Daowen Zhang/h2>
Department of Statistics
North Carolina State University
Omnibus Tests for Proportional Hazards Models
Survival time data arise frequently from biomedical research areas,
especially from clinical trials. Cox proportional hazards (PH) models are
often used to estimate the covariate effect parameters in the form of log
hazard ratios. However, the interpretation and validity of inference from
such models strongly depend on the PH assumption. As indicated by CALGB
8541, a clinical trial in breast cancer women, and other studies, sometimes
the PH assumption may be violated. We propose an omnibus test for testing
the PH assumption by representing the dynamic covariate effect as a
smoothing spline of time. Using a mixed effect representation of a smoothing
spline, the score test for the variance component of the random effects in
the mixed effect representation is derived. Using the same idea, we also
propose an omnibus score test for testing covariate effects. Simulation
studies show that the proposed testing procedures have good statistical
properties and provide reasonable power to detect general departures from PH
models. The proposed tests are illustrated by applying to the survival data
from CALGB 8541.
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