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

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

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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

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

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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

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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

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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

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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

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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

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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

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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

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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)

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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):

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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

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Predicted Outcomes for Oral Solution at Different Doses

• Dashed lines are predicted profiles• Solid lines and squares arefor 50 mg rofecoxib as reference

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Results from a Subsequent Clinical Study Comparing Oral Solution SC-75416 and

Ibuprofen

Vioxx was withdrawn by the time they conducted the next study

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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

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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