Noncompartmental Analysis (NCA) in PK, PK-based Design

Transcription

1 Noncompartmental Analysis (NCA) in PK, PK-based Design Helmut Schütz BEBAC Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

2 Bioequivalence History Surrogate of clinical equivalence (1985+) Studies in steady state in order to reduce variability Studies based on active metabolite Wider acceptance range if clinical justifiable (not FDA!) Measure of pharmaceutical quality (2+) Single dose studies preferred Generally parent drug Widening of acceptance range exceptional Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

3 Mid 198 ies Early methods FDA s 75/75 Rule BE, if 75% of subjects show ratios of 75%-125%. Not a statistic, variable formulations may pass by chance BE Cabana Assessment of 75/75 Rule: FDA Viewpoint Pharm Sci 72, (1983) JD Haynes FDA 75/75 Rule: A Response J Pharm Sci 72, 99-1 (1983) T R T/R 75%-125% % yes % yes % yes % yes % no % no % yes % yes % yes % no % yes % yes 75.% Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

4 Mid 198 ies Early methods Testing for a significant difference (t-test) at α.5 Problem: High variability in differences formulation will pass (p.5) Low variability in differences formulation will fail (p <.5) This is the opposite of what we actually want! T R T R mean SD CV% 21.4% 2.6% 94% t -table 2.21 t -calc.3687 n.s. Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

5 Example 25 2 Epanutin (Acid, Parke Davis): Reference Phenhydan (Acid, Desitin): F=151% (p>.5) Epilan-D (Na-salt, Gerot): F=139% (p>.5) Difhydan (Ca-salt, Leo): F=22% (p<.1) concentration [µmol/l] time [h] Nitsche V, Mascher H and H Schütz Comparative bioavailability of several phenytoin preparations marketed in Austria Int J Clin Pharmacol Ther Toxicol 22(2), (1984) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

6 NCA vs. PK Modeling Noncompartmental methods do not rely on a pharmacokinetic model Also called SHAM (Shape, Height, Area, Moments) Metrics (plasma) Extent of absorption (EU ), total exposure (US): AUC (area under the curve) Rate of absorption (EU ), peak exposure (US): C max t max (EU ) Early exposure (EU BE Draft 28, US): AUC tmax ; partial AUC truncated at population t max of the reference Others: C min, Fluctuation, MRT, Occupancy time, t lag, Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

7 NCA vs. PK Modeling Noncompartmental methods (cont d) Metrics (urine) Extent of absorption (EU ), total exposure (US): Ae t (cumulative amount excreted) rarely extrapolated to t= Rate of absorption (EU ), peak exposure (US): Ae max t Ae max Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

8 NCA vs. PK Modeling Pharmacokinetic models Useful for understanding the drug/formulation Study design of BA/BE! Drawbacks: Almost impossible to validate (fine-tuning of side conditions, weighting schemes, software, ) Still a mixture of art and science. Impossible to recalculate any given dataset using different pieces of software (sometimes even different versions of the same software). Not acceptable for evaluation of BA/BE studies! Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

9 NCA Single dose Calculation of Moments of Curve (AUC t, MRT t ) Linear trapezoidal rule, loglinear trapezoidal rule, or combination (lin-up, log-down). Calculation of half life (t ½ ) from elimination rate (λ z ) (Unweighted) log-linear regression If necessary (US ) extrapolation from time point of last quantified concentration to infinity C AUC = AUC + Cˆ t or better: AUC ˆt = AUC + t λ ˆt λ C max / t max directly from profile z Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May z

10 Single dose NCA Method of estimation of λ z stated in protocol! One-compartment model: TTT-method *) (Two times t max to t z ) Maximum adjusted R² (Phoenix/WinNonlin, Kinetica) 2 2 (1 R ) ( n 1) WinNonlin 5.3: Radj = 1 n 2 Multi-compartment models: starting point = last inflection Minimum AIC AIC = n ln(2 π ) n ln( RSS n) + 2 p [ ] Visual inspection of fit mandatory! C max included Phoenix/WNL 6.: C max excluded *) Scheerans C, Derendorf H and C Kloft Proposal for a Standardised Identification of the Mono-Exponential Terminal Phase for Orally Administered Drugs Biopharm Drug Dispos 29, (28) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

