In this article, we test the effects of predictors in survival regression through two well-known sufficient dimension reduction methods. Since the usual sufficient dimension reduction methods do not require pre-specified models, the predictor effect tests can be considered model-free. All of the test statistics have χ2 distributions. Numerical studies of the proposed predictor effect tests in various simulations and real data application are presented.
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Acknowledgements The authors are also grateful to the referees for many helpful comments. For Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Ministry of Education, Science and Technology (2010-0003189). The authors would like to thank Joseph Hagan from the Biostatistics program at Louisiana State University Health Sciences Center for his suggestions and inputs.
- Inverse regression
- Ordinary least square
- Predictor tests
- Sufficient dimension reduction
- Survival regression