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An Introduction to PK/PD Models Part 2

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1 An Introduction to PK/PD Models Part 2
Yaming Hang Biogen Sep. 16, 2015 FDA/Industry Workshop 2015

2 Learning Objectives for Part 2
After finishing this lecture, the attendees are expected to: Obtain general understanding of the cascade of pharmacological events between drug administration and outcome Recognize different types of pharmacodynamic endpoints Distinguish different temporal relationships between pharmacokinetics and pharmacodynamics Explain common causes for delay in drug effect Able to identify proper class of PK/PD models to describe different PK/PD relationships Give a few examples on the application of PK/PD analysis in drug development

3 Outline for Part 2 Why PD Models are Important
Cascade of Pharmacological Events Different Types of PD Endpoints Different Types of PD Models Direct link vs. indirect link Direct response vs. indirect response Case Studies

4 Changes that Potentially Lead to Different PK Profiles
Route of administration, delivery technology Dosing Regimen (dose amount and frequency) Formulation or manufacturing process Population Race Pediatric, geriatric Light vs. heavy subjects Renal impairment, liver impairment Drug-drug interaction HV vs. Diseased population

5 Why PD models are important
Population PK models aim to characterize and identify important intrinsic and extrinsic factors that influence pharmacokinetics Only with a pharmacodynamic model, we can assess the clinical significance of difference in PK under different circumstances, therefore decide whether the dose regimen should be adjusted accordingly

6 Example of Changing From Intravenous (IV) to Subcutaneous (SC) Administration
Frequently, biologics are delivered intravenously (IV) and dosage is body weight based, which complicates the drug administration process and leads to drug product waste It will bring significant convenience to patients as well as cost saving associated with reduced drug product waste/clinical site visit if drug can be self-administered (e.g. SC) and at a fixed dose amount However, variability in PK has to be evaluated and ultimately what matters is whether the different regimen can deliver similar efficacy/safety profile

7 PK/PD Modeling Facilitated Abatacept SC Program
Weight-tiered IV regimen approved for treatment of rheumatoid arthritis in 2005 Flat SC dosing regimen subsequently tested and approved in 2011 Knowledge in the IV program was utilized to design a bridging program: Pop PK and PK/PD models developed for simulation Dose-ranging study was not needed A PK study with SC route was followed directly by a Phase 3 study

8 Cascade of Pharmacological Events
Site of Action Target Engagement Blood

9 TYSABRI®: MoA, Target and Biomarker
↑ Nat ↑ α4 Sat ↓ Total α4 ↑ Lymphocyte Questions to be addressed by PK/PD modeling: Extent of receptor occupancy Lymphocyte elevation Relationship between receptor occupancy and clinical efficacy

10 description of time-course and factors
Pharmacokinetics/Pharmacodynamics (PK/PD): description of time-course and factors controlling drug effects on the body H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, , 1999

11 Biological Turnover Rates of Structure or Functions
Electrical Signals (msec) Neurotransmitters (msec) Chemical Signals (min) Mediators, Electrolytes (min) Hormones (hr) mRNA (hr) Proteins / Enzymes (hr) Cells (days) Tissues (mo) Organs (year) Person (.8 Century) Fast B IOMARKERS CLINICAL EFFECTS Slow William J. Jusko, PK-PD Modeling Workshop

12 Different PD Outcomes: by Role in Pharmacology Cascade
Biomarker Measurable physiological or biochemical parameters that reflect some pharmacodynamic activity of the drug E.g. Alpha-4 Integrin Saturation Surrogate marker Observed earlier than clinical outcome, easily quantified, predicts clinical outcome Does not change as fast as biomarker E.g. MRI Gd enhancing lesions Clinical outcome E.g. Relapse Rate, EDSS

