Statistical Inference of Pharmacokinetic Models of Theophylline and Warfarin Data

Abstract: Pharmacokinetics is the study of how drugs are absorbed and distributed in the body and is used by pharmacists to ensure that they prescribe the appropriate dosage of medicine. The process used to determine the drug concentration in the body when medicine is prescribed is ADME; absorption, distribution, metabolism and excretion. The body is viewed as consisting of compartments between which a drug moves. This project focuses on a two compartment model where the body proceeds at a rate that is dependent on the concentration of the drug. Compartmental models can be described in terms of a set of linear, first-order, constant-coefficient, ordinary differential equations. A change of concentration in one of the compartments is a linear function of the concentrations in all other compartments. There are two sets of data that were evaluated. The first is Theophylline which is a drug used for respiratory disease. The data given consisted of twelve patients who took one single oral dose of Theophylline and their drug concentration in blood was sampled multiple times over a period of 24 hours. The next data was from 31 patients who were given one single oral dose of Warfarin. Warfarin is an anticoagulant used as a blood thinner. The concentration of Warfarin was examined over a longer period of time, roughly five days. The aim of the project was to fit and statistically evaluate the dynamics of the concentration of the drugs administered to the subjects. When the parameters were estimated and the estimates were plotted an interesting occurrence was discovered. The lack of rising concentration values for most of the Warfarin Patients and for Patient 9 from the Theophylline data cause a poor estimate for the rate of absorption. It proved that an over parameterization had occurred and that a one compartment model might have given a better outcome. Patients who had rising concentration values also had more accurate estimates, this can also be seen in the plots. 95% confidence intervals and standard errors were also calculated. Lastly, correlations between the patients and the parameters were plotted andvisuallyevaluated. TheTheophyllinepatientshadnonoticeablecorrelations whichcouldbearesultofthesmallnumberofpatients. TheWarfarincorrelation plots appeared to have slight correlations for the weight of the subjects and the rate of elimination as well as the volume of distribution. There may also have been a correlation of gender and parameters for the Warfarin data, but because there was only5 female subjects of 31 itis unclear ifthere is acorrelation or not.