Martingale difference residuals as a diagnostic tool for the Cox model

• 成果类型: Article
• 署名作者: Sasieni, PD; Winnett, A
• 署名单位: University of London; Queen Mary University London; Cancer Research UK
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/90.4.899
• 发表日期: 2003
• 页码: 899912
• 关键词: regression-models; splines

摘要

The proportional hazards model makes two major assumptions: the hazard ratio is constant over time, and the relationship between the hazard and continuous covariates is log-linear. Methods exist for checking and relaxing each of these assumptions, but in both cases the methods rely on the other assumption being true. Problems can occur if neither of the assumptions is appropriate, or even if only one of the assumptions is appropriate but it is not known which. We propose a new kind of residual for checking the two assumptions simultaneously. The smoothed residuals provide a flexible estimate of the hazard ratio, which may deviate from the standard proportional hazards model by having a time-dependent hazard ratio, transformed covariates or both. The methods are illustrated using data from the Medical Research Council's myeloma trials.