11 NCA 1 plasma profile (linear scale) 8 concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

12 NCA 1 plasma profile (semilogarithmic scale) concentration 1 C t Cˆt time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

13 Single dose NCA Unconventional parameters describing the shape of the profile C max /AUC HVD (Half value duration: time interval where C(t) 5% of C max ) t 75% (Plateau time: interval where C(t) 75% of C max ) Occupancy time, t MIC (time interval where C(t) is above some limiting concentration) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

14 NCA 1 plasma profile (linear scale) 8 concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

15 Multiple dose NCA Calculation of AUC τ (τ: dosage interval); AUC ss,24h if more than o.a.d. and chronopharmacological variation) No extrapolation! C ss,max / C ss,min directly from profile Peak-Trough-Fluctuation: (C ss,max C ss,min ) / C ss,av, where C ss,av = AUC τ / τ Swing: (C ss,max C ss,min ) / C ss,min Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

16 Multiple dose NCA Assessment whether steady state is reached (in a linear PK system: AUC τ = AUC ) No recommendations in GLs (except EU/US Veterinary) MANOVA-model (sometimes mentioned in Canada, rarely used) t-test of last two pre-dose concentrations Hotelling s T² Linear regression of last three pre-dose concentrations, individually for each subject/treatment Only the last method allows the exclusion of subjects being not in stead state. Other methods give only a yes no result! Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

17 NCA 2 plasma profile (linear scale) concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May C av slope: % CI: [ ] steady state demonstrated

18 PK Modeling concentration [µg/ml] simultaneous fit parent [plasma] metabolite [plasma] parent [urine] metabolite [urine] urine: midpoint time [h] cumulative amount [mg] plasma: sampling time [h] Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

19 PK Modeling time [h] Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

20 PK Modeling WinNonlin s Exp1.pwo, Model 11, w=1/pred² Time (hr) Observed Predicted Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

21 Partial Derivatives 2 PK Modeling Time (hr) V1_F K1 K1 K12 K21 Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

22 PK Modeling Partial Derivatives Time (hr) Observed Predicted Time (hr) V1_F K1 K1 K12 K21 Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

23 Some Problems Missing values I Procedure for Imputation must be stated in the Protocol; recommended: in the Absorption Phase (t < t max ) by linear Interpolation of two adjacent values in the Elimination Phase (t t max ) by log/linear Interpolation of two adjacent values estimated value must not be used in calculation of the terminal half life! Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

24 Some Problems Missing values I concentration [µg/ml] original value: 3.85 linear interpolation: log/linear interpolation: time [h] Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

25 Some Problems Missing values I Recommended Procedure may not be the default in your software (has to be actively set, e.g., in WinNonlin 5+) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

26 Some Problems Missing values I Do you see a missing value at all? Subject=5 c t 3 2 Subject=5 1 c t Hour (h) 2 original value linear interpol. log/linear interpol. t/c [%] 88.3% 92.1% 9.4% bias [%] +4.3% +2.4% Hour (h) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May ?

27 Some Problems Missing values II At the end of the profile Example: t ½abs =.5, t ½el = 24 T/R theoret. = 95%, LLOQ = 1 AUC 72 : T = 2835, R = 2984 T/R = 95% Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t

28 Some Problems 1 8 Reference Test LLOQ = 1 concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

29 Some Problems 1 8 Reference Test LLOQ = 1 concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

30 Some Problems Missing values II Last value of T missing (e.g., vial broken) AUC tlast (48) T = 247 AUC tlast (72) R= 2984 T/R = 8.67% biased! Using AUC to t where C LLOQ for both formulations (48) AUC 48 T = 2534 AUC 48 R = 247 T/R = 95% Not available in software Regulatory acceptance? Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May time Reference conc BLQ AUC -t conc BLQ Missing Test AUC -t NA

