Bayesian analysis for mixed-effects model defined by stochastic differential equations  

混合效应随机微分方程的贝叶斯分析(英文)

作　　者：言方荣[1,2,3] 张萍[2,3] 陆涛[4,3] 林金官[1] 

机构地区：[1]东南大学数学系,南京210096 [2]中国药科大学数学系,南京210009 [3]中国药科大学天然药物活性组分与药效国家重点实验室,南京210009 [4]中国药科大学分子设计与药物发现实验室,南京210009

出　　处：《Journal of Southeast University(English Edition)》2014年第1期122-127,共6页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11171065,81130068);the Natural Science Foundation of Jiangsu Province(No.BK2011058);the Fundamental Research Funds for the Central Universities(No.JKPZ2013015)

摘　　要：The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.采用带有随机微分方程的非线性混合效应模型对群体药物代谢动力学数据建模,通过在状态方程中引入随机项,将常微分方程扩展到随机微分方程.和常微分方程相比,随机微分方程可解决群体药物代谢动力学模型中相关残差问题.利用贝叶斯估计对非线性混合效应随机微分方程模型参数进行估计,给出群体参数及个体参数的精确后验分布,将Gibbs和Metropolis-Hastings算法相结合,给出参数估计值.通过计算机模拟和实例分析验证了方法的可靠性,结果表明利用非线性混合效应随机微分方程模型及贝叶斯估计方法分析群体药物代谢动力学数据是可行的.

关 键 词：population pharmacokinetics mixed-effectsmodels stochastic differential equations Bayesian analysis 

分 类 号：O212[理学—概率论与数理统计]