Cole T J
Department of Paediatric Epidemiology and Biostatistics, Institute of Child Health, London WC1N 1EH, UK.
Stat Med. 2000 Nov 30;19(22):3109-25. doi: 10.1002/1097-0258(20001130)19:22<3109::aid-sim558>3.0.co;2-f.
The results of analyses on log transformed data are usually back-transformed and interpreted on the original scale. Yet if natural logs are used this is not necessary--the log scale can be interpreted as it stands. A difference of natural logs corresponds to a fractional difference on the original scale. The agreement is exact if the fractional difference is based on the logarithmic mean. The transform y = 100 log(e)x leads to differences, standard deviations and regression coefficients of y that are equivalent to symmetric percentage differences, standard deviations and regression coefficients of x. Several simple clinical examples show that the 100 log(e) scale is the natural scale on which to express percentage differences. The term sympercent or s% is proposed for them. Sympercents should improve the presentation of log transformed data and lead to a wider understanding of the natural log transformation.
对经对数变换后的数据进行分析的结果通常会进行逆变换,并在原始尺度上进行解释。然而,如果使用自然对数,就没有必要这样做——对数尺度本身就可以进行解释。自然对数的差值对应于原始尺度上的分数差值。如果分数差值基于对数均值,则二者完全一致。变换y = 100 log(e)x会使y的差值、标准差和回归系数等同于x的对称百分比差值、标准差和回归系数。几个简单的临床实例表明,100 log(e)尺度是表达百分比差值的自然尺度。为此提出了“sympercent”或“s%”这一术语。对称百分比应能改进经对数变换后的数据呈现方式,并使人们对自然对数变换有更广泛的理解。