Guedj J, Thiébaut R, Commenges D
INSERM, U875 (Biostatistique), Bordeaux, F-33076, France.
Biometrics. 2007 Dec;63(4):1198-206. doi: 10.1111/j.1541-0420.2007.00812.x. Epub 2007 May 8.
The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these models leads to great difficulties for inference and only the Bayesian approach has been attempted by now. We propose a full likelihood inference, adapting a Newton-like algorithm for these particular models. We consider a relatively complex ODE model for HIV infection and a model for the observations including the issue of detection limits. We apply this approach to the analysis of a clinical trial of antiretroviral therapy (ALBI ANRS 070) and we show that the whole algorithm works well in a simulation study.
基于非线性常微分方程（ODE）系统的HIV感染动力学模型研究，极大地增进了我们对其发病机制的了解。虽然最初的模型使用简化的ODE系统并分别分析每个患者，但最近的研究借助整个样本的力量处理非简化模型中的推断问题。这些模型的复杂性给推断带来了巨大困难，到目前为止仅尝试了贝叶斯方法。我们提出一种全似然推断方法，针对这些特定模型采用类牛顿算法。我们考虑一个相对复杂的HIV感染ODE模型以及一个包含检测限问题的观测模型。我们将此方法应用于抗逆转录病毒疗法临床试验（ALBI ANRS 070）的分析，并表明整个算法在模拟研究中运行良好。
