School of Pharmacy, University of Otago, Dunedin, New Zealand.
J Pharmacokinet Pharmacodyn. 2011 Apr;38(2):205-22. doi: 10.1007/s10928-010-9189-6. Epub 2010 Dec 14.
The aim of the current work was to evaluate graphical diagnostics for assessment of the fit of logistic regression models. Assessment of goodness of fit of a model to the data set is essential to ensure the model provides an acceptable description of the binary variables seen. For logistic regression the most common diagnostic used for this purpose is binning the data and comparing the empirical probability of the occurrence of a dependent variable with the model predicted probability against the mean covariate value in the bin. Although intuitively appealing this method, which we term simple binning, may not have consistent properties for diagnosing model problems. In this report we describe and evaluate two different diagnostic procedures, random binning and simplified Bayes marginal model plots. These procedures were assessed via simulation under three different designs. Design 1: studies which were balanced on binary variables and a continuous covariate. Design 2: studies that were balanced on binary variables but unbalanced on the continuous covariate. Design 3: studies that were unbalanced on both the binary variables and the covariate. Each simulated study consisted of 500 individuals. Thirty studies were simulated. The covariate of interest was dose which could range from 0 to 20 units. The data were simulated with the dose being related to the outcome according to an E (max) model on the logit scale. A logit E (max) model (correct model) and a logit linear model (wrong model) were fitted to all data sets. The performance of the above diagnostics, in addition to simple binning, was compared. For all designs the proposed diagnostics performed at least as well and in many instances better than simple binning. In case of design 1 random binning and simple binning are identical. In the case of designs 2 and 3 random binning and simplified Bayes marginal model plots were superior in assessing the model fit when compared to simple binning. For the examples tested, both random binning and simplified Bayesian marginal model plots performed acceptably.
本研究旨在评估逻辑回归模型拟合情况的图形诊断方法。评估模型对数据集的拟合程度对于确保模型对所观察的二项变量提供可接受的描述至关重要。对于逻辑回归，最常用于此目的的诊断方法是对数据进行分箱，并比较因变量的经验概率与分箱中协变量均值的模型预测概率。尽管这种方法直观上很有吸引力，但我们称之为简单分箱的方法可能不具有一致的诊断模型问题的属性。在本报告中，我们描述并评估了两种不同的诊断程序，即随机分箱和简化贝叶斯边际模型图。这两种方法是在三种不同设计下通过模拟来评估的。设计 1：在二项变量和连续协变量上平衡的研究。设计 2：在二项变量上平衡但在连续协变量上不平衡的研究。设计 3：在二项变量和协变量上都不平衡的研究。每个模拟研究包含 500 个个体。模拟了 30 项研究。感兴趣的协变量是剂量，范围从 0 到 20 个单位。数据是根据对数刻度上的 E(max)模型模拟的，剂量与结果有关。对所有数据集拟合了逻辑 E(max)模型（正确模型）和逻辑线性模型（错误模型）。比较了上述诊断方法（除了简单分箱）的性能。对于所有设计，所提出的诊断方法的性能至少与简单分箱一样好，在许多情况下甚至更好。在设计 1 的情况下，随机分箱和简单分箱是相同的。在设计 2 和 3 的情况下，与简单分箱相比，随机分箱和简化贝叶斯边际模型图在评估模型拟合方面表现更好。对于测试的示例，随机分箱和简化贝叶斯边际模型图的性能都可以接受。
