EXTERNAL VALIDTION of the POPULATION MODELS for CARBAMAZEPINE PHARMACOKINETICS and the INDIVIDUALIZING CBZ DOSAGE REGIMEN PROCEDURE BONDAREVA K. student, Moscow State University, Department of Computational Mathematics and Cybernetics, Russia Contact information: Polini Osipenko str, , Moscow, Russia phone: (7-915) # year 3.7 years1.5 years Results: TDM data of adult epileptic patients on chronic CBZ or CBZ-retard monotherapy were used to estimate predictability of the CBZ PK models separately (98 and 42 predictions, respectively) (see Figure 2 A, B). All prediction related to 1 year horizon. The Kolmogorov-Smirnov test demonstrated that the residuals had approximately normal distribution (p=0.7 and 0.5), the mean errors were not statistically significantly different from zero (p=0.25 and 0.18) (random errors). Bias of the predictions was not observed. The mean absolute percentage errors (MAE) were 14.7±11.4% and 17.0±10.1%, respectively. A statistically significant bias and higher MAE were observed in predictions when patients were switched from CBZ to CBZ-retard (n= 42, overestimation, mean = %, p<0.05) (see Figure 2 C). TDM data of patients with repeated CBZ measurements were used to estimate intraindividual variability and influence of time horizon (558 predictions). The mean prediction error was calculated and used as a measure of accuracy (bias): ME = -1.7±22.5% (p=0.1). The mean absolute error was used as a measure of precision: MAE = 17.4±14.2%; R 2 = 64.3 (see Figure 3). Absolute value of prediction error was less or equal to 25% and considered as “acceptable” in 429 (77.0%) cases. In this analysis, prediction horizon values varied from 0.1 up to 84 months (15.04±16.3 months). Linear regression analysis demonstrated dependence of abs percentage prediction error on horizon (p=0.004). In some patients with multiple repeated measurements, precision of predictions decreased with increasing of prognosis horizon. Absolute value of prediction error was less or equal to 25% in 88% cases within 1 month horizon compared to 69.1% for time horizon longer than 2 years ( p<0.001 ). Interoccasion variability of predictions was estimated as 14.9%. Intraindividual variability was estimated as 24.4% (from 16.0% within 1 month horizon up to 32.4% for horizon longer than 2 years). Visually, abs percentage prediction error was slightly higher at relatively low CBZ serum levels (see Figure 5B). It might be probably explained by non-compliance. Conclusion: The study demonstrated that, in most cases, predictions of future CBZ concentrations (for each dosage form) based on the population PK models, TDM data and a patient-specific Bayesian posterior parameter values provided clinically acceptable estimates. Objectives: The objective of external validation is to examine whether the model can equally describe a new data set, which has not been used for model parameter estimation. The study aimed at evaluating the predictability of the patient- specific Bayesian posterior PK models for carbamazepine (CBZ) monotherapy in the post-induction period. During long- term AED therapy, concentrations appear to vary due to inexplicable day-to-day or moment-to-moment kinetic (i.e., interoccasion) variability, due to errors in concentration measurement, due to changes in PK parameter values in time, as well as due to model misspecification. Estimates of residual intrasubject and interoccasion variability are important for individualizing dosage regimen procedure based on therapeutic drug monitoring using the Bayesian approach. When intraindividual variability is relatively small, information on serum levels measured at only one occasion is useful from a prediction standpoint. Methods: Patient data of anticonvulsant monitoring were routinely collected in the Laboratory of Pharmacokinetics of Moscow Medical University since CBZ levels were measured by high performance liquid chromatography. The assay error pattern was used as: SD= C (where SD is standard deviation of the assay at measured CBZ concentration C). Usually adult and pediatric epileptic outpatients from different epilepsy clinics attended these consultations to evaluate potential reasons for lack or loss of efficacy and/or for toxicity of their antiepileptic therapy, as well as to establish or to check their “baseline” effective concentrations during a period of remission. Compliance was assessed by interview with the patients’ families and the attending