Impact of concentrations below the limit of quantification on pharmacodynamic predictions. A preclinical example, using new features of NONMEM VI.

Transcription

1 Impact of concentrations below the limit of quantification on pharmacodynamic predictions. A preclinical example, using new features of NONMEM VI. Celine Dartois, Jean-Louis Steimer, Mick Looby and Colin Pillai Novartis, Modeling and Simulation Muncie, May 19, 2009

2 Study objective To compare 2 drugs, a lead compound and its backup, on a pharmacodynamic endpoint based on their relative potency in animals These 2 drugs are from the same therapeutic class PK and PD collected for the two drugs The pharmacodynamic endpoint studied is a biomarker activity inhibition 2 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

3 Design PK and PD data Dose levels, time collections, number of animals Lead Backup Dose mg/kg Study 1 N=4 animals Study 2 N= 6 animals N= 6 animals N= 6 animals Study 1. n samples =7 Study 2 0 h 24 h 48 h 3 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. PK collected at the same time as PD. n samples =12

4 PK data Exploratory analysis Concentrations (ng/ml) (1) (2) Study 1: 2 & 10 mg/kg Study 2: 0.1 mg/kg Study 2: 0.3 mg/kg Study 2: 1 mg/kg Study 2: 10 mg/kg LEAD (3) Concentrations (ng/ml) (1) Study 1: 2 & 10 mg/kg Study 2: 10 mg/kg Study 2: 30 mg/kg Study 2: 100 mg/kg BACKUP Time post dose [h] Time post dose [h] 4 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

5 PK data limit of quantification (LOQ) definition LOQ is the lowest concentration of the standard curve that can be measured with acceptable accuracy and precision.* Should be established using at least five samples independent of standards and determining the coefficient of variation and/or appropriate confidence interval (<20 %) * signal LOQ Blank LOD LOQ Concentrations * Source: FDA guidance. Bioanalytical Method Validation 5 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

6 LEAD PK data Exploratory analysis data below the limit of quantification (BLQ) LOQ Study 1 LOQ Study 2 6 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

7 LEAD PK data Exploratory analysis data below the limit of quantification (BLQ) LOQ Study 1 LOQ Study 2 7 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

8 PD data Exploratory analysis Biomarker activity Study 1: 2 mg/kg Study 1: 10 mg/kg Study 2: 0.1 mg/kg Study 2: 0.3 mg/kg Study 2: 1 mg/kg Study 2: 10 mg/kg (1) LEAD Biomarker activity Study 1: 2 mg/kg Study 1: 10 mg/kg Study 2: 10 mg/kg Study 2: 30 mg/kg Study 2: 100 mg/kg BACKUP (1) (2) Time post dose [h] Time post dose [h] 8 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

9 PKPD data Exploratory analysis / / Observations for PK greater than LOQ Biomarker activity / / LEAD (LOQST2) (1) (LOQST1) NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. Concentrations (ng/ml)

10 PKPD data Exploratory analysis / / Observations for PK greater than LOQ Biomarker activity / / LEAD (LOQST2) (1) (LOQST1) (2) 10 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. Concentrations (ng/ml)

11 PKPD data Exploratory analysis Biomarker activity / / (LOQST2) BACKUP Observations for PK greater than LOQ (LOQST1) (1) / / Concentrations (ng/ml) 11 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

12 Method model structure Per os Ka L, lag time L, F1 L Per os Ka B, lag time B, F1 B Volume central Q L Volume peripheral Volume central Volume peripheral Q B CL L CL B LEAD BACKUP DADT(1)= -KA*A(1) DADT(2)= KA*A(1)-K23*A(2)+K32*A(3)-K*A(2) DADT(3)= K23*A(2)-K32*A(3) 12 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

13 Method model structure Per os Ka L, lag time L, F1 L Per os Ka B, lag time B, F1 B Volume central Q L Volume peripheral Volume central Volume peripheral Q B LEAD CL L No delay IC50 L Imax L Effect=BASE* (1-IMAX*CONC/(IC50+CONC)) active Biomarker - CL B IC50 B Imax B inactive Biomarker No delay BACKUP 13 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

14 Method Modeling approach Sequential PKPD A lot of data below the LOQ in PK for the LEAD (75/292), only two for the backup A few PK data in IC50 region Noisy PD data in the recovery phase PK estimation Handling the BLQ data 14 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

