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

• Published in: Statistics in medicine Vol. 21; no. 21; pp. 3279 - 3289
• Main Authors: Frankel, Paul, Longmate, Jeffrey
• Format: Journal Article
• Language: English
• 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
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.1273

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.