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首页> 外文会议>Annual conference of the International Society of Exposure Science >To log-transform or not to log-transform: Regression on log-normal data, in models with abdominal adiposity as predictor for inflammation and insulin resistance
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To log-transform or not to log-transform: Regression on log-normal data, in models with abdominal adiposity as predictor for inflammation and insulin resistance

机译：要进行对数转换或不进行对数转换：在以腹部肥胖作为炎症和胰岛素抵抗的预测因子的模型中，对数正态数据进行回归

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Background and Aims Much data in medical and environmental science can be described by a log-normal distribution, whereas many statistical analyses assume a normal distribution. It is common to log-transform the response variable in a regression analysis. Regression on a log-transformed response results in an exponential model (and an estimate of the relative effect of each predictor), whereas an untransformed response variable yields a linear model (and an estimate of the absolute effect). For two outcomes, CRP (inflammation marker) and HOMA-IR (insulin resistance), we fitted both an exponential and a linear model. The aim was to determine which model that fitted each outcome best. Data and Methods Data from a study of 64-year-old women (n=629), with different degrees of glucose tolerance, were used to quantify how each outcome (CRP and HOMA-IR) was associated with waist circumference (a known association). Ordinary least squares regression on log-transformed data (LSexp) was used to estimate the exponential model, and a maximum likelihood method based on the log-normal likelihood function (MLLN) was used to estimate the linear model. The best fit was assessed by explanatory power (R2). Also the log-scale residuals from each model (rLS and rML) were examined to see if the assumptions of constant variance, normality and random residuals were met. Results CRP: Neither rLS nor rML showed signs of heteroscedasticity. The residuals of LSexp deviated from normality and showed signs of an inverted U-pattern. The rML were normally distributed and showed no pattern. MLLN had a higher R2 than LSexp. HOMA-IR: Both rLS and rML had a skewed distribution and showed signs of heteroscedasticity. The rML showed a U-pattern. LSexp had a higher R2 than ML. Conclusions Based on the residuals and coefficient of determination, the linear model (estimated with MLLN) had a better fit for CRP, while the exponential model (estimated with LSexp) had a better fit for HOMA-IR.
机译：背景和目标医学和环境科学中的许多数据都可以用对数正态分布来描述，而许多统计分析都采用正态分布。通常在回归分析中对响应变量进行对数转换。对数转换后的响应的回归会生成指数模型（以及每个预测变量的相对效果的估计值），而未转换的响应变量会生成线性模型（以及绝对效果的估计值）。对于两个结果，CRP（炎症标记物）和HOMA-IR（胰岛素抵抗），我们同时拟合了指数模型和线性模型。目的是确定哪种模型最适合每个结果。数据和方法来自一项对64岁女性（n = 629），具有不同程度的糖耐量的研究得出的数据用于量化每个结局（CRP和HOMA-IR）如何与腰围相关（已知的关联） ）。使用对数转换数据的普通最小二乘回归（LSexp）估计指数模型，并使用基于对数正态似然函数（MLLN）的最大似然方法估计线性模型。最佳拟合度通过解释能力（R2）进行评估。还检查了每个模型（rLS和rML）的对数刻度残差，以查看是否满足恒定方差，正态性和随机残差的假设。结果CRP：rLS和rML均未显示异方差迹象。 LSexp的残差偏离正态性，并显示出倒U型的迹象。 rML呈正态分布，未显示任何模式。 MLLN的R2高于LSexp。 HOMA-IR：rLS和rML都有偏斜的分布，并显示出异方差的迹象。 rML显示为U型。 LSexp具有比ML高的R2。结论根据残差和确定系数，线性模型（用MLLN估计）更适合CRP，而指数模型（用LSexp估计）更适合HOMA-IR。

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