13 Different PD Outcomes: by Accessibility
Readily accessible, e.g. In circulation Receptor saturation, cell count, enzyme/protein level/activity Electrical signal Electroencephalography (EEG), Electrocardiography (ECG) Clinical measurement/assessment Intensive sampling feasible Less accessible, e.g. Imaging technique for brain lesions, Amyloid plaque, receptor binding outside blood, tumor size CSF fluid Invasive tissue biopsy Infrequent sampling

14 Different PD Outcomes: by Data Type
Types of variables Continuous: e.g. blood pressure Categorical: e.g. AE Occurrence, AE severity, Pain Likert Score, Sleep State Count data: e.g. number of MRI lesions in Multiple Sclerosis Time-to-event: e.g. repeated time to bleeding in treatment of hemophilia A with ELOCTATE® Longitudinal vs. cross-sectional

15 Different PK/PD Model Types
Empirical Models Models that describe the data well but without biological meaning Interpretation of parameters can be challenging E.g., polynomial function to describe an exposure-response relationship Mechanistic Models Reflecting underlying physiological process Preferred due to better predictive power Reversible Direct link/response model Indirect link/response model Irreversible Chemotherapy Enzyme Inactivation

16 Model Components Structure Model Stochastic Model
The underlying relationship between PK, time and PD response For mechanistic models, understanding of Mechanism of Action is required Stochastic Model Inter-subject variation Intra-subject variation Residual error

17 Direct Link Model Appropriate to visually assess
the relationship between concentration and response collected at the same time PK model can be used to predict missing concentration where PD is available but not PK Examples: heart rate change receptor binding some acute pain medication H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, , 1999

18 Hysteresis: Concept PK PD PK vs. PD

19 Hysteresis: Real Example
Three subjects showing different degree of hysteresis between plasma drug concentration and QTc interval Salazar et al, A Pharmacokinetic-Pharmacodynamic Model of d-Sotalol Q-Tc Prolongation During Intravenous Administration to Healthy Subjects, J. Clin Pharmacol. 37: (1997)

20 Indirect Link Model Hysteresis due to DISTRIBUTION DELAY TO SITE OF ACTION Also called Effect Compartment Model or Biophase Distribution Model Blood H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, , 1999

21 Extent of Hysteresis Under Different Doses or Distribution Rate Constants
Effect under Different Doses D. Mager, E. Wyska, W. Jusko, Diversity of Mechanism-based Pharmacodynamic Models, Drug Metabolism and Disposition, 31: , 2003

22 Indirect Response Model
H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, , 1999

23 Indirect Response Model (cont’d)
D. Mager, E. Wyska, W. Jusko, Diversity of Mechanism-based Pharmacodynamic Models, Drug Metabolism and Disposition, 31: , 2003

24 Indirect Response Model (cont’d)
Type I (inhibition of production) Inhibition of BACE1 enzyme leads to reduced production of amyloid-β peptide Type II (inhibition of clearance) Tysabri® hinders the migration of lymphocyte out of blood Type III (stimulation of production) Epogen® stimulate the growth of red blood cell Type IV (stimulation of clearance) Aducanumab ® stimulate the clearance of amyloid-β

25 Case Study One: PK/PD Modeling to Support Q2W Regimen vs. Q4W Regimen in Label for Plegridy® Highlight An example of Empirical Model Both PK and PD samples are sparse PD endpoint, a clinical endpoint, changes much slower than PK Modeling results used to support labeling claim Y Hang et al, Pharmacokinetic and Pharmacodynamic Analysis of Longitudinal Gd-Enhanced Lesion Count in Subjects with Relapsing Remitting Multiple Sclerosis Treated with Peginterferon beta-1a, Population Approach Group in Europe 2014 Annual Conference

26 Background Plegridy® is a PEGylated form of human IFN beta-1a; it increases half-life and exposure to IFN beta-1a compared with non-pegylated, intramuscular IFN A pivotal Phase 3 study for Plegridy® compared Plegridy® 125 ug SC every 2 weeks (Q2W) Plegridy® 125 ug SC every 4 weeks (Q4W) Placebo Both Plegridy® regimens are better than placebo, but difference between them were not statistically significant in some of the key efficacy endpoints (e.g. annual relapse rate) Regulatory agency proposed to include both regimens in the label in the review process PK/PD analysis on Relapse and Gd+ Lesion Count were performed to demonstrate Q2W provides better exposure coverage than Q4W

