技術 Wikipedia article "Bonferroni correction".
2009年 01月 29日 13:26
去 年四月，《英國皇家學會會報-B輯》(Proceedings of the Royal Society B)刊登了一篇研究報告──《你是由你母親吃什麼決定的》(You Are What Your Mother Eats)，在全球引起巨大反響。來自艾克斯特大學和牛津大學的研究人員請740名懷孕婦女記錄下她們在孕期和懷孕之前的飲食。結果並不出人意料，孕婦懷 孕期的飲食和胎兒性別沒什麼聯系。
美 國國家統計科學研究院(National Institute of Statistical Sciences)的副主任斯坦﹒榮格(Stan Young)說，可以這麼看：拿到的一把牌中全是方片牌的可能性微乎其微，但要把范圍擴大到全世界的所有牌局，這還是有可能的。他獲得了上述研究數據，對 其重新進行了分析，並在本期《英國皇家學會會報》上撰文評論說，谷類食品攝入量與胎兒性別的關系純屬偶然。
統 計學家表示，此類研究經常會出現偶然性聯系，這也是為什麼研究結果許多都相互矛盾的原因。為了証明這一點，安大略的研究人員研究了住院患者的星座，發現射 手座的人容易骨折，雙魚座的人容易產生心臟問題，如此等等。這種聯系符合“具統計學意義”的傳統數學標準，但卻是完全偶然性的，換一個不同的樣本重新研 究，此前的結果就不存在了。
一些統計學家認為，研究人員在分析大量數據時應該採取更為嚴格的証明標準。一個方法是採取 Bonferroni調整，要求用相關數學公式除以變量的數目；如果研究的是100種食物，那麼必須有比尋常高100倍的關聯度才能被認為具統計學意義。 否則，統計學家表示只有進行嚴格的臨床試驗，對比一個控制組、一個測試組以及一個變量，才能真正証明因果關系。
流行病學家則認 為，Bonferroni調整忽視了許多合理發現，而且同時研究多少其他因素並不會影響研究結果。他們還指出，控制性的臨床試驗代價不菲、耗時持久，有時 還不道德。拿吸煙和肺癌之間關系的研究來說，許多觀察性研究都發現了這一點，但要迫使研究對象吸煙多年來証明這一點恐怕是不可能的。
Does Bran Make the Man? What Statistics Really Tell Us
Can eating breakfast cereal determine the sex of your baby?
A debate over that question in a British scientific journal shows why some observational studies should be taken with a big shaker of salt.
The original study, "You Are What Your Mother Eats," in the journal Proceedings of the Royal Society B, made headlines around the world last April. Researchers at Exeter and Oxford universities asked 740 pregnant women to record what they ate during pregnancy and just before. Not surprisingly, their diets during pregnancy had no correlation with their babies' gender.
But 56% of women who consumed the most calories before conception gave birth to boys, compared with 45% of those who consumed the least. Of 132 individual foods tracked, breakfast cereal was the most significantly linked with baby boys.
How could that be? The authors said animal studies also found male offspring are more common in times of plenty; they speculated that higher glucose levels in mothers may favor the survival of male embryos, which are slightly heavier than females.
Baloney, said some U.S. statisticians, who suspected the finding was simply a false association that can occur by chance in a large set of data.
Making Sense of Studies
Following health news is a lot like watching a ping-pong match: reports linking fat or coffee or alcohol with various ills one week often get contradicted the next. Often, such findings come from observational studies that aren't as precise as randomized controlled trials. Some experts think they shouldn't be published until they've been confirmed with repeat studies.
What's your view? How much do you trust the health news you hear?
"Think of it this way: The probability of getting all spades in a given bridge hand is infinitesimally small, but in all the bridge games all over the world, somebody might," says Stan Young, assistant director of the National Institute of Statistical Sciences in Research Triangle Park, N.C. He obtained the study data, re-analyzed it and wrote a commentary in the journal's current issue saying the cereal finding was pure chance.
The study's authors wrote a rebuttal disputing Dr. Young's analysis and standing by their findings.
Behind the cereal squabble lies a deep divide between statisticians and epidemiologists about the nature of chance in observational studies in which researchers track peoples' habits and look for associations with their health but don't intervene at all.
Statisticians say random associations are rampant in such studies, which is why so many have contradictory findings. To prove the point, researchers in Ontario studied the astrological signs of hospital patients and found that Sagittarians are susceptible to fractures, Pisces are prone to heart failure, and so on. The links met the traditional mathematical standard for "statistical significance" but were completely random, and disappeared when the study was repeated with a different sample.
Some statisticians argue for a tougher standard of proof when researchers are fishing in large data sets. One method, a Bonferroni adjustment, requires dividing the usual mathematical formula by the number of variables; if 100 foods are studied, the link must be 100 times as strong as usual to be considered significant. Otherwise, statisticians say only strict clinical trials with a control group and a test group and one variable can truly prove a cause-and-effect association.
Epidemiologists argue that a Bonferroni adjustment throws out many legitimate findings, and that it's irrelevant how many other factors are studied simultaneously. They also note that controlled clinical trials are costly, time-consuming and sometimes unethical. The link between smoking and cancer, for example, was seen in many observational studies, but forcing subjects to smoke for years to prove it would be untenable.
In the cereal study, Dr. Young argues that the data collected on the mothers' diets at mid-pregnancy should be factored into the adjustment for statistical significance, and that when it is, the significance of breakfast cereal vanished. "If you can pick and choose your data after the fact, you can make them look however you want," he says.
"There's no way that the mother's diet in mid-pregnancy would affect the gender of her infant," counters Fiona Mathews, the lead author and a lecturer in mammalian biology at Exeter, who says that data was included only for comparison.
So does breakfast cereal affect a baby's gender? Don't paint the nursery yet. A good rule of thumb is to wait and see if an observation association pops up again when the study is repeated, something Dr. Mathews says she plans to do.
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