Microarray technology has the potential to lead to a better understanding of biological processes and diseases such as cancer. When failure time outcomes are also available, one might be interested in relating gene expression profiles to the survival outcome such as time to cancer recurrence or time to death. This is statistically challenging because the number of covariates greatly exceeds the number of observations. While the majority of work has focused on regularized Cox regression model and accelerated failure time model, they may be restrictive in practice. We relax the model assumption and and consider a nonparametric transformation model that makes no parametric assumption on either the transformation function or the error distribution. We propose a more flexible estimator, called penalized smoothed partial rank estimator, by regularizing the partial rank estimator with SCAD penalty. We also develop an efficient algorithm to obtain the whole solution path. Extensive simulations demonstrate the advantages of the proposal and the new method has been applied to a real genomic study.



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