31 Some Problems 1 8 Reference Test LLOQ = 1 concentration 6 4 C 72 set to time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

32 Some Problems Missing values II Last value of T missing (e.g., vial broken) Setting the first concentration in the profile where C<LLOQ to zero. AUC all, invented by Pharsight AUC all (72) T = 2692 AUC all (72) R = 2984 T/R = 9.22% biased! Available in WinNonlin, Kinetica Regulatory acceptance? = * 2692 Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t

33 Some Problems 1 8 Reference Test LLOQ = 1 concentration 6 4 C 72 estimated from C 24 C time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

34 Some Problems Missing values II Last value of T missing (e.g., vial broken) Estimating the missing value from elimination phase. AUC 72* T = 2835 AUC 72 R = 2984 T/R = 95% Not available in software Regulatory acceptance ± *11.88 *2835 Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t

35 Some Problems Missing values II Values below the lower limit of quantitation (LLOQ) Example as before, but LLOQ = 12.5 (instead 1) AUC 72 : T =?, R = 2984 T/R =? AUC 48 : T = 247, R = 2534 T/R = 95% AUC all : T = 2692, R = 2984 T/R = 9.22% biased! AUC 72* : T =?, R = 2984 T/R =? Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May time time time Reference conc AUC -t Reference conc AUC -t Reference conc AUC -t conc BLQ conc = * conc *11.88 Test Test Test AUC -t NA AUC -t AUC -t NA

36 Some Problems What would you do? 1 8 Reference Test LLOQ = 12.5 concentration time Reference Test LLOQ = 12.5 BQL concentration concentration Reference Test LLOQ = time time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

37 Trapezoidal rule(s!) Yes, but which one? linear logarithmic lin/log R. Purves Lagrange 6 4 R: theoretical T: theoretical R: linear T: linear R: logarithmic T: logarithmic Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

38 Trapezoidal rule(s!) Bias of methods and effects on T/R AUC th 1% lin AUC t 1.5% AUC 1.5% lin-log AUC t 1.6% AUC 1.2% Purves AUC t 99.5% AUC 99.11% R: theoretical T: theoretical 1 R: linear T: linear 45 R: logarithmic T: logarithmic R theoretical T theoretical R linear R: theoretical T linear T: theoretical 2 R logarithmic R: linear T logarithmic T: linear R: logarithmic T: logarithmic Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

39 Sampling at C max Theoretical (T/R) t max : 6.11/4.2 ( 2.9), C max : 41.9/53.5 (81.2%) Sampling [2 12] n=4 C max 78.3% t max 4 n=5 C max 78.3% t max 4 n=6 C max 79.8% t max 1 n=7 C max 81.2% t max R theoretical T theoretical R sampled T sampled Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

40 Sampling at C max With any (!) given sampling scheme the true C max is missed It is unlikely that you sample exactly at the true C max for a given subject High inter- and/or intra-subject variability (single point metric) Variability higher than for AUCs In many studies the win/loose metric! Try to decrease variability Increase sample size (more subjects) Increase sampling within each subject (maybe better) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

41 Sampling at C max C max was observed within two to five hours after administration Elimination is drug specific, but what about absorption? Formulation specific! Dependent on the sampling schedule (in a strict sense study-specific) Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

42 Sampling at C max hrs k a = [ ] arithmetic mean geometric mean median Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

43 Sampling at C max hrs arithmetic mean geometric mean median 3 k a =.182 t lag = [ 2.5] Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

44 Another Problem Gastro-resistant (enteric coated) preparations Gastric emptying of single unit dosage forms non-disintegrating in the stomach is prolonged and highly erratic. The consequences of this effect on the enteric coating of delayed release formulations are largely unpredictable. Sampling period should be designed such that measurable concentrations are obtained, taking into consideration not only the half-life of the drug but the possible occurrence of this effect as well. This should reduce the risk of obtaining incomplete concentration-time profiles due to delay to the most possible extent. These effects are highly dependent on individual behaviour. Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

