This document provides an overview of pharmacokinetic (PK) and pharmacodynamic (PD) modeling concepts and applications. It discusses the cascade of pharmacological events between drug administration and clinical outcome. Different types of PD endpoints and PK/PD models are described, including direct response, indirect response, and effect compartment models. Examples are provided of how PK/PD modeling can facilitate drug development, such as supporting a change in dosing regimen based on route of administration. The document concludes with a case study demonstrating how PK/PD modeling was used to support including both every 2 week and every 4 week dosing regimens in the label for the drug Plegridy® for the treatment of multiple sclerosis.

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

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
2

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
3

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
4

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
5

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
6

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
7

8. Cascade of Pharmacological Events
Blood
Site of
Action
Target
Engagement …
8

9. TYSABRI®: MoA, Target and Biomarker
https://www.youtube.com/watch?v=9zLYxr2Tv7I
↑ 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
• …
9

10. 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, 176-185, 1999
10

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
Slow
B
I
O
M
A
R
K
E
R
S
CLINICAL
EFFECTS
William J. Jusko, PK-PD Modeling Workshop
11

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
12

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
13

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
14

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
15

16. Model Components
• Structure 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
16

17. Direct Link Model
H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, 176-185, 1999
• 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
17

18. Time (hr)
QTcProlongation(msec)
0
5
10
15
0 20 40 60 80 100
Hysteresis: Concept
0.0 0.5 1.0 1.5 2.0
051015
Concentration (ng/ml)
QTcProlongation(msec)
PK vs. PD
Time (hr)
Concentration(ng/ml)
0.0
0.5
1.0
1.5
2.0
0 20 40 60 80 100
PK PD
18

19. Hysteresis: Real Example
Salazar et al, A Pharmacokinetic-Pharmacodynamic Model of d-Sotalol Q-Tc Prolongation During Intravenous Administration to Healthy Subjects, J. Clin Pharmacol. 37: 799-809 (1997)19
Three subjects showing different
degree of hysteresis between
plasma drug concentration and
QTc interval

20. Indirect Link Model
H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, 176-185, 1999
• Hysteresis due to DISTRIBUTION DELAY TO SITE OF ACTION
• Also called Effect Compartment Model or Biophase Distribution Model
Blood
20

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: 510-519, 2003
21

22. Indirect Response Model
H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD) Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, 176-185, 1999
22

23. Indirect Response Model (cont’d)
D. Mager, E. Wyska, W. Jusko, Diversity of Mechanism-based Pharmacodynamic Models, Drug Metabolism and Disposition, 31: 510-519, 2003
23

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
24

25. 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
25
Case Study One:
PK/PD Modeling to Support Q2W Regimen vs. Q4W
Regimen in Label for Plegridy®
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
26

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):798‒80827

28. 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;
NCT00906399)1
1Calabresi PA. et al. Lancet Neurol 2014:
doi:10.1016/S1474-4422(14)70068-7
2Hu X, et al. Poster presentation at AAN 2014, April 26–3 May,
Philadelphia, PA, USA (P3.194)
†Intensive blood sampling in a subset of 25 patients who provided additional consent
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 4† 12 24† 48 56 84 96
Blood sampling
MRI scans
 Population PK model: A one-compartment model described the peginterferon
beta-1a PK profiles well2
, no exposure accumulation was observed with both
dose regimens
MRI = magnetic resonance imaging PD = pharmacodynamic; PK =
pharmacokinetic; Q2W = every 2 weeks; Q4W = every 4 weeks; SC
= subcutaneous
28

29. Gd+ Lesion Count Over Time
Placebo-treated patients
 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
0
20
40
60
-400 -200 0 200 400 600 800
Placebo Q2W
0
20
40
60
Q4W
~ 40% of patients had data
at Week 96
Time Since First Active Dose (day)
ObservedGd+LesionCount
Week
0
10
20
30
:ID 240309
0 10 20 30 40 50
:ID 241303 :ID 121301
:ID 101307 :ID 137304
0
10
20
30
:ID 450305
0
10
20
30
:ID 251303 :ID 303302 :ID 430302
0 10 20 30 40 50
:ID 317306 :ID 437325
0 10 20 30 40 50
0
10
20
30
:ID 441302
ObservedGd+LesionCount
29

30. Relationship between Steady State 4-
Week AUC and Gd+ Lesion Count
 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
0
20
40
60
0 50 100 150
Placebo
Q2W
Q4W
Placebo->Q2W
Placebo->Q4W
Estimated Individual Cumulative AUC Over 4 Weeks (ng/mL*hr)
ObservedGd+LesionCount
30

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

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 − 𝑝0 ∗ λ, Var X = 1 − 𝑝0 ∗ (λ + 𝑝0 ∗ λ2
)
• 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 − 𝑝0 ∗
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 − 𝑝0 ∗ λ, 𝑉𝑎𝑟 𝑋 = 1 − 𝑝0 ∗ λ ∗ 1 + λ ∗ 𝑂𝑉𝐷𝑃 + 𝑝0 ∗ λ2
32

