Mike Anderson at Harvard's Social Science Statistics Blog looks at the recent change in recommendations for women with regard to breast cancer screening from the perspective of Bayes' Theorem. This calculation was particularly interesting:
So if you're a woman in your 40s, and you get a positive result from your latest mammogram, you'll still only have an 11.9% probability of having breast cancer -- basically the same as a woman's lifetime risk of 12%.
Of course none of this takes into account the myriad other factors (cost of a false positive or negative, improved understanding of risk factors, etc.) but it does shed some light on the controversial recommendation change.
Update Nov 20: As noted here in the comments, the linked post has been removed, possibly due to an error in its calculations.
Update Dec 3: The post has since been replaced.
Social Science Statistics Blog: breast cancer, mammograms, rare diseases, and bayes rule (via @drewconway)