A Mechanism-Based PK/PD Model Predicts the Time-Course of Hematological responses for Epoetin beta

Transcription

1 A Mechanism-Based PK/PD Model Predicts the Time-Course of Hematological responses for Epoetin beta N. Hayashi, K. P. Zuideveld, P. Jordan & R. Gieschke Modeling & Simulation Group & Biometrics, F. Hoffmann-La Roche AG, Basel, Switzerland June 13th, 2003, PAGE meeting, Verona, Italy 1

2 Objectives to develop a Mechanism-Based PK/PD model: to describe the hematological responses in healthy volunteers study to predict the hematological responses in renal anemia patients studies to predict not only mean values but also individual values distribution to predict the responses for different dose routes & different dose frequencies Mechanism of Epoetin pharmacodynamics Outline PK/PD modeling with healthy volunteers study Simulation for renal anemia patients studies 2

3 Mechanism of Epoetin pharmacodynamics Physiological background (1) Erythropoietin stimulates the release of RBC (reticulocyte) from Bone Marrow Erythropoietin is a glycoprotein produced in the kidneys Renal dysfunction patients show anemia because the endogenous EPO production is reduced 3

4 Mechanism of Epoetin pharmacodynamics Physiological background (2) Bone marrow RBC precursors > 1 day 1 day Blood RBC Death Stemcells RET RET Mature RBC EPO Endogenous stimulation EPO 120 days ± 1 wk Release Kidneys Hemoglobin 4

5 Mechanism of Epoetin pharmacodynamics Characteristics of PK/PD model an identical life span for all RBC (zero order elimination) a homeostatic negative feed back a lag time an indirect response model for reticulocyte with a variable k out (immature reticulocyte increase) an E max model with a variable base line a blood sampling effect 5

6 Mechanism of Epoetin pharmacodynamics Model equations P'(t) = P(t) 0 + E EC max 50 + C C p (t) p (t) CERA Concentration RBC + k in RET = Reticulocytes RBC = Red Blood Cell 6

7 Mechanism of Epoetin pharmacodynamics Model equations P(t) P 0 0 = RBC( 0)/ SPAN ( Slope Hb(t) ) = P exp 0 CERA Concentration Negative Feedback + - k in RBC RET = Reticulocytes RBC = Red Blood Cell 7

8 Mechanism of Epoetin pharmacodynamics Model equations dp(t) dt = τ 1 ( P'(t) P(t) ) CERA Concentration Negative Feedback + - k in lag-time RBC RET = Reticulocytes RBC = Red Blood Cell 8

9 Mechanism of Epoetin pharmacodynamics Model equations CERA Concentration RBC(t) VOL Hb(t) = = t n = RBC( 0) + ( P(t) P0 ) dt WT (t / n 13 < RBC(t)* Ht(t) = RBC(t)* Negative Feedback t, 0 i = 1 t MCH MCV < / / SPAN) t RBC(t i )* VOL SAM i RBC + - k in k lag-time zero order RET = Reticulocytes RBC = Red Blood Cell 9

10 Mechanism of Epoetin pharmacodynamics Model equations CERA Concentration Negative Feedback dret(t) dt k k out out = = k = out P 0 P(t) RET( 0) P 0 P(t) RET(t) POW k out RBC + - k in lag-time RET k out k zero order RET = Reticulocytes RBC = Red Blood Cell 10

11 PK/PD modeling with healthy volunteers study Study design Subjects: 46 healthy volunteers Dosage of Epoetin beta: 1) 50 IU/kg x3 / week sc 2) 150 IU/kg x1 / week sc 3) 300 IU/kg x1 / 2 weeks sc Administration period: 4 weeks Variables: RBC, Hb, Ht, reticulocyte & plasma erythropoietin concentrations 11

12 PK/PD modeling with healthy volunteers study PK analysis The PK analysis was performed using a one compartment, first order absorption, first order elimination model including an endogenous level ka Central comp. C 0 : constant ke The following PK/PD analysis considered the Bayes estimated PK parameters of each subject 12

13 PK/PD modeling with healthy volunteers study PK analysis with a simple model was enough for the following PK/PD analysis Cp [miu/ml] Cp [miu/ml] Cp [miu/ml] Observed values [miu/ml] Observed values [miu/ml] days Bayes estimated values [miu/ml] 13

14 PK/PD modeling with healthy volunteers study Hematological responses for each cohort 50 IU/kg RBC IU/ kg RET RBC RET Hb Hb IU/ kg 150 IU/kg IU/ kg 300 IU/kg mean±se 14

