A model can be fit to joint PK/PD data (concentration and effect) either simultaneously or sequentially. The results of a companion paper suggested that when the data-analytic and true models agree, a particular sequential approach is computationally faster than the simultaneous one, yet produces hardly less precise PD parameter estimates, and for suitable designs, about as accurate PD standard error estimates. In this paper, we compare the performance of various methods for the case that the data-analytic model is misspecified. We illustrate these methods by applying them to a set of real data. Using NONMEM, population PK/PD observations were simulated under various study designs according to a one- or two-compartment PK model and direct Emax or sigmoid Emax model. A one-compartment PK model and Emax PD model were fit to the simulated observations by simultaneous and sequential methods. Predictive performance (interpolation and extrapolation) of PD and the type-I error rate of a likelihood ratio test are compared. The real data set consists of PK and (more frequent) PD observations after administration of the muscle relaxant vecuronium. When only the PK data-analytic model is misspecified, the simultaneous method has greater precision than the sequential methods. However a sequential method that uses a non-parametric PK model performs better than both other methods when PK model misspecification is severe. When the PD data-analytic model is misspecified, sequential and simultaneous methods perform similarly. The analysis of the real data shows that the PK fitted with the simultaneous method can be quite sensitive to PD model misspecification, yielding a possible diagnostic for this type of misspecification.

中文翻译：

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人口PK / PD数据的同时分析与顺序分析II：方法的鲁棒性。

模型可以同时或顺序地适合联合PK / PD数据（浓度和效应）。随附论文的结果表明，当数据分析模型与真实模型相符时，一种特定的顺序方法在计算上比同时模型要快，但产生的PD参数估计值几乎不那么精确，对于合适的设计，其精确度与PD标准误差相当。估计。在本文中，我们比较了数据分析模型指定不正确的情况下各种方法的性能。我们通过将它们应用于一组真实数据来说明这些方法。使用NONMEM，根据一室或两室PK模型和直接Emax或S型Emax模型，在各种研究设计下模拟了人口PK / PD观察。通过同时和顺序方法，将一室PK模型和Emax PD模型拟合到模拟观察值。比较PD的预测性能（内插和外推）和似然比检验的I型错误率。实际数据集由肌肉松弛剂维库溴铵给药后的PK和（更频繁地）PD观察组成。当仅错误地指定PK数据分析模型时，同时方法比顺序方法具有更高的精度。但是，当PK模型错误指定严重时，使用非参数PK模型的顺序方法的效果要优于其他两种方法。当PD数据分析模型指定不正确时，顺序方法和同时方法会执行类似的操作。