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Martingale difference residuals as a diagnostic tool for the Cox model

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  • Peter D. Sasieni

Abstract

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. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Peter D. Sasieni, 2003. "Martingale difference residuals as a diagnostic tool for the Cox model," Biometrika, Biometrika Trust, vol. 90(4), pages 899-912, December.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:899-912
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    Cited by:

    1. Mariagrazia Squicciarini, 2008. "Science Parks’ tenants versus out-of-Park firms: who innovates more? A duration model," The Journal of Technology Transfer, Springer, vol. 33(1), pages 45-71, February.
    2. B. Ganguli & M. Naskar & E.J. Malloy & E.A. Eisen, 2015. "Determination of the functional form of the relationship of covariates to the log hazard ratio in a Cox model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 1091-1105, May.
    3. Li, Jianbo & Zhang, Riquan, 2011. "Partially varying coefficient single index proportional hazards regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 389-400, January.
    4. Mariagrazia Squicciarini, 2009. "Science parks: seedbeds of innovation? A duration analysis of firms’ patenting activity," Small Business Economics, Springer, vol. 32(2), pages 169-190, February.

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