Significant advances in high-throughput genomic technologies have enabled the simultaneous measurement of the expression levels of tens of thousands of genomic features from individual patient samples and, thus, generate enormous amounts of data that require analysis and interpretation. Examples include next-generation sequencing, DNA methylation and copy number variation (CNV), single-nucleotide polymorphism (SNP) arrays and compound screening, among others. There has been growing interest in studying the relationship between features measured on different scales using these technologies and their effect on patient outcomes such as overall and recurrence-free survival with the ultimate goal of developing a predictive genomic profile. In this paper, we study the associations between digital gene expression, SNPs and patient survival in the presence of correlated covariates such as methylation and CNV. We develop two different analytical approaches and compare their performance in elucidating this relationship using publicly available genomic data on head and neck cancer from The Cancer Genome Atlas. We validate our findings using enrichment analyses of the resulting feature sets.