But from JPAD, the specific effects that are supposed to show aspirin benefits weren't what this study measured! They were looking at:

Primary end points were atherosclerotic events, including fatal or nonfatal ischemic heart disease, fatal or nonfatal stroke, and peripheral arterial disease.

This doesn't include anything related to cancer. And to the extent that the study did look at all-cause mortality, it showed exactly what you would expect from a relatively small (n=2539) and short ("median follow-up of 4.37 years") trial where aspirin was yielding benefits: a large but non-statistically-significant effect

A total of 34 patients in the aspirin group and 38 patients in the nonaspirin group died from any cause (HR, 0.90; 95% CI, 0.57-1.14; log-rank test, p=.67).