Data-driven smooth tests of the proportional hazards assumption
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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.
KeywordsCox model Neyman’s smooth test Proportional hazards assumption Schwarz’s selection rule
I would like to thank two anonymous reviewers for their detailed insightful comments that lead to a significant improvement of the paper and inspired me for further research. I gratefully acknowledge that the work has been supported by the GAČR Grant No. 201/05/H007 and the GAAV Grand No. IAA101120604. Computations have been carried out in METACentrum (Czech academic supercomputer network).
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