Noncompartmental Analysis (NCA) in PK, PK-based Design
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1 Noncompartmental Analysis (NCA) in PK, PK-based Design Helmut Schütz BEBAC Consultancy Services for Bioequivalence and Bioavailability Studies 17 Vienna, Austria Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
2 Main Topics NCA vs. PK Modeling PK metrics derived by NCA Methods (single dose vs. steady state) Common problems Pitfalls Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
3 NCA vs. PK Modeling Noncompartmental methods do not rely on a pharmacokinetic model 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 Budapest, 11 May
4 NCA vs. PK Modeling Noncompartmental methods (cont d) Metrics (urine) Extent of absorption (EU ), total exposure (US): Ae (cumulative amount excreted): Rate of absorption (EU ), peak exposure (US): Ae max t Ae max (?) Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
5 NCA vs. PK Modeling Pharmacokinetic models Useful for understanding the drug/formulation If limited samples are available (phase II, paediatrics) 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 Budapest, 11 May
6 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 Budapest, 11 May z
7 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 (WinNonlin, Kinetica) 2 2 (1 R ) ( n 1) 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! *) 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 Budapest, 11 May
8 NCA 1 plasma profile (linear scale) 8 concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
9 NCA 1 plasma profile (semilogarithmic scale) concentration 1 C t Cˆt time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
10 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 Budapest, 11 May
11 NCA 1 plasma profile (linear scale) 8 concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
12 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 Budapest, 11 May
13 Multiple dose NCA Assessment whether steady state is reached (in a linear PK system: AUC τ = AUC ) No recommendations in guidelines 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 Budapest, 11 May
14 NCA 2 plasma profile (linear scale) concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May C av slope: % CI: [ ] steady state demonstrated
15 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 Budapest, 11 May
16 PK Modeling time [h] Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
17 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 Budapest, 11 May
18 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 Budapest, 11 May
19 Some Problems Missing values I Recommended Procedure may not be the default in your software (has to be actively set, e.g., in WinNonlin 4+) Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
20 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 Budapest, 11 May
21 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 Budapest, 11 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t
22 Some Problems 1 8 Reference Test LLOQ = 1 concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
23 Some Problems 1 8 Reference Test LLOQ = 1 concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
24 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 Budapest, 11 May time Reference conc BLQ AUC -t conc BLQ Missing Test AUC -t NA
25 Some Problems 1 8 Reference Test LLOQ = 1 concentration 6 4 C 72 set to time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
26 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 Budapest, 11 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t
27 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 Budapest, 11 May
28 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 Budapest, 11 May time Reference conc BLQ AUC -t conc BLQ Test AUC -t
29 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 Budapest, 11 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
30 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 Budapest, 11 May
31 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 Budapest, 11 May
32 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 Budapest, 11 May
33 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 Budapest, 11 May
34 Sampling at C max With any given sampling scheme the true C max is missed High inter- and/or intra-subject variability (single point metric) Variability higher than for AUC s In many studies the win/loose metric! Try to decrease variability Increase sample size (more subjects) Increase sampling within each subject (probably better) Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
35 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! Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
36 Sampling at C max k a = [ ] arithmetic mean geometric mean median Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
37 Sampling at C max 5 4 arithmetic mean geometric mean median 3 k a =.182 t lag = [ 2.5] Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
38 Another Problem Gastro-resistant (enteric coated) preparations Gastric emptying of single unit dosage forms nondisintegrating 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 Budapest, 11 May
39 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, 22 January 29 Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
40 Drug specific, but Half lives The terminal phase presents the slowest rate constant (controlled release, topicals, transdermals) not necessarily elimination! 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 Budapest, 11 May
41 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 > 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 Budapest, 11 May
42 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 Budapest, 11 May
43 Washout in MD Studies EMEA (21) Subsequent treatments should be separated by adequate wash out periods. In steady-state studies wash out 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 three times the terminal half-life). Justified by Superposition Principle Switch-over Design Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
44 Washout in MD Studies 2 15 t ½ = 12 τ = 24 washout vs. switch-over concentration time Bioequivalence and Bioavailability, Pre-conference workshop Budapest, 11 May
45 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 Budapest, 11 May
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