27 Endpoint Gadolinium-enhanced lesions are associated with blood-brain barrier disruption and inflammation, an informative biomarker for disease progression Objective To develop a PK and PD model to assess the effect of monthly exposure of Plegridy® on the reduction of Gd+ lesion count over time in patients with relapsing-remitting multiple sclerosis Gd+ = gadolinium-enhancing; MRI = magnetic resonance imaging; MS = multiple sclerosis; PD = pharmacodynamic; PK = pharmacokinetic 1Hu X, et al. J Clin Pharmacol 2012;52(6):798‒808

28 1512 patients randomized (1:1:1)
Study Design Study design: 2-year, multicenter, randomized, double-blind, parallel-group Phase 3 study in RRMS patients, with a 1-year placebo-controlled period (ADVANCE; NCT )1 1512 patients randomized (1:1:1) and dosed Peginterferon beta-1a 125 μg Q2W SC Placebo (n=500) Peginterferon beta-1a 125 μg Q2W SC (n=512) Peginterferon beta-1a 125 μg Q4W SC (n=500) Year 1 Follow-up Peginterferon beta-1a 125 μg Q4W SC Year 2 Week † † Blood sampling MRI scans †Intensive blood sampling in a subset of 25 patients who provided additional consent Population PK model: A one-compartment model described the peginterferon beta-1a PK profiles well2, no exposure accumulation was observed with both dose regimens 1Calabresi PA. et al. Lancet Neurol 2014: doi: /S (14) 2Hu X, et al. Poster presentation at AAN 2014, April 26–3 May, Philadelphia, PA, USA (P3.194) MRI = magnetic resonance imaging PD = pharmacodynamic; PK = pharmacokinetic; Q2W = every 2 weeks; Q4W = every 4 weeks; SC = subcutaneous

29 Gd+ Lesion Count Over Time
Placebo-treated patients Observed Gd+ Lesion Count ~ 40% of patients had data at Week 96 Time Since First Active Dose (day) Observed Gd+ Lesion Count Week Large inter-subject variation was observed There was a significant proportion of patients without Gd+ lesions throughout the trial Distribution shifted toward 0 while on treatment Gd+ = gadolinium-enhancing; Q2W = every 2 weeks; Q4W = every 4 weeks

30 Relationship between Steady State 4-Week AUC and Gd+ Lesion Count
Observed Gd+ Lesion Count Estimated Individual Cumulative AUC Over 4 Weeks (ng/mL*hr) What is the proper statistical distribution to describe these data? How can we quantify the effect of exposure on the distribution of Gd+ lesion count? AUC = area under the curve; Gd+ = gadolinium-enhancing; Q2W = every 2 weeks; Q4W = every 4 weeks

