Data-driven smooth tests of the proportional hazards assumption - Kraus, David (Lifetime data analysis, 2007)
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.
Keywords: biometrie; interpretace statistických dat; Biometry; Proportional Hazards Models; statistické modely; lidé; proporcionální rizikové modely; Data Interpretation, Statistical; Computer Simulation; Models, Statistical; počítačová simulace; Humans