The past two decades have witnessed significant advances in high-throughput ``omics" technologies such as genomics, proteomics, metabolomics, transcriptomics and radiomics. These technologies have enabled the simultaneous measurement of the expression levels of tens of thousands of features from individual patient samples and have generated enormous amounts of data that require analysis and interpretation. One specific area of interest has been in studying the relationship between these features and patient outcomes such as overall and recurrence-free survival with the goal of developing a predictive ``omics" profile. In this paper, we propose a supervised dimension reduction method for feature selection and survival prediction. Our approach utilizes continuum power regression - a framework that includes ordinary least squares, principal components regression and partial least squares - in conjunction with the parametric or semi-parametric accelerated failure time model, and enables feature selection under possible non-proportional hazards. The proposed approach can handle censored observations using robust Buckley-James estimation in this high-dimensional setting and the parametric version employs the flexible generalized F model that encompasses a wide spectrum of well known survival models. We evaluate the predictive performance of our methods via extensive simulation studies and compare it to existing methods using publicly available data sets in cancer genomics.


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