辛普森悖論解決之道：以新英格蘭醫學雜誌之羅格列酮統合分析為例

The Solution of Simpson's Paradox: A Meta-analysis of Rosiglitazone from the New England Journal of Medicine as an Example

目的：在做研究之統計分析時，有時數值不宜直接相加再重新計算總比值，否則可能陷入辛普森悖論(Simpson’s paradox)的情境，導致完全相反的結果，過去鮮少有探討其如何解決的方法，我們發現可用統合分析(meta-analysis)方法快速計算。

方法：關鍵詞為“Simpson’s paradox”或“Simpson paradox”，搜尋2020年10月前之PubMed medline、Cochrane、Web of Science及中文電子期刊C.E.P.S.等資料庫，並找一篇國際學術期刊文獻為例做比較分析及說明。

結果：共找到69篇文獻，其中一篇是討論羅格列酮(Rosiglitazone)統合分析做辛普森悖論的說明，其是以Nissen於新英格蘭醫學雜誌發表文章為例做分析，其中有36個小型研究合併成一個數值，因為心血管事件很少，使用Peto方法計算勝算比(odds ratio, OR)和95%信賴區間(CI)，結果OR (95% CI)為1.45 (0.88-2.39)，再加上另2個較大型研究DREAM (OR 1.65, 0.74-3.68)及ADOPT (OR 1.33, 0.80-2.21)，最後統合分析結果為1.43 (1.03-1.98)，表示Rosiglitazone會增加43%心肌梗塞風險。若分別將全部個案數合併後重算，會導致相反結果，其OR 0.97 (0.71-1.32)，表示Rosiglitazone能降低3%心肌梗塞風險，雖未達統計學上顯著的差異，亦顯示了辛普森悖論現象。

結論：不宜直接相加各不同研究的個案再重算總比值，否則可能導致辛普森悖論現象的相反結論，此時可用統合分析軟體解決。

 

Objectives: The cases’ numbers in statistical analysis sometimes should not be aggregated directly to recalculate the overall ratio as this, according to Simpson’s paradox, can lead to reversed results. How to solve the paradox has remained an understudied issue, yet it has come to our attention that meta-analysis method seems to be a potential solution.

Methods: To identify an international journal article as an example for analysis, the study used the keywords “Simpson’s paradox” and “Simpson paradox” to search for journal papers published prior to October 2020 in the following databases: PubMed Medline, Cochrane, Web of Science and C.E.P.S.

Results: A total of 69 articles were found, and one discussed the Simpson’s paradox with analysis of Rosiglitazone trials. The study by Nissen, published in the New England Journal of Medicine had 36 small trials aggregated into one value. There were few cardiovascular events, so the Peto method was used to calculate the odds ratio (OR) and 95% confidence interval. The result was 1.45 (0.88-2.39). Together with the results of two other larger studies DREAM (OR 1.65, 0.74-3.68) and ADOPT (1.33, 0.80-2.21), the final meta-analysis result emerged to be 1.43 (1.03-1.98), indicating that Rosiglitazone increased the risk of myocardial infarction by 43%. If all cases are combined and recalculated, an opposite result, OR 0.97 (0.71-1.32), indicated that Rosiglitazone reduced the myocardial infarction risk by 3%.

Conclusion: It is not recommended to directly aggregate the cases’ numbers of different studies and then recalculate the overall ratio since it may lead to the phenomenon of Simpson’s paradox. Meanwhile, meta-analysis software can be used to solve the problem.