title: Data-driven smooth tests of the proportional hazards assumption.
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.
authors.affiliation: Institute of Information Theory and Automation, Pod Vodárenskou vezí 4, CZ-182 08 Prague 8, Czech Republic. kraus@karlin.mff.cuni.cz
authors.forename: David
authors.initials: D
authors.lastname: Kraus
mesh_terms: D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D016016:Proportional Hazards Models