15 PK/PD modeling with healthy volunteers study The values of PK/PD parameters were reasonable Theta Eta EMAX (x10 4 /ul/day) E-06 CV(%) EC50 (miu/ml) CV(%) SLOPE (dl/g) CV(%) POW transit time (day) CV(%) MCH (pg) SD MCV (ul) SD RBC0 (x10 4 /ul/day) SD RET0 (x10 4 /ul/day) CV(%) SIGMA RET (x10 4 /ul/day) 14.9 CV(%) RBC (x10 4 /ul/day) 15.8 SD Hb (g/dl) SD Ht (%) 1.46 SD 15

16 PK/PD modeling with healthy volunteers study The values of PK/PD parameters were reasonable Theta Eta EMAX (x10 4 /ul/day) E-06 The E max -to CV(%) -P 0 ratio was EC50 (miu/ml) approximately The theta CV(%) of EC1.2, 50 was similar similar to that with for SLOPE (dl/g) the mice one and of CV(%) dogs in vitro (reserved study capacity) POW transit time (day) CV(%) MCH (pg) The theta SDand eta for MCH, MCV MCV (ul) RBC0 and SD RET0 was identical with RBC0 (x10 4 /ul/day) SD the predose values RET0 (x10 4 /ul/day) CV(%) SIGMA RET (x10 4 /ul/day) 14.9 The CV(%) predose intra-individual RBC (x10 4 /ul/day) 15.8 variability SD (SAS proc MIXED) Hb (g/dl) matches SD these sigma value Ht (%) 1.46 SD 16

17 PK/PD modeling with healthy volunteers study Bayes estimated values showed a high correlation with the observed values reticulocyte RBC Bayes estimated values Bayes estimated values Observed values Observed values HB HT Bayes estimated values Bayes estimated values Observed values Observed values 17

18 PK/PD modeling with healthy volunteers study Simulated values distribution matches the ones of observed values (PPC) Dose: 50 ug/kg Dose: 50 ug/kg RET RBC DAYS Dose: 150 ug/kg DAYS RET DAYS Dose: 300 ug/kg RET Dose: 150 ug/kg RBC DAYS Dose: 300 ug/kg RBC DAYS Reticulocyte DAYS RBC 80%CI for simulation (lines) & observed values (circles) 18

19 Simulation for renal anemia patients studies Simulation method Only RBC baseline and clearance were modified from HV The studies for the reference were selected for SC weekly SC daily IV x 3 / week Simulation was performed using Trial Simulator (n = 10000) for each cohort 19

20 Simulation for renal anemia patients studies Clearance in renal anemia patients 100 HV sc Patients sc CL/F (ml/h/kg) 10 Patients iv Dose (IU/kg) mean±cv 20

21 Simulation for renal anemia patients studies Study 1: sc weekly, Hb time course was predicted for 8 weeks 1500IU SC x 1/week 3000IU SC x 1/week 6000IU SC x 1/week increase in Hb[g/dL] increase in Hb[g/dL] increase in Hb[g/dL] days days days n=27-35 n=31-35 n=24-33 Line: median & 90%CI for simulation Circle: mean of observed values Hb 0 : 7.7 g/dl 21

22 Simulation for renal anemia patients studies Study 1: sc weekly, the distribution of Hb was predicted probability density IU SC x 1/week n=35 probability density IU SC x 1/week n=36 probability density Delta Hb for 8 weeks [g/dl] 6000IU SC x 1/week n=34 broken line: mean of simulated values real line: mean of observed values red curve: distribution of simulated values 22

23 Simulation for renal anemia patients studies Study 2: sc daily, the distribution of Ht slope was predicted probability density IU /kg sc x 7/week n=33 probability density IU /kg sc x 7/week n=32 probability density DHt(%)/week 20 IU /kg sc x 7/week n=33 broken line: median of simulated values real line: median of observed values red curve: distribution of simulated values 23

24 Simulation for renal anemia patients studies Study 3: iv x3 / week, the distribution of Ht slope was predicted probability density IU/kg iv x 3 / week n=31 probability density IU/kg iv x 3 / week n=29 probability density IU/kg iv x 3 / week DHt(%)/week n=30 broken line: median of simulated values real line: median of observed values red curve: distribution of simulated values 24

25 Simulation for renal anemia patients studies Maintenance study: the model could also predict the distribution of maintenance dose % for total patients The observed dose distribution (from literature) for 988 hemodialysis patients (Ht was maintained 35.9 ± 3.7 %) dose [IU/kg/week] Red line: simulation for IV x3 / week 25

26 Conclusions A mechanism-based PK/PD model was developed which is able to describe the time courses of hematological responses for Epoetin beta in healthy volunteers This model also predicted the time courses in renal anemia patients The model predicts not only the mean values but also the individual values distribution The model was useful for predicting responses with different dose routes, different dose frequency The model was useful for predicting maintenance dose 26