Traditional Chinese medicine (TCM) is a very complex mixture containing many different ingredients. Thus, statistical analysis of traditional Chinese medicine data becomes challenging, as one needs to handle the association among the observed data across different time points and across different ingredients of the multivariate response. This paper builds a 3-stage Bayesian hierarchical model for analyzing multivariate response pharmacokinetic data. Usually, the dimensionality of the parameter space is very huge, which leads to the parameter-estimation difficulty. So we take the hybrid Markov chain Monte Carlo algorithms to obtain the posterior Bayesian estimation of corresponding parameters in our model. Both simulation study and real-data analysis show that our theoretical model and Markov chain Monte Carlo algorithms perform well, and especially the correlation among different ingredients can be calculated very accurately.
Keywords: MCMC algorithm; hierarchical model; pharmacokinetic; traditional Chinese medicine.
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