Brief Bioinform. 2017 Nov 1;18(6):962-972. doi: 10.1093/bib/bbw074.
Logistic regression is the most common technique used for genetic case-control association studies. A disadvantage of standard maximum likelihood estimators of the genotype relative risk (GRR) is their strong dependence on outlier subjects, for example, patients diagnosed at unusually young age. Robust methods are available to constrain outlier influence, but they are scarcely used in genetic studies. This article provides a non-intimidating introduction to robust logistic regression, and investigates its benefits and limitations in genetic association studies. We applied the bounded Huber and extended the R package 'robustbase' with the re-descending Hampel functions to down-weight outlier influence. Computer simulations were carried out to assess the type I error rate, mean squared error (MSE) and statistical power according to major characteristics of the genetic study and investigated markers. Simulations were complemented with the analysis of real data. Both standard and robust estimation controlled type I error rates. Standard logistic regression showed the highest power but standard GRR estimates also showed the largest bias and MSE, in particular for associated rare and recessive variants. For illustration, a recessive variant with a true GRR=6.32 and a minor allele frequency=0.05 investigated in a 1000 case/1000 control study by standard logistic regression resulted in power=0.60 and MSE=16.5. The corresponding figures for Huber-based estimation were power=0.51 and MSE=0.53. Overall, Hampel- and Huber-based GRR estimates did not differ much. Robust logistic regression may represent a valuable alternative to standard maximum likelihood estimation when the focus lies on risk prediction rather than identification of susceptibility variants.
逻辑回归是用于遗传病例对照关联研究的最常用技术。基因型相对风险（GRR）的标准极大似然估计的一个缺点是它们对异常值个体的强烈依赖，例如，在异常年轻的年龄被诊断出的患者。有可用的稳健方法来约束异常值的影响，但它们在遗传研究中很少使用。本文提供了对稳健逻辑回归的一种不令人生畏的介绍，并研究了其在遗传关联研究中的优势和局限性。我们应用了有界 Huber 和扩展的 R 包'robustbase'，使用重新下降的 Hampel 函数来降低异常值的影响。进行了计算机模拟，以根据遗传研究和调查标记的主要特征评估Ⅰ型错误率、均方误差（MSE）和统计功效。模拟结果补充了真实数据的分析。标准和稳健估计都控制了Ⅰ型错误率。标准逻辑回归显示出最高的功效，但标准 GRR 估计也显示出最大的偏差和 MSE，特别是对于相关的罕见和隐性变体。为了说明问题，在一项 1000 例病例/1000 例对照研究中，对真实数据的分析中，对一个隐性变体进行了研究，该变体的真实 GRR=6.32，次要等位基因频率=0.05，标准逻辑回归的结果是功效=0.60，MSE=16.5。基于 Huber 的估计的相应数字为功效=0.51，MSE=0.53。总体而言，Hampel 和 Huber 基于的 GRR 估计值差异不大。当重点在于风险预测而不是识别易感性变体时，稳健逻辑回归可能是标准最大似然估计的一种有价值的替代方法。