physicians. However, compliance cannot be absolutely guaranteed. The rhythm of consultation was irregular, and repeated consultations on some patients after their dosage regimen corrections and adjustments helped to test and validate the procedure in clinical practice. The PK analysis was performed using the USC*PACK software based on the earlier developed linear one-compartment population PK models for CBZ and routine TDM data (peak – trough strategy) [1, 2, 3]. This study included epileptic patients for whom at least two pairs of measured serum levels related to different CBZ dosages were available. These data were not included in the population CBZ PK models. Some patients had long and rich TDM stories: repeated measurements during 1 – 7 year periods on CBZ monotherapy. The first pair of each patient’s serum levels on a specific dosage regimen was used to estimate the individual PK parameter values and to predict future serum levels according to the planned changes in CBZ regimen. Then the observed serum levels on the new CBZ regimen were compared with those predicted initially by the patient-specific Bayesian posterior PK model (see Figure 1, examples). The prediction error was estimated as the difference between observed and predicted levels, the percentage prediction error was estimated as the difference between observed and predicted levels compared to observed level. Distributions and statistical summary of the prediction errors were analysed to test normality and bias. Linear regression was used to determine the relationship between the abs percentage prediction error and prediction time horizon. Absolute value of this error less or equal to 25% was considered as “acceptable”. Besides, intraindividual proportional errors were expressed as Cij = Ĉij(1 + eij), where Cij is the observed concentration in serum for the ith individual at time j, Ĉij is the concentration in serum for the ith individual at time j predicted by the model, and eij is the residual or intraindividual error with mean zero and variance s 2. Intraindividual variability expressed as coefficients of variation (CV) was calculated as the square root of s 2. Interoccasion variability was estimated from TDM data of patients who have repeatedly measured their CBZ serum levels on unchanged dosage regimens within 2-week period. References: 1. Bondareva I.B., Sokolov A.V., Tischenkova I.F., Jelliffe R.W. Population Pharmacokinetic Modeling of Carbamazepine by Using the Iterative Bayesian (IT2B) and the Nonparametric EM (NPEM) Algorithms: Implications for Dosage. J Clin Pharmac and Therapeutics 2001; 26: Bondareva I.B., Jelliffe R.W., Gusev E.I., Guekht A.B., Melikyan E.G., Belousov Y.B. Population Pharmacokinetic Modeling of Carbamazepine in Epileptic Elderly Patients. J Clin Pharmac and Therapeutics 2006; 31: 1 – Bondareva I., Jelliffe R. "Modeling of Nonlinear Pharmacokinetics of Phenytoin, and of Carbamazepine during its Autoinduction Period". In Troch I., F.Breitenecker (Eds) Proceedings of 4th MATHMOD (IMACS International Symposium on Mathematical Modelling, Feb 5-7, 2003, Vienna, Austria), ARGESIM- Verlag, Vienna, 2003, p.190. The full paper is in Vol. 2 of the Proceedings, on CD. 1.5 years 35 years Figure 2. Regression lines for predictions of future CBZ behaviour on the basis of population modelling in: A - adult epileptic patients on CBZ- monotherapy; B - adult epileptic patients on CBZ-retard – monotherapy; C - adult epileptic patients on CBZ-monotherapy switched to CBZ-retard. Lines A and B are not significantly different from the line of identity. Figure predictions of CBZ future serum levels: A – distribution of percentage prediction errors; B – scatterplot of the predicted – measured CBZ serum level relationships. Figure 4. Relationships between categorized abs percentage prediction errors and categorized prediction horizon (months): A – dichotomous variable - absolute value of the error less or equal to 25% considered as “acceptable”; B – 5 – point scale for abs percentage prediction error. Figure 5. Scatterplots for: A - percentage prediction errors and time horizon (months); B - abs percentage prediction errors and measured CBZ concentrations. Figure 1. Visualization of individual time course of CBZ serum concentrations simulated via the MB program based on the individual PK parameter values estimated from the patient’s first pair of measured serum levels (yellow line). Red crosses – measured CBZ serum levels. ABC A B C AB AB BA