  Identifying genes underlying cancer development is critical to cancer biology
and has important implications across prevention, diagnosis and treatment.
Cancer sequencing studies aim at discovering genes with high frequencies of
somatic mutations in specific types of cancer, as these genes are potential
driving factors (drivers) for cancer development. We introduce a hierarchical
Bayesian methodology to estimate gene-specific mutation rates and driver
probabilities from somatic mutation data and to shed light on the overall
proportion of drivers among sequenced genes. Our methodology applies to
different experimental designs used in practice, including one-stage, two-stage
and candidate gene designs. Also, sample sizes are typically small relative to
the rarity of individual mutations. Via a shrinkage method borrowing strength
from the whole genome in assessing individual genes, we reinforce inference and
address the selection effects induced by multistage designs. Our simulation
studies show that the posterior driver probabilities provide a nearly unbiased
false discovery rate estimate. We apply our methods to pancreatic and breast
cancer data, contrast our results to previous estimates and provide estimated
proportions of drivers for these two types of cancer.