15 Method Modeling approach BLQ data* Method 1 (M1): Discard BLQ observations and apply extended least squares to the remaining observations. Method 2 (M2): Discard BLQ observations and apply the method of maximum conditional likelihood to the remaining observations. Method 3 (M3): Maximize the likelihood for all the data treating BLQ observation as censored. Method 4 (M4): Like M3 but the likelihoods for data above and below the LOQ are conditioned on the observations being greater than zero. Method 5 (M5): Replace BLQ observations with LOQ/2 and apply extended least squares estimation. Method 6 (M6): Replace first BLQ observation with LOQ/2 and discard the rest of them as in M1. Method 7 (M7): Replace first BLQ observation with 0 and discard the rest of them. *source: Beal. JPP, 2001,28(5): NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

16 Method Modeling approach BLQ data* Method 1 (M1): Discard BLQ observations and apply extended least squares to the remaining observations. - The lower of the remaining observations misrepresent the true lower concentrations; the lower remaining observations are selectively too high.* 16 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. *source: Beal. (2001) and Ahn et al (2008)

17 Method Modeling approach BLQ data* Method 1 (M1): Discard BLQ observations and apply extended least squares to the remaining observations. - The lower of the remaining observations misrepresent the true lower concentrations; the lower remaining observations are selectively too high. Method 5 (M5): Replace BLQ observations with LOQ/2 and apply extended least squares estimation. Method 6 (M6): Replace first BLQ observation with LOQ/2 and discard the rest of them as in M1. - Replacement withtout real justification, arbitrary. May yield greater bias and imprecision in estimates for IIV. Sampling schedule important for performance of LOQ/2 substitution.* 17 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. *source: Beal. (2001) and Ahn et al (2008)

18 Method Modeling approach BLQ data* Method 1 (M1): Discard BLQ observations and apply extended least squares to the remaining observations. - The lower of the remaining observations misrepresent the true lower concentrations; the lower remaining observations are selectively too high. Method 5 (M5): Replace BLQ observations with LOQ/2 and apply extended least squares estimation. Method 6 (M6): Replace first BLQ observation with LOQ/2 and discard the rest of them as in M1. - No real justification, arbitrary. May yield greater bias and imprecision in estimates for IIV. Sampling schedule important for performance of LOQ/2 substitution. Method 7 (M7): Replace first BLQ observation with 0 and discard the rest of them. - Replacement is always too low, induces the greatest bias * 18 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. *source: Beal. (2001) and Ahn et al (2008)

19 Method Modeling approach BLQ data* Method 2 (M2): Discard BLQ observations and apply the method of maximum conditional likelihood to the remaining observations. - When time of BLQ data not available, the best method.* Method 3 (M3): Maximize the likelihood for all the data treating BLQ observation as censored. - Data above the LOQ (extended least square method) - Data below the LOQ (integrating density function from inf to LOQ* Method 4 (M4): Like M3 but the likelihoods for data above and below the LOQ are conditioned on the observations being greater than zero. - No much superiority despite its complexity and longer computation time.* 19 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. *source: Beal. (2001) and Ahn et al (2008)

20 Method Modeling approach NONMEM VI M3 method * *Source: Bergstrand et al, PAGE NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

21 NONMEM version VI Method M3 NONMEM VI has a new functionality to simplify simultaneous modelling of continuous and categorical data Likelihood of data above/below the LOQ is included in the calculation of the objective function Laplacian method should be used A F_FLAG = indicator variable whether Y (or F) should be set to a prediction or a likelihood - Prediction: F_FLAG=0 (default) - Likelihood: F_FLAG=1 For data above LOQ continuous data log transformed IF (TYPE.EQ.0) THEN F_FLAG=0 Y=LOG(F)+ERR(1) ENDIF 21 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. Source: Ahn et al (2008)

