Transcript open

# 1570
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
98 CBZ predictions
A
Measured CBZ-retard levels
8
Measured levels
8
6
4
7
6
5
4
3
2
2
1
0
2
4
6
8
10
12
10
8
6
4
2
0
0
0
2
R = 0,573
12
9
10
42 CBZ - CBZ-retard predictions
C
R2 = 0,619
10
12
Measured levels
42 CBZ-retard predictions
B
R2 = 0,7939
14
0
2
4
6
8
10
0
12
2
4
6
8
10
12
14
Predicted levels from CBZ measurements
Predicted levels
Predicted levels
Figure 2. Regression lines for predictions of future CBZ behaviour on the basis of population modelling in: A - adult epileptic patients on CBZmonotherapy; 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.
Drug
80
A
CBZ
B
20,00
60
CBZ_retard
15,00
C_Predicted
Frequency
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 patientspecific Bayesian posterior PK models for carbamazepine (CBZ) monotherapy in the post-induction period. During longterm 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 1996. CBZ levels were measured by high performance liquid chromatography. The
assay error pattern was used as: SD=0.2+0.1C (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 s2. Intraindividual
variability expressed as coefficients of variation (CV) was calculated as the square root of s2. 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:
40
10,00
5,00
20
Mean = -1,6283
Std. Dev. = 22,41325
N = 556
0,00
0
-90,00
-60,00
-30,00
0,00
30,00
0,00
60,00
5,00
10,00
15,00
20,00
C_Measured
C_Error_percent
Figure 3. 418 predictions of CBZ future serum levels: A – distribution of percentage prediction errors; B – scatterplot of the predicted – measured
CBZ serum level relationships.
1. Bondareva I.B., Sokolov A.V., Tischenkova I.F., Jelliffe R.W. Population Pharmacokinetic Modeling of Carbamazepine by Using the Iterative Bayesian
0 to 0.5
A
0,5 to 1
1 to 2
2 to 6
6 to 12
80,0%
8,0%
B
4,0%
0,0%
12,0%
8,0%
4,0%
12 to 24
Percent
0,0%
12,0%
8,0%
4,0%
0,0%
12,0%
Percent
8,0%
4,0%
Percent
0,0%
12,0%
8,0%
4,0%
Percent
0,0%
12,0%
0,5 to 1 0 to 0.5
8,0%
4,0%
0,0%
12,0%
Percent
20,0%
1 to 2
40,0%
2 to 6
Percent
60,0%
8,0%
4,0%
0,0%
0,0%
Abs error <= 25%
Abs error > 25%
0 - 10%
10 - 25%
Error_25
1 year
B
Drug
CBZ
CBZ_retard
B
0,00
-30,00
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.
CBZ
CBZ_retard
0,00
-30,00
-60,00
-90,00
-90,00
20,00
40,00
60,00
80,00
100,00
Prediction Horizon, months
35 years
Drug
60,00
-60,00
0,00
1.5 years
> 50%
30,00
C_Error_percent
C_Error_percent
30,00
C
40 - 50%
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.
A
3.7 years
25 - 40
C_abs_Error_scale, %
60,00
1.5 years
Horizon_scale, months
24 and longer
A
Percent
100,0%
12,0%
Percent
Horizon_scale
24 and
longer 12 to 24 6 to 12
(IT2B) and the Nonparametric EM (NPEM) Algorithms: Implications for Dosage. J Clin Pharmac and Therapeutics 2001; 26: 213-223.
2. 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 – 11.
3. 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), ARGESIMVerlag, Vienna, 2003, p.190. The full paper is in Vol. 2 of the Proceedings, on CD.
0,00
5,00
10,00
15,00
20,00
C_Measured
Figure 5. Scatterplots for: A - percentage prediction errors and time horizon (months); B - abs percentage prediction errors and measured CBZ concentrations.
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 = - 14.2%, 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%; R2 = 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.
Contact information: Polini Osipenko str, 20-1-91, 123007 Moscow, Russia
[email protected]; phone: (7-915)423-3291