From www.xscx.info:
McDonald wanted to test a hypothesis that the difference in cancer rates between the species could be due to differences in the way their cells self-destroy themselves — an important biological process known as programmed cell death or apoptosis.
The researchers saw that some of the genes for apoptosis were expressed differently in humans than in chimps, and their data suggests that human cells are not as efficient at carrying out programmed cell death as chimp cells, at least in the brain and other studied tissues.
What does apoptosis have to do with cancer?
Reduced amounts of apoptosis have been associated with an increased risk of cancer. Also, several genes involved in apoptosis are thought to “malfunction” in cancer cells. This makes sense: cancer cells divide uncontrollably and somehow seem to override the signal to self-destruct.
And what does that have to do with a large brain? During human evolution, it is thought that people were naturally selected for larger brains and increased cognition. There is also another hypothesis that to get these larger brains, we needed to have a high rate of neuron synthesis.
More here.