Mathematics Of Making Up Your Mind

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In the article The Mathematics of Making Up Your Mind by Will Hively, the author summarizes the analysis of the statistical difference between two medications, tissue plasminogen activator (t-PA) and streptokinase, used for treating heart attack victims. The author says that all cardiologists agree that both drugs work well, but they disagree on which of the drugs should be used. In order to help doctors decide which drug to use, James Brophy, a cardiologist interested in knowing which drug is superior, teams up with a biostatistician named Lawrence Joseph, and the two published a controversial paper. Brophy and Joseph claimed that to make a rational decision, physicians should follow Bayes' theorem. Bayes' theorem was essentially a formula for updating any kind of belief when confronted with new evidence. According to the author, current wisdom suggests that t-PA "probably does work better", but costs $1,530 per use, compared to the $220 price tag of streptokinase. In order to prove the difference, Genentech, t-PA's manufacturer, sponsored a huge clinical trial called GUSTO, whose results "looked so good for t-PA that the trial's leading researchers declared the drug clinically superior to streptokinase". GUSTO showed that 93.7% of patients who received t-PA survived versus 92.7% of patients who received streptokinase survived. One percent may not seem significant, but when there are approximately half a million people who die of a heart attack each year, this means 5,000 more people would be saved. According to Brophy and Joseph, "the probability of t-PA being clinically superior is at best 50-50," since t-PA's one percent better survival rate has a margin of error. They say that although t-PA might do better in 999 out of 1,000 trials, it would do approximately one percent better about half those times, at best. The article then raises the question

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