Abstract
We apply the univariate sliced inverse regression to survival data. Our approach is different from the other papers on this subject. The right-censored observations are taken into account during the slicing of the survival times by assigning each of them with equal weight to all of the slices with longer survival. We test this method with different distributions for the two main survival data models, the accelerated lifetime model and Cox’s proportional hazards model. In both cases and under different conditions of sparsity, sample size and dimension of parameters, this non-parametric approach finds the data structure and can be viewed as a variable selector.
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References
Cook DR, Ni L (2005) Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J Am Stat Assoc 100:410–428
Cook DR, Weisberg S (1991) Discussion of “sliced inverse regression” by K.C. Li. J Am Stat Assoc 86:328–332
Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc 34:187–200
Efron B (1981) Censored data and bootstrap. J Am Stat Assoc 76(374):312–319
Li KC (1991) Sliced inverse regression for dimension reduction. J Am Stat Assoc 86(414):316–327
Li L (2010) Dimension reduction for high-dimensional data. In: Statistical methods in molecular biology, vol 620. Springer Protocols, New York, pp 417–434
Li L, Li H (2004) Dimension reduction methods for microarrays with application to censored survival data. Bioinformatics 20(18):3406–3412
Li L, Lu W (2008) Sufficient dimension reduction with missing predictors. J Am Stat Assoc 103(482):822–831
Li KC, Wang JL, Chen CH (1999) Dimension reduction for censored regression data. Ann Stat 27(1):1–23
Lu W, Li L (2011) Sufficient dimension reduction for censored regressions. Biometrics 67:513–523
Nadkarni NV, Zhao Y, Kosorok M (2011) Inverse regression estimation for censored data. J Am Stat Assoc 106(493):178–190
Rotnitzky A, Robins J (2005) Inverse probability weighted estimation in survival analysis. Eucycl of Biostat. doi:10.1002/0470011815.b2a11040
Wen X, Cook DR (2009) New approaches to model-free dimension reduction for bivariate regression. J Stat Plan Inference 139(3):734–748
Acknowledgments
The authors gratefully acknowledge the support by the Swiss National Science Foundation. The authors would also like to thank the referees for their helpful and constructive criticisms.
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Shevlyakova, M., Morgenthaler, S. Sliced inverse regression for survival data. Stat Papers 55, 209–220 (2014). https://doi.org/10.1007/s00362-013-0552-8
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DOI: https://doi.org/10.1007/s00362-013-0552-8