33. Candidate Models (cont’d)
• Marginal (Naïve Pooled) Model
– 𝝀𝒊𝒋 = 𝝀 𝟎 ∗ 𝐞𝐱𝐩 𝜷 ∗ 𝑨𝑼𝑪𝒊𝒋 ∗ (𝟏 − 𝒆𝒙𝒑 −𝒌 ∗ 𝒕𝒊𝒋 )
– 𝑙𝑜𝑔𝑖𝑡 𝑝0 = 𝛼0 + 𝛼1 ∗ 𝐴𝑈𝐶𝑖𝑗
• Mixed Effect Model
⁻ 𝝀𝒊𝒋 = 𝝀𝒊𝟎 ∗ 𝐞𝐱𝐩 𝜷 ∗ 𝑨𝑼𝑪𝒊𝒋 ∗ (𝟏 − 𝒆𝒙𝒑 −𝒌 ∗ 𝒕𝒊𝒋 )
• Mixed Effect Negative Binomial Model
– λ𝑖0~𝐿𝑁(μ, ω2
), OVDP constant
• Mixture Negative Binomial Model
– λ𝑖0 = λ𝑖0,1 ∗ 𝐼 𝑌 = 1 + λ𝑖0,2 ∗ 𝐼 𝑌 = 0
– 𝑌~𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖(1, 𝑝)
– λ𝑖0,1~𝐿𝑁(μ1, 𝜔1
2
), λ𝑖0,2~𝐿𝑁(μ2, 𝜔2
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
33

34. Model Comparison
Model -2LL β SE
Poisson 21792.2 -0.0248 0.0036
ZIP 15804.0 -0.0111
0.0156
0.0041
0.0014
NB 11112.5 -0.0197 0.0016
ZINB 11105.0 -0.025
-0.455
Model unstable
Mixed NB 10552.8 -0.0269 0.0024
Mixture NB 10238.8 -0.0257 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
34

35. Goodness-of-Fit Assessed by
Marginal Probabilities
NB = negative binomial; ZINB = zero-inflated NB; ZIP = Zero-inflated Poisson
0.0
0.2
0.4
0.6
0.8
Naive Poisson
0 2 4 6 8 10
Naive NB
ZIP
0.0
0.2
0.4
0.6
0.8
ZINB
0.0
0.2
0.4
0.6
0.8
0 2 4 6 8 10
Mixed NB Mixture NB
Gd+ Lesion Count
MarginalProbability
Model Prediction
Observed
0.000
0.001
0.002
0.003
Naive Poisson
10 20 30 40 50 60 70
Naive NB
ZIP
0.000
0.001
0.002
0.003
ZINB
0.000
0.001
0.002
0.003
10 20 30 40 50 60 70
Mixed NB Mixture NB
Gd+ Lesion Count
Below 10 Above 10
35

36. Final Model Parameter Estimates
Model
Parameter
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)
-0.026
(11.0%)
-0.0259 (10.7%)
(-0.033, -0.021)
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
36

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
37

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
38

39. 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
39
Case Study Two:
PK/PD Analysis to Identify Reason for Study
Failure and Supporting 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, 857-866, 2008

40. Background
• A selective COX-2 Inhibitor
• Preclinical potency estimates and PK model from
HV suggests 60 mg SC-75416 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-75416
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-75416 groups than
rofecoxib
40

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 41

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-75416 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)
42

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 𝑃𝑅𝑖𝑗 ≥ 𝑚 η𝑖 = 𝑓𝑝 𝑡𝑗, 𝑚 + 𝑓𝑑 𝑐𝑖𝑗 + (𝑡𝑗) 𝑥 𝜂𝑖
𝑓𝑝 𝑡𝑗, 𝑚 : placebo effect; 𝑓𝑑 𝑐𝑖𝑗 : drug effect; 𝑐𝑖𝑗: 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 𝑇𝑖 = 𝑡𝑗+1 𝑇𝑖 ≥ 𝑡𝑗, 𝑃𝑅𝑖𝑗 = 𝑚 = 1 − exp(−
𝑡 𝑗
𝑡 𝑗+1
𝜆 𝑡, 𝑚 𝑑𝑡)
43

44. Goodness of Fit for Capsule PR and
Drop-out Model
Solid line represent the mean of predicted pain reduction for 50000 hypothetical subjects
based on both PR and drop-out model, and LOCF imputation method applied 44

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
45

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 46

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
47

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
48

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
49

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) 12-35.
• Pinheiro, J.C. and D.M. Bates, Mixed-Effects Models in S and S-Plus, Springer, New York,
2004.
• The Comprehensive R Network, http://cran.r-project.org/
• Pharma Stat Sci, http://www.pharmastatsci.com/
• H. Derendorf, B. Meibohm, Modeling of Pharmacokinetic/Pharmacodynamic (PK/PD)
Relationships: Concepts and Perspectives, Pharmaceutical Research, Vol. 16, No.2, 176-185,
1999
• Salazar et al, A Pharmacokinetic-Pharmacodynamic Model of d-Sotalol Q-Tc Prolongation
During Intravenous Administration to Healthy Subjects, J. Clin Pharmacol. 37: 799-809
(1997)
• D. Mager, E. Wyska, W. Jusko, Diversity of Mechanism-based Pharmacodynamic Models,
Drug Metabolism and Disposition, 31: 510-519, 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,
857-866, 2008
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