Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).

中文翻译：

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群体药代动力学协变量模型的功效，选择偏见和预测性能。

协变量关系的识别和量化通常是群体药代动力学/药效学（PK / PD）建模的重要组成部分。协变量模型通常以逐步方式构建。使用这种方法，如果仅在模型中接受统计上显着的协变量，则选择偏差可能会成为问题。多个协变量之间的竞争可能会进一步增加选择偏向，尤其是当协变量之间存在中度到高度相关性时。这也可能导致失去寻找真正协变量的能力。本模拟研究的目的是研究当更改研究设计和与系统相关的数量时，对协变量模型的功效，选择偏倚和预测性能的影响。调查了20-1000名受试者的数据集。通过从多元标准正态分布中采样来创建五个协变量。真正的协变量设置为分别与其他四个协变量没有，低，中和高相关。使用单室静脉推注模型模拟每个人有两个或三个PK观察值的数据集。真正的协变量会根据几个量级之一影响清除率。在结构模型参数中还引入了不同程度的残余误差和个体间变异性。对于上述条件的每种组合，总共独立模拟了7400个重复数据集。将具有影响清除的五个模拟协变量之一的模型和没有任何协变量的模型拟合到数据。记录选择（根据预先指定的P值）不同协变量的概率以及估算的协变量系数。结果表明，对于偏弱协变量效应模拟的小数据集（<或= 50个受试者），选择偏差非常高。如果在这些情况下选择，则平均估计协变量系数为其真实值的两倍以上，从而使协变量模型对预测目的无用。出人意料的是，即使与错误协变量的竞争导致选择真正协变量的能力大大降低，但本已很高的选择偏见却仅略有增加。这意味着如果协变量选择也需要统计显着性，则竞争引起的偏差可以忽略不计。偏差和预测绩效是权力的直接功能，仅间接受到研究设计和与系统相关的数量的影响。主要是由于选择偏差，选择低功率协变量可能会损害其预测性能。出于同样的原因，这些低倍协变量在被选择时可能会错误地显得与临床相关。如果分析的目的是预测性建模，则我们不建议在较小或中等规模的数据集（<50-100个对象）上进行逐步选择或对协变量进行显着性检验。