The development of non-linear mixed pharmacokinetic/pharmacodynamic models for continuous variables is usually guided by graphical assessment of goodness of fit and statistical significance criteria. The latter is usually the likelihood ratio test (LR). When the variable to be modeled is categorical, on the other hand, the available graphical methods are less informative and/or more complicated to use and the modeler needs to rely more heavily on statistical significance assessment in the model development. The aim of this study was to evaluate the type I error rates, obtained from using the LR test, for inclusion of a false parameter in a non-linear mixed effects model for ordered categorical data when modeling with NONMEM. Data with four ordinal categories were simulated from a logistic model. Two nested multinomial models were fitted to the data, the model used for simulation and a model containing one additional parameter. The difference in fit (objective function value) between models was calculated. Three types of models were explored; (i) a model without interindividual variability (IIV) where the addition of a parameter describing IIV was assessed, (ii) a model with IIV where the addition of a drug effect parameter (either categorical or continuous drug exposure measure) was evaluated, and (iii) a model including IIV and drug effect where the inclusion of a random effects parameter on the drug effect was assessed. Alterations were made to the simulation conditions, for example, varying the number of individuals and the size and distribution of the IIV, to explore potential influences on the type I error rate. The estimated type I error rate for inclusion of a false random effect parameter in model (i) and (iii) were, as expected, lower than the nominal. When the additional parameter was a fixed effects parameter describing drug effect (model(II)) the estimated type I error rates were in agreement with the nominal. None of the different simulation conditions tried changed this pattern. Thus, the LR test seems appropriate for judging the statistical significance of fixed effects parameters when modeling categorical data with NONMEM.

中文翻译：

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在NONMEM中对有序分类数据建模时，对I型错误率的评估。

连续变量的非线性混合药代动力学/药效学模型的开发通常以拟合优度和统计显着性标准的图形评估为指导。后者通常是似然比检验（LR）。另一方面，当要建模的变量是分类变量时，可用的图形方法的信息量较少和/或使用起来更复杂，建模人员在模型开发中需要更多地依赖统计显着性评估。这项研究的目的是评估使用LR测试获得的I型错误率，以便在使用NONMEM建模时，在有序分类数据的非线性混合效应模型中包含错误参数。从逻辑模型模拟了具有四个序数类别的数据。将两个嵌套的多项式模型拟合到数据，该模型用于仿真，模型包含一个附加参数。计算模型之间的拟合差异（目标函数值）。探索了三种类型的模型。（i）没有评估个体间变异性（IIV）的模型，其中评估了描述IIV的参数；（ii）具有IIV的模型，其中评估了添加的药物作用参数（分类或持续性药物暴露量度），以及（iii）包含IIV和药物效应的模型，其中评估了对药物效应的随机效应参数。对模拟条件进行了更改，例如，更改了个体数量以及IIV的大小和分布，以探讨对I型错误率的潜在影响。如预期的那样，在模型（i）和（iii）中包含错误的随机效应参数的估计的I型错误率低于标称值。当附加参数是描述药物效应的固定效应参数（模型（II））时，估计的I型错误率与标称值一致。尝试使用的所有不同仿真条件均未更改此模式。因此，当使用NONMEM对分类数据建模时，LR测试似乎适合判断固定效果参数的统计显着性。尝试使用的所有不同仿真条件均未更改此模式。因此，当使用NONMEM对分类数据建模时，LR测试似乎适合判断固定效果参数的统计显着性。尝试使用的所有不同仿真条件均未更改此模式。因此，当使用NONMEM对分类数据建模时，LR测试似乎适合判断固定效果参数的统计显着性。