31 Some Key Features of Data
Large over-dispersion Large Proportion of Zero Lesion Count

32 Candidate Models Poisson, Zero-inflated Poisson
𝑷 𝒙=𝒎|λ, 𝒑 𝟎 = 𝒑 𝟎 + 𝟏− 𝒑 𝟎 ∗ 𝐞𝐱𝐩 −λ , 𝒎=𝟎 𝟏− 𝒑 𝟎 ∗ 𝝀 𝒎 𝒎! ∗𝒆𝒙𝒑(−λ), 𝒎>𝟎 𝐸 𝑋 = 1− 𝑝 0 ∗λ, Var X = 1− 𝑝 0 ∗(λ+ 𝑝 0 ∗ λ 2 ) Negative Binomial (NB), Zero-inflated NB 𝑷 𝒙=𝒎|λ,𝑶𝑽𝑫𝑷, 𝒑 𝟎 = 𝒑 𝟎 + 𝟏− 𝒑 𝟎 ∗ 𝟏 𝟏+𝑶𝑽𝑫𝑷∗𝝀 𝟏 𝑶𝑽𝑫𝑷 , 𝒎=𝟎 1− 𝑝 0 ∗ 𝜞 𝒎+ 𝟏 𝑶𝑽𝑫𝑷 𝜞 𝒎+𝟏 ∗𝜞 𝟏 𝑶𝑽𝑫𝑷 ∗ 𝟏 𝟏+𝑶𝑽𝑫𝑷∗𝝀 𝟏 𝑶𝑽𝑫𝑷 ∗ 𝝀 𝝀+ 𝟏 𝑶𝑽𝑫𝑷 𝒎 , 𝒎>𝟎 OVDP is overdispersion parameter 𝐸 𝑋 = 1− 𝑝 0 ∗λ, 𝑉𝑎𝑟 𝑋 = 1− 𝑝 0 ∗ λ∗ 1+λ∗𝑂𝑉𝐷𝑃 + 𝑝 0 ∗ λ 2 Meaning of the model and parameters

33 Candidate Models (cont’d)
Marginal (Naïve Pooled) Model 𝝀 𝒊𝒋 = 𝝀 𝟎 ∗ 𝐞𝐱𝐩 𝜷∗ 𝑨𝑼𝑪 𝒊𝒋 ∗(𝟏−𝒆𝒙𝒑 −𝒌∗ 𝒕 𝒊𝒋 ) 𝑙𝑜𝑔𝑖𝑡 𝑝 0 = 𝛼 0 + 𝛼 1 ∗ 𝐴𝑈𝐶 𝑖𝑗 Mixed Effect Model 𝝀 𝒊𝒋 = 𝝀 𝒊𝟎 ∗ 𝐞𝐱𝐩 𝜷∗ 𝑨𝑼𝑪 𝒊𝒋 ∗(𝟏−𝒆𝒙𝒑 −𝒌∗ 𝒕 𝒊𝒋 ) Mixed Effect Negative Binomial Model λ 𝑖0 ~𝐿𝑁(μ, ω 2 ), OVDP constant Mixture Negative Binomial Model λ 𝑖0 = λ 𝑖0,1 ∗𝐼 𝑌=1 + λ 𝑖0,2 ∗𝐼 𝑌=0 𝑌~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(1, 𝑝) λ 𝑖0,1 ~𝐿𝑁( μ 1 , 𝜔 1 2 ), λ 𝑖0,2 ~𝐿𝑁( μ 2 , 𝜔 2 2 ), OVDP1 and OVDP2 for two subpopulations† †The two subpopulations in the model were patients with lower Gd+ lesion activity and patients with higher Gd+ lesion activity at baseline. Gd+ = gadolinium-enhancing; OVDP = over dispersion parameter

34 Model Comparison Model -2LL β SE Poisson 21792.2 -0.0248 0.0036 ZIP
0.0156 0.0041 0.0014 NB 0.0016 ZINB -0.025 -0.455 Model unstable Mixed NB 0.0024 Mixture NB 0.0028 AUC in zero-inflated models may be related to both probability of zero as well as the mean of the non-zero part, its effect estimate cannot be compared with other models directly Naïve NB model yielded a different AUC effect parameter estimate Slope parameter β were estimated similarly across different models, but the uncertainty estimation could be very different AUC = area under the curve; NB = negative binomial, SE = standard error; ZINB = zero-inflated NB; ZIP = Zero-inflated Poisson

35 Goodness-of-Fit Assessed by Marginal Probabilities
Below 10 Above 10 Gd+ Lesion Count Marginal Probability Gd+ Lesion Count Model Prediction Observed NB = negative binomial; ZINB = zero-inflated NB; ZIP = Zero-inflated Poisson

