an introduction to pk/pd models part 2 yaming hang biogen sep. 16, 2015 fda/industry workshop 2015 1
TRANSCRIPT
1
An Introduction to PK/PD ModelsPart 2
Yaming HangBiogen
Sep. 16, 2015FDA/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
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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
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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
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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
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Cascade of Pharmacological Events
BloodSite of Action
Target Engagement …
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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• …
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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
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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
BIOMARKERS
CLINICALEFFECTS
William J. Jusko, PK-PD Modeling Workshop
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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
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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
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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
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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
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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
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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
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Time (hr)
QT
c P
rolo
ng
atio
n (
mse
c)
0
5
10
15
0 20 40 60 80 100
Hysteresis: Concept
0.0 0.5 1.0 1.5 2.0
05
1015
Concentration (ng/ml)
QT
c P
rolo
ngat
ion
(mse
c)
PK vs. PD
Time (hr)
Co
nce
ntr
atio
n (
ng
/ml)
0.0
0.5
1.0
1.5
2.0
0 20 40 60 80 100
PK PD
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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)
Three subjects showing differentdegree of hysteresis betweenplasma drug concentration andQTc interval
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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
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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
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
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
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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
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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
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
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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
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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
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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
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Gd+ Lesion Count Over TimePlacebo-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 Q2W0
20
40
60
Q4W
~ 40% of patients had data at Week 96
Time Since First Active Dose (day)
Obs
erve
d G
d+ L
esio
n Co
unt
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
Obs
erve
d G
d+ L
esio
n Co
unt
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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
PlaceboQ2WQ4WPlacebo->Q2WPlacebo->Q4W
Estimated Individual Cumulative AUC Over 4 Weeks (ng/mL*hr)
Obs
erve
d G
d+ L
esio
n Co
unt
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Some Key Features of Data
Large Proportion of Zero Lesion Count Large over-dispersion
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Candidate Models
• Poisson, Zero-inflated Poisson– ,
• Negative Binomial (NB), Zero-inflated NB– OVDP is overdispersion parameter
33
Candidate Models (cont’d)
• Marginal (Naïve Pooled) Model
• Mixed Effect Model
• Mixed Effect Negative Binomial Model– , OVDP constant
• Mixture Negative Binomial Model
– ), ), – 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
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Model ComparisonModel -2LL β SE
Poisson 21792.2 -0.0248 0.0036
ZIP 15804.0 -0.01110.0156
0.00410.0014
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 differentAUC = 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
NB = negative binomial; ZINB = zero-inflated NB; ZIP = Zero-inflated Poisson
0.0
0.2
0.4
0.6
0.8Naive Poisson
0 2 4 6 8 10
Naive NB
ZIP
0.0
0.2
0.4
0.6
0.8ZINB
0.0
0.2
0.4
0.6
0.8
0 2 4 6 8 10
Mixed NB Mixture NB
Gd+ Lesion Count
Mar
gina
l Pro
babi
lity
Model PredictionObserved
0.000
0.001
0.002
0.003Naive Poisson
10 20 30 40 50 60 70
Naive NB
ZIP
0.000
0.001
0.002
0.003ZINB
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
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Final Model Parameter EstimatesModel
Parameter DescriptionPoint
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
σ2Variance 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
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
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
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
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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 believedto 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-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)
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:
: placebo effect; : drug effect; : 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):
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
45
Predicted Outcomes for Oral Solution at Different Doses
• Dashed lines are predicted profiles• Solid lines and squares arefor 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) 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