Clinical decisions in cancer rely on precisely assessing patient risk. To improve our ability to accurately identify the most aggressive malignancies, we constructed genome-wide survival models using gene expression, copy number, methylation, and mutation data from 10,884 patients with known clinical outcomes. We identified more than 100,000 significant prognostic biomarkers and demonstrate that these genomic features can predict patient outcomes in clinically-ambiguous situations. While adverse biomarkers are commonly believed to represent cancer driver genes and promising therapeutic targets, we show that cancer features associated with shorter survival times are not enriched for either oncogenes or for successful drug targets. Instead, the strongest adverse biomarkers represent widely-expressed housekeeping genes with roles in cell cycle progression, and, correspondingly, nearly all therapies directed against these features have failed in clinical trials. In total, our analysis establishes a rich resource for prognostic biomarker analysis and clarifies the use of patient survival data in preclinical cancer research and therapeutic development.

Aneuploidy is a hallmark of human cancers, but the effects of aneuploidy on protein expression remain poorly understood. To uncover how chromosome copy number changes influence the cancer proteome, we have conducted an analysis of hundreds of human cancer cell lines with matched copy number, RNA expression, and protein expression data. We found that a majority of proteins exhibit dosage compensation and fail to change by the degree expected based on chromosome copy number alone. We uncovered a variety of gene groups that were recurrently buffered upon both chromosome gain and loss, including protein complex subunits and cell cycle genes. Several genetic and biophysical factors were predictive of protein buffering, highlighting complex post-translational regulatory mechanisms that maintain appropriate gene product dosage. Finally, we established that chromosomal aneuploidy has an unexpectedly moderate effect on the expression of oncogenes and tumor suppressors, demonstrating that these key cancer drivers can be subject to dosage compensation as well. In total, our comprehensive analysis of aneuploidy and dosage compensation across cancers will help identify the key driver genes encoded on altered chromosomes and will shed light on the overall consequences of aneuploidy during tumor development.

Density estimation in sequence space is a fundamental problem in machine learning that is of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy, i.e. calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates. Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data is plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data is sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyper-parameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5 splice sites found in the human genome and to understand the accumulation of chromosomal abnormalities during cancer progression.