I haven't looked at the JPAD paper yet, but that Cochrane study plots JPAD results for cancer endpoints as well as major vascular and extracranial bleeds. In the same graphs I don't see large effects.
It's worth pointing out the general low cancer rates (in the controls as well) in the JPAD study.
(For Round 1, see this comment from last year.)
NYT: Studies Link Daily Doses of Aspirin to Reduced Risk of Cancer
The article is worth reading in its entirety, but here's an especially interesting paragraph:
The evidence still isn't perfect, but the purpose of rationality is making good decisions with limited information. I am a healthy 28-year-old and these studies make me even more confident that taking daily low-dose aspirin is the right thing for me to do.
On a related note, if society were more rational, I wouldn't have to be sad reading paragraphs like this one:
Or these ones from A Cheap Drug Is Found to Save Bleeding Victims, published on the same day: