Functional form diagnostics for Cox's proportional hazards model
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Updated: Aug 25, 2026

An R-Based Landscape Validation of a Competing Risk Model
Published on: September 16, 2022
1Department of Biostatistics, Harvard University, Boston, MA 02115, USA. lleon@hsph.harvard.edu
Abstract:
We propose a new type of residual and an easily computed functional form test for the Cox proportional hazards model. The proposed test is a modification of the omnibus test for testing the overall fit of a parametric regression model, developed by Stute, González Manteiga, and Presedo Quindimil (1998, Journal of the American Statistical Association93, 141-149), and is based on what we call censoring consistent residuals. In addition, we develop residual plots that can be used to identify the correct functional forms of covariates. We compare our test with the functional form test of Lin, Wei, and Ying (1993, Biometrika80, 557-572) in a simulation study. The practical application of the proposed residuals and functional form test is illustrated using both a simulated data set and a real data set.
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