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