22 NONMEM version VI Method M3 - code - For data below LOQ categorical data - approximation of the cumulative normal density IPRED=LOG(F) DUM=(LLOQ-IPRED)/SIG ARG=ABS(DUM) W1= W2= B1= B2= B3= B4= B5= AA=EXP(-0.5*ARG**2) R=1./(1.+W2*ARG) AUC=((((B1*R+B2)*R+B3)*R+B4)*R+B5)*R PHITL=AA*AUC*W1 IF (DUM.LT.0) CUMD=PHITL IF (DUM.GT.0) CUMD=1-PHITL IF (DUM.EQ.0) CUMD=0.5 IF (TYPE.EQ.1) THEN F_FLAG=1 Y=CUMD ENDIF Source: Ahn et al (2008) 22 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

23 Method Modeling approach PK estimation Log transformation of the data, add a lag time NONMEM VI - F_FLAG best model - IIV and IOV on Ka and F1 Winbugs - Upper Lower - each occasion = a different animal PD estimation Same baseline Different Imax for the two drugs IC50 ratio estimated Error model different for each study 23 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

24 Results PK goodness of fit LEAD NONMEM VI - Winbugs NONMEM VI M3 F_FLAG Winbugs 24 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

25 Results PK goodness of fit observed data <= 2 ng/ml (IC 50 region) NONMEM VI - Winbugs LEAD NONMEM VI M3 F_FLAG Winbugs 25 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

26 Results PD goodness of fit NONMEM VI - Winbugs NONMEM VI M3 F_FLAG LEAD Winbugs DV biomarker activity DV biomarker activity 26 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

27 Results PK goodness of fit BACKUP NONMEM VI - Winbugs NONMEM VI M3 F_FLAG Winbugs 27 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

28 Results PD goodness of fit BACKUP NONMEM VI - Winbugs NONMEM VI M3 F_FLAG Winbugs DV biomarker activity DV biomarker activity 28 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

29 Results PK distribution non observed data NONMEM VI - Winbugs NONMEM VI M3 F_FLAG LEAD Winbugs 29 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

30 Results PKPD observed PK data only LEAD NONMEM VI - M3 F_FLAG / / DV biomarker activity IC50 = 0.34 / / Observations for PK greater than LOQ Predictions (LOQST2) (LOQST1) Log (Concentrations) run151.txt 30 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

31 Results PKPD goodness of fit LEAD NONMEM VI - Winbugs NONMEM VI M3 F_FLAG Winbugs DV biomarker activity DV biomarker activity IC50=0.95 IC50= NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

32 Results PKPD goodness of fit BACKUP NONMEM VI - Winbugs NONMEM VI M3 F_FLAG Winbugs DV biomarker activity DV biomarker activity IC50=22 IC50=21 32 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

33 Results PKPD goodness of fit NONMEM VI - Winbugs LEAD BACKUP / / NONMEM VI M3 F_FLAG / / Winbugs DV biomarker activity Vildagliptin IC50 = 0.95 / / Concentrations (ng/ml) Sitagliptin IC50 = t DV biomarker activity Vildagliptin IC50 = 0.49 / / Concentrations (ng/ml) Sitagliptin IC50 = 21.1 IC50 ratio = 23 (SE=5.7 (24 %)) IC50 ratio = 43 (SE=7.6 (18 %)) 151 t 33 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

34 Conclusion Handling BLQ data, already important for PK, can be crucial for PD estimation when IC50 around LOQ A large diversity of methodologies exists * Until recently, due to implementation complexity and no big difference in efficiency, the simplest method (M1: discarding all BLQ data) was encouraging in NONMEM V. * Now NONMEM VI,with the F-FLAG option, allows to apply very easily a more efficient method (method M3). * In this study, this method is tested against Winbugs (for which LOQ is also taken into account to explain BLQ data) 34 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN. * Beal. (2001) and Ahn et al (2008)

35 Conclusion The only graphic allowing for distinguishing the methods was the BLQ distribution against the LOQ : Winbugs showed better results on PK, predicting only a few concentrations above LOQ. PK results had a great impact on PD estimation and reduced bias on relative potency (ratio of 43 instead of 23) As drugs are more and more potent and analytical methods cannot always quantify with accuracy the concentrations of interest, a real need exists for handling BLQ data in PKPD modeling. For this example, NONMEM VI did not show very convincing results. 35 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.

36 Acknowledgments Jerry Nedelman (Novartis, Modeling and Simulation) David James (Novartis, Modeling and Simulation) 36 NONMEM VI BLQ data Dartois, C et all May, 19 Muncie, IN.