回歸至平均值的謬誤及診斷

很多臨床研究者對「迴歸至平均值」效應，都不甚暸解。因此，本文參考及整理這方面的文獻，介紹「迴歸至平均值」一詞之起源，如何發生，數理推導，診斷及解决方法。此外，爲使讀者能暸解及診斷「迴歸至平均值」效應，模擬不同條件的資料，另有一組原始資料，讀者可用一般統計軟體自行練習，學以致用。所謂「迴歸至平均值」通常發生於不同世代或時間有兩次相同測量，主要發生於沒有對照組的臨床試驗，因爲只對最高或最低測量的族群作二次測量，第二次測量的平均值會傾向總平均值。如果使用paired t來檢定兩次測量有沒有差異，容易得到一錯誤結果。「迴歸至平均值」的效應受兩個因素影響：(1)選擇族群之第一次測量有多極端，(2)兩次測量相關係數的數值大小。診斷方法為使用簡單線性迴歸檢定截距(intercept)與測量的總平均有沒有差異，如果沒差異表示第二次測量與第一次測量之差異屬於「迴歸至平均值」的效應；相反，第二次測量與第一次測量有差異則不可歸因於「迴歸至平均值」的效應。儘管可以利用統計方法來診斷「迴歸至平均值」的效應，强烈建議采用有隨機分配對照組的臨床試驗來檢定治療的效果。

關鍵字

迴歸至平均值；簡單線性迴歸；模擬

並列摘要

As ”regression toward the mean” is not well known to many clinical researchers, the aim of this study was to introduce the concept of how it occurs, as well as the mathematical theory, diagnosis and solution of this issue. Furthermore, simulations using different parameters were provided to help readers understand ”regression toward the mean”. A set of raw data was also given so readers could practice using the commercial statistical package to determine how ”regression toward the mean” occurs and how to make diagnoses. ”Regression toward the mean” mainly occurred in clinical trials. When the same measurements were made before and after treatment for patients who had the highest or lowest scores before treatment (no control group), the scores measured after treatment tended to be close to the overall mean. Bias resulted from the use of a paired-t test to examine the differences between the two measurements. There were two factors that determined the effects of ”Regression toward the mean” which included (1) the extremity of the condition of the patients first selected, and (2) the magnitude of correlation between the two measurements. Diagnoses were suggested to determine whether intercepts were different from the overall mean using a t-test in a simple linear regression. If significant differences were not seen, the differences between the two measurements were due to the effect of ”regression toward the mean”. Although ”regression toward the mean” can be easily diagnosed using the above method, a randomized clinical trial with a control group is strongly recommended to examine the treatment effects.

並列關鍵字

regression toward the mean ； simple linear regression ； simulation

國際替代計量

回歸至平均值的謬誤及診斷

未授權

主題瀏覽