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首页> 美国卫生研究院文献>Springer Open Choice >Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood
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Using sensitivity equations for computing gradients of the FOCE and FOCEI approximations to the population likelihood

机译：使用灵敏度方程来计算FORCE和FORCE近似于总体似然的梯度

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摘要

The first order conditional estimation (FOCE) method is still one of the parameter estimation workhorses for nonlinear mixed effects (NLME) modeling used in population pharmacokinetics and pharmacodynamics. However, because this method involves two nested levels of optimizations, with respect to the empirical Bayes estimates and the population parameters, FOCE may be numerically unstable and have long run times, issues which are most apparent for models requiring numerical integration of differential equations. We propose an alternative implementation of the FOCE method, and the related FOCEI, for parameter estimation in NLME models. Instead of obtaining the gradients needed for the two levels of quasi-Newton optimizations from the standard finite difference approximation, gradients are computed using so called sensitivity equations. The advantages of this approach were demonstrated using different versions of a pharmacokinetic model defined by nonlinear differential equations. We show that both the accuracy and precision of gradients can be improved extensively, which will increase the chances of a successfully converging parameter estimation. We also show that the proposed approach can lead to markedly reduced computational times. The accumulated effect of the novel gradient computations ranged from a 10-fold decrease in run times for the least complex model when comparing to forward finite differences, to a substantial 100-fold decrease for the most complex model when comparing to central finite differences. Considering the use of finite differences in for instance NONMEM and Phoenix NLME, our results suggests that significant improvements in the execution of FOCE are possible and that the approach of sensitivity equations should be carefully considered for both levels of optimization.
机译：一阶条件估计（FOCE）方法仍然是用于人群药代动力学和药效学的非线性混合效应（NLME）建模的参数估计主力之一。但是，由于此方法涉及两个嵌套的优化级别，因此相对于经验贝叶斯估计值和总体参数，FOCE可能在数值上不稳定并且运行时间长，这对于需要微分方程数值积分的模型最为明显。我们为NLME模型中的参数估计提出了FOCE方法和相关FOCEI的替代实现。代替从标准有限差分近似中获得两级准牛顿优化所需的梯度，而是使用所谓的灵敏度方程来计算梯度。使用非线性微分方程定义的不同版本的药代动力学模型证明了该方法的优势。我们表明，可以大大提高梯度的准确性和精度，这将增加成功收敛参数估计的机会。我们还表明，所提出的方法可以显着减少计算时间。新颖的梯度计算的累积效果范围从最小复杂模型的运行时间减少10倍（与正向有限差相比）到最复杂模型的运行时间减少100倍（与中心有限差相比）。考虑到在NONMEM和Phoenix NLME中使用有限差分，我们的结果表明FOCE的执行有可能得到显着改善，并且在两个优化级别上都应仔细考虑灵敏度方程的方法。

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