36 Final Model Parameter Estimates
Description Point Estimate (RSE %) Non-parametric bootstrap (500 replicates) Median (RSE %) 95% CI λ0_1 Baseline mean Gd+ lesion count for a typical subject in lower lesion activity subpopulation 0.546 (13.2%) 0.543 (12.7%) (0.428, 0.693) λ0_2 Baseline mean Gd+ lesion count for a typical subject in higher lesion activity subpopulation 1.624 1.615 σ2 Variance of random effect on baseline λ in log scale for the higher lesion activity subpopulation 1.26 (9.5%) 1.25 (9.6%)    (1.02, 1.51) r1 Dispersion parameter for baseline λ in the lower lesion activity group 44.6 (6.7%) 44.26 (6.5%) (38.5, 50.9) r2 Dispersion parameter for baseline λ in the higher lesion activity group 0.452 (9.9%) 0.446 (10.0%) (0.357, 0.541) P Proportion of lower lesion activity subpopulation 0.593 0.594 (0.550, 0.641) β Slope of AUC effect on log(λ) (11.0%) (10.7%) (-0.033, ) t1/2 Half-life of drug effect onset time (day) 111 (25.5%) 112.3 (25.0%) (69.2, 207.6) AUC = area under the curve; CI = confidence interval; Gd+ = gadolinium-enhancing; RSE = relative standard error

37 More Reduction in Gd+ Lesion Count was Driven by Greater Exposure
Observed data aligned with model predicted data Correlation between cumulative monthly AUC and Gd+ lesion data Steep Gd+ decline in the AUC range of Q4W, vs. a more flat curve in the AUC range of Q2W

38 Conclusions for Case Study One
An example of Empirical Model Multiple models were compared and quantified the relationship between Plegridy® AUC and Gd+ lesion count Demonstrated that Q4W regimen is more likely to result in sub-optimal exposure Only Q2W regimen was approved in the label

39 Case Study Two: PK/PD Analysis to Identify Reason for Study Failure and Supporting Dose Selection Highlight An example of Direct Link/Response Model Intensive PK and PD samples Modeling results used to identify reason for trial failure predict outcome for new formulation facilitate dose selection KG Kowalski, S Olson, AE Remmers and MM Hutmacher, Modeling and Simulation to Support Dose Selection and Clinical Development of SC-75416, a Selective Cox-2 Inhibitor for the Treatment of Acute and Chronic Pain, Clinical Pharmacology & Therapeutics, Vol83, , 2008

40 Background A selective COX-2 Inhibitor
Preclinical potency estimates and PK model from HV suggests 60 mg SC should provide pain relief (PR) similar to 50 mg rofecoxib (Vioxx) In a dose-ranging study for pain relief in post-surgical dental patients: Single oral dose of placebo, 3, 10, and 60 mg SC CAPSULES were compared with 50 mg rofecoxib 10 and 60 mg doses were better than placebo, but did not achieve PR comparable to 50 mg rofecoxib Drop out rate was higher in SC groups than rofecoxib

41 Formulation Difference was Behind PK Difference
capsule formulation had slower and more erratic absorption at critical early time points compared to oral solution data in Phase I, which is believed to be the reason for poor pain relief response

42 PK/PD Analyses for Pain Relief and Drop Out
A PK/PD model was developed to predict how a 60 mg ORAL SOLUTION dose may have performed in the post-oral surgery pain study A nonlinear mixed effects logistic-normal model related plasma concentration of SC and rofecoxib to the PR scores on a 5-point Likert scale (0=no PR, 4=complete PR) Survival model was fit to time of dropout (time of rescue)

