The application of proportional odds models to ordered categorical data using the mixed-effects modeling approach has become more frequently reported within the pharmacokinetic/pharmacodynamic area during the last decade. The aim of this paper was to investigate the bias in parameter estimates, when models for ordered categorical data were estimated using methods employing different approximations of the likelihood integral; the Laplacian approximation in NONMEM (without and with the centering option) and NLMIXED, and the Gaussian quadrature approximations in NLMIXED. In particular, we have focused on situations with non-even distributions of the response categories and the impact of interpatient variability. This is a Monte Carlo simulation study where original data sets were derived from a known model and fixed study design. The simulated response was a four-category variable on the ordinal scale with categories 0, 1, 2 and 3. The model used for simulation was fitted to each data set for assessment of bias. Also, simulations of new data based on estimated population parameters were performed to evaluate the usefulness of the estimated model. For the conditions tested, Gaussian quadrature performed without appreciable bias in parameter estimates. However, markedly biased parameter estimates were obtained using the Laplacian estimation method without the centering option, in particular when distributions of observations between response categories were skewed and when the interpatient variability was moderate to large. Simulations under the model could not mimic the original data when bias was present, but resulted in overestimation of rare events. The bias was considerably reduced when the centering option in NONMEM was used. The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.

中文翻译：

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使用NONMEM和NLMIXED为某些模型的重复测量序数数据估计总体参数的偏差。

在过去的十年中，在药代动力学/药效学领域，使用混合效应建模方法将比例优势模型应用于有序分类数据的情况越来越多。本文的目的是研究在使用有可能的似然积分的不同近似方法估计有序分类数据模型时参数估计的偏差。NONMEM中的Laplacian逼近（不带居中选项）和NLMIXED，NLMIXED中的高斯正交逼近。特别是，我们关注的是响应类别的分布不均匀以及患者间变异性的影响。这是蒙特卡洛模拟研究，其中原始数据集是从已知模型和固定研究设计中得出的。模拟的响应是顺序级别上的四个类别变量，类别分别为0、1、2和3。将用于模拟的模型拟合到每个数据集，以评估偏差。此外，还基于估计的种群参数对新数据进行了仿真，以评估估计模型的有效性。对于测试条件，在参数估计中没有明显偏差的情况下执行了高斯正交。但是，使用拉普拉斯估计方法而没有居中选项时，会获得明显偏差的参数估计值，尤其是当响应类别之间的观察值分布偏斜并且患者之间的差异为中等到较大时。在存在偏差的情况下，该模型下的模拟无法模拟原始数据，但会导致高估罕见事件。当使用NONMEM中的居中选项时，偏差会大大降低。估计偏差的原因似乎与估计过程中个体间随机效应的非信息性和不确定性经验贝叶斯估计以及正态性假设有关。