The Non-Linear Mixed Effect Models In Population Pharmacokinetics And Its Discussion Based On Stochastic Differential Equations

Pharmacokinetics research on the dynamic law of drug in the body through setting up the mathematics models. It contains the procedure of absorption, distribution, metabolism and elimination. Pharmacokinetics models has great advantage and widely application, especially in the drug research and development aspects. For many reasons, drug research and development costs much and has low efficiency.Therefore, it needs us to improve experimental design, build appropriate mathematics models and seek the optimal methods to estimate the value of parameters of PK/PD. It can guide the clinical practice, reaching the best effect, deciding the safe dosage levels and reducing the side effects.This paper introduces the development of pharmacokinetics in the forty years, from the initial simple models such as compartmental models, generally dosage--effect models to complex models based on physiological change in the body such as the feedback models. Especially, for different patients have different effects on the same drug, population pharmacokinetics has its importance. We emphasis on the introduction of nonlinear mixed effects models in the population pharmacokinetics, and explore the advantage of nonlinear mixed effects models based on stochastic differential equation on the aspect of model optimization and diagnoses.In this paper, we use the R Statistical software and set up the population pharmacokinetics mathematical models.By using the computer, we simulate the patient data and set up the linear mixed effects models and nonlinear mixed effects models of two-compartmental. Through the analysis of results, we get the dynamic law of drug in the body. More importantly, it shows the advantage of linear mixed effects models for dealing the grouped data. In the second example, the nonlinear mixed effects models can analysis the data better, determine the fixed effects and random effects, the results shows well. It provide the reference for the drug research and development, as well as personalized medicine.In the last, we show an example to make sure that the nonlinear mixed effects models based on based on stochastic differential equation can optimization and diagnosis the model. It can be expected that this model will be developed more perfect in the future.