43 PK/PD Models for Pain Relief and Drop Out
PR Model to describe the distribution of Pain Reduction (PR) at each time point tj for individual i: 𝑙𝑜𝑔𝑖𝑡 Pr 𝑃𝑅 𝑖𝑗 ≥𝑚 η 𝑖 = 𝑓 𝑝 𝑡 𝑗 ,𝑚 + 𝑓 𝑑 𝑐 𝑖𝑗 + ( 𝑡 𝑗 ) 𝑥 𝜂 𝑖 𝑓 𝑝 𝑡 𝑗 ,𝑚 : placebo effect; 𝑓 𝑑 𝑐 𝑖𝑗 : drug effect; 𝑐 𝑖𝑗 : plasma concentration Drop-out Model to describe the probability of an individual dropout in the time interval (tj, tj+1) given he/she was still in the study in the previous time interval (tj-1, tj): Pr 𝑇 𝑖 = 𝑡 𝑗+1 𝑇 𝑖 ≥ 𝑡 𝑗 , 𝑃𝑅 𝑖𝑗 =𝑚 =1−exp⁡(− 𝑡 𝑗 𝑡 𝑗+1 𝜆 𝑡,𝑚 𝑑𝑡 )

44 Goodness of Fit for Capsule PR and Drop-out Model
Solid line represent the mean of predicted pain reduction for hypothetical subjects based on both PR and drop-out model, and LOCF imputation method applied

45 Predicted Outcomes for Oral Solution at Different Doses
Dashed lines are predicted profiles Solid lines and squares are for 50 mg rofecoxib as reference

46 Results from a Subsequent Clinical Study Comparing Oral Solution SC-75416 and Ibuprofen
Vioxx was withdrawn by the time they conducted the next study

47 Conclusions for Case Study Two
An example of Direct Link/Response Model Identified formulation as cause for not achieving anticipated PR effect size PK/PD analysis predicted dose levels which will yield intended effect size using a different formulation PK/PD prediction guided dose selection for a subsequent dose-ranging study and outcome was consistent with prediction

48 Take Home Message for Statisticians
Improve understanding on Basic pharmacology principles Mechanistic components of the PD models The role of Dose and Time in PK/PD relationship Involve Provide constructive suggestions on analysis method of non-trivial data types Perform hands-on analysis Contribute to methodology development Engage with pharmacometricians one-on-one

49 Learning Objectives for Part 2
After finishing this lecture, the attendees are expected to: Obtain general understanding of the cascade of pharmacological events between drug administration and outcome Recognize different types of pharmacodynamic endpoints Distinguish different temporal relationships between pharmacokinetics and pharmacodynamics Explain common causes for delay in drug effect Able to identify proper class of PK/PD models to describe different PK/PD relationships Give a few examples on the application of PK/PD analysis in drug development

50 References for Parts 1 and 2
Davidian, M. and D. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman and Hall, New York, 1995. Gabrielsson, J. and D. Weiner, Pharmacokinetic and Pharmacodynamic Data Analysis: Concepts and Applications, Swedish Pharmaceutic, 2007. Pinheiro, J.C. and D.M. Bates, Approximations to the log-likelihood function in the nonlinear effects model, J. Comput. Graph. Statist., 4 (1995) Pinheiro, J.C. and D.M. Bates, Mixed-Effects Models in S and S-Plus, Springer, New York, 2004. The Comprehensive R Network, Pharma Stat Sci, H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, , 1999 Salazar et al, A Pharmacokinetic-Pharmacodynamic Model of d-Sotalol Q-Tc Prolongation During Intravenous Administration to Healthy Subjects, J. Clin Pharmacol. 37: (1997) D. Mager, E. Wyska, W. Jusko, Diversity of Mechanism-based Pharmacodynamic Models, Drug Metabolism and Disposition, 31: , 2003 Y Hang et al, Pharmacokinetic and Pharmacodynamic Analysis of Longitudinal Gd-Enhanced Lesion Count in Subjects with Relapsing Remitting Multiple Sclerosis Treated with Peginterferon beta-1a, Population Approach Group in Europe 2014 Annual Conference KG Kowalski, S Olson, AE Remmers and MM Hutmacher, Modeling and Simulation to Support Dose Selection and Clinical Development of SC-75416, a Selective Cox-2 Inhibitor for the Treatment of Acute and Chronic Pain, Clinical Pharmacology & Therapeutics, Vol83, , 2008


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