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The added value of new covariates to the brier score in cox survival models

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  • Glenn Heller

    (Memorial Sloan Kettering)

Abstract

Calibration is an important measure of the predictive accuracy for a prognostic risk model. A widely used measure of calibration when the outcome is survival time is the expected Brier score. In this paper, methodology is developed to accurately estimate the difference in expected Brier scores derived from nested survival models and to compute an accompanying variance estimate of this difference. The methodology is applicable to time invariant and time-varying coefficient Cox survival models. The nested survival model approach is often applied to the scenario where the full model consists of conventional and new covariates and the subset model contains the conventional covariates alone. A complicating factor in the methodologic development is that the Cox model specification cannot, in general, be simultaneously satisfied for nested models. The problem has been resolved by projecting the properly specified full survival model onto the lower dimensional space of conventional markers alone. Simulations are performed to examine the method’s finite sample properties and a prostate cancer data set is used to illustrate its application.

Suggested Citation

  • Glenn Heller, 2021. "The added value of new covariates to the brier score in cox survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 1-14, January.
    • Handle: RePEc:spr:lifeda:v:27:y:2021:i:1:d:10.1007_s10985-020-09509-x
    DOI: 10.1007/s10985-020-09509-x
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    References listed on IDEAS

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    1. Uno, Hajime & Cai, Tianxi & Tian, Lu & Wei, L.J., 2007. "Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 527-537, June.
    2. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    3. Thomas A. Gerds & Martin Schumacher, 2007. "Efron-Type Measures of Prediction Error for Survival Analysis," Biometrics, The International Biometric Society, vol. 63(4), pages 1283-1287, December.
    4. Lu Tian & Tianxi Cai & Els Goetghebeur & L. J. Wei, 2007. "Model evaluation based on the sampling distribution of estimated absolute prediction error," Biometrika, Biometrika Trust, vol. 94(2), pages 297-311.
    5. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    6. Thomas J. DiCiccio & Anna Clara Monti & G. Alastair Young, 2006. "Variance stabilization for a scalar parameter," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 281-303, April.
    7. Limin Peng & Yijian Huang, 2007. "Survival analysis with temporal covariate effects," Biometrika, Biometrika Trust, vol. 94(3), pages 719-733.
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