45 Another Problem Gastro-resistant (enteric coated) preparations Therefore, but only under the conditions that sampling times are designed to identify very delayed absorption and that the incidence of this outlier behaviour is observed with a comparable frequency in both, test and reference products, these incomplete profiles can be excluded from statistical analysis provided that it has been considered in the study protocol. EMEA, CHMP Efficacy Working Party therapeutic subgroup on Pharmacokinetics (EWP-PK) Questions & Answers: Positions on specific questions addressed to the EWP therapeutic subgroup on Pharmacokinetics EMEA/61864/28, 23 July 29 What is comparable? For a study in 24 subjects, we get a significant difference for 5/ (Fisher s exact test: p.496). Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

46 Another Problem EMA GL on BE (21) Section Reasons for exclusion 1) A subject with lack of any measurable concentrations or only very low plasma concentrations for reference medicinal product. A subject is considered to have very low plasma concentrations if its AUC is less than 5% of reference medicinal product geometric mean AUC (which should be calculated without inclusion of data from the outlying subject). The exclusion of data [ ] will only be accepted in exceptional cases and may question the validity of the trial. Remark: Only possible after unblinding! Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

47 Another Problem EMA GL on BE (21) Section Resons for exclusion 1) cont d The above can, for immediate release formulations, be the result of subject non-compliance [ ] and should as far as possible be avoided by mouth check of subjects after intake of study medication to ensure the subjects have swallowed the study medication [ ]. The samples from subjects excluded from the statistical analysis should still be assayed and the results listed. Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

48 Case Study (PPI) Attempt to deal with high variability in C max Powered to 9% according to CV from previous studies; 14 (!) subjects and to 8% for expected dropout rate. Sampling every 3 min up to 14 hours (7785 total). t max 15 h C max 3.5 LLOQ time (hr) First time t max t ½.76 h t ½ 3.15 h t ½ 12 h Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

49 Drug specific, but Half lives The apparent elimination presents the slowest rate constant (controlled release, topicals, transdermals) not necessarily elimination! Avoid the term terminal elimination might not be true Important in designing studies To meet AUC t 8% AUC criterion To plan sufficiently long wash-out To plan saturation phase for steady state Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

50 Half lives Dealing with literature data What if only mean ±SD is given? Assuming normal distribution: µ ± σ covers 68.27% of values (15.87% of values are expected outside µ ± σ) Example: 8.5 ± 2.4 hours, 36 subjects = 5.71 or in at least five subjects we may expect a half life of > 1.9 hours. Plan for 95% coverage (z.95 = 1.96): 8.5 ± = [3.8,13.2] hours. We may expect a half life of > 13.2 hours in ~one subject (.5/2 36 =.9). Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

51 Half lives µ 1.96σ µ 1.96σ µ µ σ µ µ µ + σ µ σ µ σ µ σ Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

52 Washout in MD Studies EMA GL on BE (21) The treatment periods should be separated by a wash out period sufficient to ensure that drug concentrations are below the lower limit of bioanalytical quantification in all subjects at the beginning of the second period. Normally at least 5 elimination half-lives are necessary to achieve this. In steady-state studies, the wash out period of the previous treatment last dose can overlap with the build-up of the second treatment, provided the build-up period is sufficiently long (at least 5 times the terminal half-life). Justified by Superposition Principle Switch-over Design 21 NfG: 3 half-lives Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

53 Washout in MD Studies 2 15 t ½ = 12 τ = 24 washout vs. switch-over concentration time Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May

54 Thank You! Noncompartmental Analysis (NCA) in PK, PK-based Design Open Questions? Helmut Schütz BEBAC Consultancy Services for Bioequivalence and Bioavailability Studies 17 Vienna, Austria Bioequivalence and Bioavailability, Pre-Conference Workshop Ljubljana, 17 May