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Abstract:
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Due to the semi-parametric nature of Cox Regression, conducting cross validation for Cox models has always been a challenge. While cross validation is a commonly used approach for selecting tuning parameters in penalized regression, little research has been done to study cross validation methods for penalized Cox regression. We propose two new cross-validation methods for Cox Regression, and compare them to traditional information criteria as well as a cross-validated partial likelihood approach originally proposed by Verweij et al. Our simulation studies show that, in general, cross-validation tends to be conservative (i.e., select smaller models than the ideal choice of tuning parameters) for penalized Cox regression models. However, our proposed approach of cross-validating the linear predictors generally offers the best balance of stability and performance. We also illustrate these approaches on data from a study of gene expression and progression-free survival in cancer patients.
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