Wang Yuchen, Pei Xinyi, Niu Tao, Korth-Bradley Joan, Fostvedt Luke
Pfizer Inc., South San Francisco, California, USA.
Department of Statistics, Purdue University, West Lafayette, Indiana, USA.
CPT Pharmacometrics Syst Pharmacol. 2025 Feb;14(2):351-364. doi: 10.1002/psp4.13279. Epub 2024 Dec 9.
Fully Bayesian approaches are not commonly implemented for population pharmacokinetic (PK) modeling. In this paper, we evaluate the use of Stan with R and Torsten for population PK modeling of somatrogon, a recombinant long-acting growth hormone approved for the treatment of growth hormone deficiency. As a software for Bayesian inference, Stan provides an easy way to conduct MCMC sampling for a wide range of models with efficient sampling algorithms, and there are several diagnostic tools to evaluate the MCMC convergence and other potential issues. Three different sets of priors were evaluated for estimation and prediction: a weakly informative uniform set, a moderately informative set, and a very informative set of priors. All three prior sets showed good performance and all chains mixed well. There were some minor differences in the final parameter posterior distributions while implementing different prior sets, but the posterior predictions covered the observations nicely, not only for the individuals included in posterior sampling but also for new individuals. The impact of a centered versus non-centered parameterization were evaluated, with the non-centered approach improving the estimation time, but it was still computationally intensive. Computational resources had the biggest impact on sampling time. Stan took approximately 2.5 h total for the MCMC sampling on a high-performance computing platform (6 cores) and may be reduced further with additional computational resources. The model and comparisons presented show that with adequate computational resources, the Bayesian approaches using Stan and Torsten are useful for population PK analysis, especially for the analysis of special populations, small sample datasets, and when complex model structures are needed.
全贝叶斯方法在群体药代动力学（PK）建模中并不常用。在本文中，我们评估了使用Stan结合R和Torsten对索马促生长素进行群体PK建模的情况，索马促生长素是一种已获批准用于治疗生长激素缺乏症的重组长效生长激素。作为一种贝叶斯推理软件，Stan提供了一种简便的方法，可通过高效的采样算法对各种模型进行马尔可夫链蒙特卡罗（MCMC）采样，并且有多种诊断工具可用于评估MCMC收敛性和其他潜在问题。我们评估了三组不同的先验分布用于估计和预测：一组弱信息均匀先验、一组中等信息先验和一组强信息先验。所有这三组先验分布都表现出良好的性能，且所有链的混合效果都很好。在实施不同的先验分布时，最终参数后验分布存在一些细微差异，但后验预测很好地涵盖了观测值，不仅对于后验采样中包含的个体，对于新个体也是如此。我们评估了中心化参数化与非中心化参数化的影响，非中心化方法缩短了估计时间，但计算量仍然很大。计算资源对采样时间的影响最大。在高性能计算平台（6核）上，Stan进行MCMC采样总共耗时约2.5小时，增加计算资源可能会进一步缩短时间。本文展示的模型及比较结果表明，在有足够计算资源的情况下，使用Stan和Torsten的贝叶斯方法对于群体PK分析很有用，特别是在分析特殊人群、小样本数据集以及需要复杂模型结构时。
