BREAST SELF EXAMINATION AND BAYESIAN STATISTICS. I posted here on the major split between two schools of statisticians and wrote: “In conducting a statistical test, one grouping (‘Bayesians’) wants to include independent knowledge and beliefs; the other wants to start from scratch (‘frequentists’).” Kids, the recent recommendation by the U.S. Preventive Services Task Force (“USPSTF”) against teaching breast self examination (apparently for women of all ages) is a good example of the difference between the two approaches to statistics. Independent knowledge, which a Bayesian would use, would suggest that breast self examination might lead to earlier detection of breast cancer and that earlier detection might reduce mortality. As for statistical evidence–which a frequentist would insist on—apparently, and perhaps understandably—there have not been a lot of studies. In 2002, the USPSTF had summarized (link here) the state of research as: “The accuracy of BSE (breast self examination) is largely unknown.” The effect of breast self examination in reducing mortality was also addressed by the USPSTF in 2002. It described three studies and concluded: “Although none of these studies provides support for BSE, the USPSTF concluded that these studies did not exclude a possible benefit, due to their limited duration of followup and questions about whether results from other countries are generalizable to women in North America.” Seven years later, the frequentists seem to have won a complete victory. As far as I can tell, there has been no additional controlled experiment. (You can imagine that a large statistical study would be required, since most women do not develop breast cancer, to measure reductions in mortality from breast self examination. And the study would have to have a control group that did not examine their breasts in some defined way.) But the recommendation has been changed for what to do when there is not much evidence either way. You can think of the difference between Bayesians and frequentists in terms of presumptions or burdens of proof. A Bayesian might begin with the thought that breast self examination might reduce mortality and there is not enough evidence to change that opinion. The frequentist would say, as the USPSTF apparently did in 2009, that if there is little evidence in controlled experiments, “evidence-based” medicine should not encourage breast self examination.

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