Statistical Inference And Algorithm Design Of Hierarchical Model In Pharmacokinetics

Pharmacokinetics is the study of dynamic change process which is about the absorption,distribution,metabolism and excretion of a drug through the effective combination of kinetic theory and mathematical methods.In the pro-cedure of developing new drugs,Pharmacokinetics plays an important part in preclinical and clinical research.The concentration-time curve is a good descrip-tion of the change of drugs in vivo.So concentration-time curve becomes the key of drug research.In this paper,according to the drug concentration and time data,the statistical model was established.Then the appropriate param-eter estimation method was selected to estimate parameters which can reflect the dynamic changes of drugs in the body.The main results axe presented as follows:Chapter 1 systematically introduces the background and development of pharmacokinetics of Western medicine and traditional Chinese medicine.Chapter 2 builds multiresponse Bayesian hierarchical model at the first.The first stage reflect the changes of the individual internal.The second stage reflects the differences between individuals and the prior distribution of each parameter is given in the third stage.Then parameters are estimated using the Markov Chain Mento Carlo method and the specific implementation steps of MCMC algorithm are given.Finally through the numerical analysis to verify the validity of the model.Chapter 3,in order to clarify whether the differences is statistically signifi-cant in two groups,analyzes the comparative test of the two samples base on the pharmacokinetic data.Firstly we provide the likelihood functions with the null hypothesis and the alternative hypothesis.Then the likelihood ratio statistic is constructed and next we proved that the limit distribution of the statistic is?2(3)when null hypothesis is true.Lastly the numerical simulation is conducted to confirm the truth of the theory.