Department of Pharmacy, Uppsala University, Uppsala, Sweden.
J Pharmacokinet Pharmacodyn. 2021 Apr;48(2):241-251. doi: 10.1007/s10928-020-09727-8. Epub 2020 Nov 26.
This article highlights some numerical challenges when implementing the bounded integer model for composite score modeling and suggests an improved implementation. The improvement is based on an approximation of the logarithm of the error function. After presenting the derivation of the improved implementation, the article compares the performance of the algorithm to a naive implementation of the log-likelihood using both simulations and a real data example. In the simulation setting, the improved algorithm yielded more precise and less biased parameter estimates when the within-subject variability was small and estimation was performed using the Laplace algorithm. The estimation results did not differ between implementations when the SAEM algorithm was used. For the real data example, bootstrap results differed between implementations with the improved implementation producing identical or better objective function values. Based on the findings in this article, the improved implementation is suggested as the new default log-likelihood implementation for the bounded integer model.
本文重点介绍了在实施复合评分建模的有界整数模型时的一些数值挑战，并提出了一种改进的实现方法。该改进基于对误差函数的对数的逼近。在提出改进的实现方法的推导后，本文比较了算法在模拟和真实数据示例中使用对数似然的简单实现的性能。在模拟设置中，当个体内变异性较小时，改进的算法使用拉普拉斯算法进行估计时，产生了更精确和偏差更小的参数估计。当使用 SAEM 算法时，两种实现方式的估计结果没有差异。对于真实数据示例，两种实现方式的自举结果存在差异，改进的实现方式产生了相同或更好的目标函数值。基于本文的研究结果，建议将改进的实现作为有界整数模型的新默认对数似然实现方法。
