 5280-5297
Abstract: Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software.
DOI Link: 10.1002/sim.6300
ISSN: 0277-6715
eISSN: 1097-0258
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2014 John Wiley & Sons, Ltd. This is the peer reviewed version of the following article: Crowther M. J., and Lambert P. C.(2014), A general framework for parametric survival analysis, Statist. Med., 33, pages 5280–5297, which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Appears in Collections:Published Articles, Dept. of Health Sciences

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