Implementing a Bayesian approach using Stan with Torsten: Population pharmacokinetics analysis of somatrogon

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.