Parametric models for accelerated and long-term survival: a comment on proportional hazards

The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel–Boag (GB) model, a...

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Published inStatistics in medicine Vol. 21; no. 21; pp. 3279 - 3289
Main Authors Frankel, Paul, Longmate, Jeffrey
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 15.11.2002
Wiley
Subjects
accelerated failure
Algorithms
Biological and medical sciences
Bone Marrow Transplantation
cure model
Humans
Leukemia, Myeloid, Acute - therapy
log-normal
Medical sciences
proportional hazards
Proportional Hazards Models
Survival Analysis
Online AccessGet full text
ISSN0277-6715
1097-0258
DOI10.1002/sim.1273

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Abstract The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel–Boag (GB) model, a log‐normal model for accelerated failure in which a proportion of subjects are long‐term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow‐up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long‐term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long‐term or short‐term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi‐parametric Cox proportional hazards model. Copyright © 2002 John Wiley & Sons, Ltd.
AbstractList The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel-Boag (GB) model, a log-normal model for accelerated failure in which a proportion of subjects are long-term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow-up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long-term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long-term or short-term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi-parametric Cox proportional hazards model.The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel-Boag (GB) model, a log-normal model for accelerated failure in which a proportion of subjects are long-term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow-up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long-term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long-term or short-term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi-parametric Cox proportional hazards model.
The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel–Boag (GB) model, a log‐normal model for accelerated failure in which a proportion of subjects are long‐term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow‐up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long‐term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long‐term or short‐term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi‐parametric Cox proportional hazards model. Copyright © 2002 John Wiley & Sons, Ltd.
The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional hazards assumption, even when the departures are not readily detected by commonly used diagnostics. We consider the Gamel-Boag (GB) model, a log-normal model for accelerated failure in which a proportion of subjects are long-term survivors. When the CPH model is fit to simulated data generated from this model, the results can range from gross overstatement of the effect size, to a situation where increasing follow-up may cause a decline in power. We implement a fitting algorithm for the GB model that permits separate covariate effects on the rapidity of early failure and the fraction of long-term survivors. When effects are detected by both the CPH and GB methods, the attribution of the effect to long-term or short-term survival may change the interpretation of the data. We believe these examples motivate more frequent use of parametric survival models in conjunction with the semi-parametric Cox proportional hazards model.
Author Frankel, Paul
Longmate, Jeffrey
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References_xml – reference: Gamel JW, George SL, Stanley WE, Seigler HF. Skin melanoma: cured fraction and survival time as functions of thickness, site, histologic type, age and sex. Cancer 1993; 72:1219-1223.
– reference: Fleming TR, Harrington DP, O'Sullivan, M. Supremum versions of the log-rank and generalized Wilcoxon statistics. Journal of the American Statistical Association 1987; 82 397:312-320.
– reference: Cantor A. Extending SAS Survival Analysis: Techniques for Medical Research. SAS Institute: Cary, N.C., 1997.
– reference: Yamaguchi K. Accelerated failure-time regression models with a regression model of surviving fraction: an application to the analysis of 'permanent employment' in Japan. Journal of the American Statistical Association 1992; 87:284-292.
– reference: Koch GG. Discussion for 'Alpha calculus in clinical trials: considerations and commentary for the new millennium'. Statistics in Medicine 2000; 19:781-785.
– reference: Boag JW. The presentation and analysis of the results of radiotherapy. British Journal of Radiology 1948; 21 Pt I: 128, PtII:189.
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Snippet The Cox proportional hazards model (CPH) is routinely used in clinical trials, but it may encounter serious difficulties with departures from the proportional...
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SubjectTerms accelerated failure
Algorithms
Biological and medical sciences
Bone Marrow Transplantation
cure model
Humans
Leukemia, Myeloid, Acute - therapy
log-normal
Medical sciences
proportional hazards
Proportional Hazards Models
Survival Analysis
Title Parametric models for accelerated and long-term survival: a comment on proportional hazards
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Volume 21
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