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Updated: Jul 18, 2026

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Data-driven smooth tests of the proportional hazards assumption
1Institute of Information Theory and Automation, Pod Vodárenskou vezí 4, CZ-182 08 Prague 8, Czech Republic. kraus@karlin.mff.cuni.cz
Abstract:
A new test of the proportional hazards assumption in the Cox model is proposed. The idea is based on Neyman's smooth tests. The Cox model with proportional hazards (i.e. time-constant covariate effects) is embedded in a model with a smoothly time-varying covariate effect that is expressed as a combination of some basis functions (e.g., Legendre polynomials, cosines). Then the smooth test is the score test for significance of these artificial covariates. Furthermore, we apply a modification of Schwarz's selection rule to choosing the dimension of the smooth model (the number of the basis functions). The score test is then used in the selected model. In a simulation study, we compare the proposed tests with standard tests based on the score process.
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