Clinical Pharmacology, Advanced PK-PD Modeling and Simulation, Johnson and Johnson Pharmaceutical R&D, Raritan, NJ, USA.
J Pharmacokinet Pharmacodyn. 2011 Jun;38(3):353-67. doi: 10.1007/s10928-011-9197-1. Epub 2011 Mar 31.
Indirect response (IDR) models have been widely applied to pharmacodynamic (PD) modeling, particularly when delayed response (hysteresis) is present. This paper proposes a class of nonlinear discrete-time autoregressive (AR) models with drug concentrations acting as a time-varying covariate on the asymptote parameter or the autocorrelation parameter of the AR models as an alternative modeling approach for delayed response data. The mathematical derivations revealed the inherent connection between IDR models and nonlinear AR models, and showed that the nonlinear AR models approximate the IDR models when the time interval between response data is small. Simulations demonstrate that the IDR models and the corresponding AR models produce similar temporal response profiles, and as the time interval decreased (i.e., more intensive sampling designs), the AR model based parameter estimates were more comparable to those estimated from the IDR models. In conjunction with mixed-effects modeling, the nonlinear AR models have been shown to well describe a set of simulated longitudinal PK/PD data for a clinical study. Further extensions of the proposed nonlinear AR models are warranted to model irregular and sparse PK/PD data.
间接反应 (IDR) 模型已广泛应用于药效学 (PD) 建模，特别是在存在延迟反应 (滞后) 时。本文提出了一类具有药物浓度作为时变协变量的非线性离散时间自回归 (AR) 模型，用于替代延迟反应数据的建模方法。数学推导揭示了 IDR 模型和非线性 AR 模型之间的内在联系，并表明当响应数据之间的时间间隔较小时，非线性 AR 模型近似于 IDR 模型。模拟结果表明，IDR 模型和相应的 AR 模型产生相似的时间响应曲线，并且随着时间间隔的减小（即更密集的采样设计），基于 AR 模型的参数估计值与从 IDR 模型中估计的参数估计值更接近。与混合效应模型相结合，该非线性 AR 模型已被证明可以很好地描述一组用于临床研究的模拟纵向 PK/PD 数据。为了对不规则和稀疏的 PK/PD 数据进行建模，需要进一步扩展所提出的非线性 AR 模型。
