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Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects
Author(s) -
Royston Patrick,
Parmar Mahesh K. B.
Publication year - 2002
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.1203
Subject(s) - covariate , proportional hazards model , weibull distribution , accelerated failure time model , statistics , hazard , survival analysis , odds , parametric statistics , logistic regression , econometrics , hazard ratio , computer science , parametric model , mathematics , confidence interval , chemistry , organic chemistry
Modelling of censored survival data is almost always done by Cox proportional‐hazards regression. However, use of parametric models for such data may have some advantages. For example, non‐proportional hazards, a potential difficulty with Cox models, may sometimes be handled in a simple way, and visualization of the hazard function is much easier. Extensions of the Weibull and log‐logistic models are proposed in which natural cubic splines are used to smooth the baseline log cumulative hazard and log cumulative odds of failure functions. Further extensions to allow non‐proportional effects of some or all of the covariates are introduced. A hypothesis test of the appropriateness of the scale chosen for covariate effects (such as of treatment) is proposed. The new models are applied to two data sets in cancer. The results throw interesting light on the behaviour of both the hazard function and the hazard ratio over time. The tools described here may be a step towards providing greater insight into the natural history of the disease and into possible underlying causes of clinical events. We illustrate these aspects by using the two examples in cancer. Copyright © 2002 John Wiley & Sons, Ltd.