Logistic Regression: A Brief Primer
Logistic Regression: A Brief Primer
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DOI：
10.1111/j.1553-2712.2011.01185.x
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发表时间：
2011-10-01
影响因子：
4.4
通讯作者：
Stoltzfus, Jill C.
中科院分区：
文献类型：
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作者：
Stoltzfus, Jill C.
回归技术在医学研究中的应用是多方面的，因为它们可以测量关联，预测结果，并控制混杂变量效应。作为这样的技术之一，逻辑回归是一种通过量化每个自变量的独特贡献来分析一组自变量对二元结果的影响的有效且强大的方法。使用反映在logit量表中的线性回归的分量，逻辑回归迭代地识别具有检测观察结果的最大概率的变量的最强线性组合。进行逻辑回归时的重要考虑因素包括选择自变量，确保满足相关假设，以及选择适当的模型构建策略。对于自变量的选择，应遵循公认的理论、先前的实证研究、临床考虑和单变量统计分析等因素，并确认应考虑的潜在混杂变量。逻辑回归必须满足的基本假设包括误差的独立性，连续变量的logit线性，不存在多重共线性，以及缺乏强影响力的离群值。此外，每个自变量应该有足够数量的事件，以避免过拟合模型，通常推荐的最小“经验法则”范围为每个协变量10至20起事件。关于模型构建策略，三种一般类型是直接/标准，顺序/分层和逐步/统计，每种都有不同的重点和目的。在从任何这些方法的结果得出明确的结论之前，应该正式量化模型的内部有效性（即，同一数据集内的可复制性）和外部有效性（即，超越当前样本的普遍性）。使用各种拟合优度测量评估所得到的逻辑回归模型与样本数据的总体拟合，更好的拟合特征在于观察值和模型预测值之间的差异较小。还建议使用诊断统计数据，以进一步评估模型的适当性。最后，独立变量的结果通常报告为比值比（OR）和95%置信区间（CI）。学术急诊医学学会2011; 18：1099-1104（C）2011
Regression techniques are versatile in their application to medical research because they can measure associations, predict outcomes, and control for confounding variable effects. As one such technique, logistic regression is an efficient and powerful way to analyze the effect of a group of independent variables on a binary outcome by quantifying each independent variable's unique contribution. Using components of linear regression reflected in the logit scale, logistic regression iteratively identifies the strongest linear combination of variables with the greatest probability of detecting the observed outcome. Important considerations when conducting logistic regression include selecting independent variables, ensuring that relevant assumptions are met, and choosing an appropriate model building strategy. For independent variable selection, one should be guided by such factors as accepted theory, previous empirical investigations, clinical considerations, and univariate statistical analyses, with acknowledgement of potential confounding variables that should be accounted for. Basic assumptions that must be met for logistic regression include independence of errors, linearity in the logit for continuous variables, absence of multicollinearity, and lack of strongly influential outliers. Additionally, there should be an adequate number of events per independent variable to avoid an overfit model, with commonly recommended minimum "rules of thumb" ranging from 10 to 20 events per covariate. Regarding model building strategies, the three general types are direct/standard, sequential/hierarchical, and stepwise/statistical, with each having a different emphasis and purpose. Before reaching definitive conclusions from the results of any of these methods, one should formally quantify the model's internal validity (i.e., replicability within the same data set) and external validity (i.e., generalizability beyond the current sample). The resulting logistic regression model's overall fit to the sample data is assessed using various goodness-of-fit measures, with better fit characterized by a smaller difference between observed and model-predicted values. Use of diagnostic statistics is also recommended to further assess the adequacy of the model. Finally, results for independent variables are typically reported as odds ratios (ORs) with 95% confidence intervals (CIs).ACADEMIC EMERGENCY MEDICINE 2011; 18:1099-1104 (C) 2011 by the Society for Academic Emergency Medicine