Significant advances have been made in genomics in the past two decades due to developments in high-throughput technologies such as microarrays, array CGH, SNP and methylation arrays, next-generation sequencing, proteomics and metabolomics. These technologies enable the simultaneous measurement of the expression levels of tens of thousands of genomic features 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 genomic 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 accelerated failure time model and enables feature ranking under possible non-proportional hazards. We evaluate the predictive performance of our methods using extensive simulation studies and publicly available data in cancer genomics.