Population PKPD Mode.. - Pharsight Corporation

Population PK/PD Modeling – The Pharsight Approach 

Daniel Weiner, Ph.D. 

Chief Technology Officer 

June 26, 2008 

© Pharsight Corporation All Rights Reserved

Today’s Presenter 

Dan Weiner 

● 

● 

● 

● 

● 

● 

● 

Expert consultant to the U.S. Food and Drug Administration (FDA) 

Executive sponsor for Pharsight’s Cooperative Research and Development Agreement 

(CRADA) with FDA 

Senior positions at Merrell-Dow, Syntex, Quintiles, IVAX and Pharsight 

Trained over 1000 scientists in PK/PD modeling 

Original author of WinNonlin® 

Coauthor of Pharmacokinetic & Pharmacodynamic Data Analysis: 

Concepts and Applications 

PhD in Mathematical Statistics 

slide 2 


Agenda 

Pharsight Company Overview 

Reporting and Analysis Services (RAS) 

● 

● 

Expertise, Workflow and Communication Plan 

Regulatory Population Pharmacokinetics Workflow 

Case Study: Population PK/PD to Support NDA Submission 

Model Building: Adding Covariates 

Model Discrimination, Evaluation and Diagnosis 

slide 3 


Pharsight Company Overview 

Helping pharmaceutical customers 

improve their drug development 

process, regulatory compliance and 

strategic decision-making. 


Who Is Pharsight? 

A company that helps pharmaceutical customers improve their drug 

development process, regulatory compliance and strategic decision-making. 

A Global Business 

● 

● 

● 

Over 100 Employees 

Two North American Headquarters 

World Wide Sales and Consulting Locations 

A Diverse And Skilled Group of People 

● 

● 

● 

Scientists (> 25 PhDs and/or MDs) 

Engineers (>15 software developers) 

Professionals (10 MBAs & JDs) 

An Established & Trusted Organization 

● 

● 

● 

● 

More than 10 years in business 

A public company (PHST) 

Over 1000 professional service engagements 

More than 2000 software customers 

slide 5 


What Are Pharsight Capabilities? 

One theme: efficient drug development 

Software 

Strategic Consulting 

Metadata 

Improve productivity and 

compliance 

Quantify your decisionmaking 

Understand the competitive 

landscape 

Enterprise and desktop products 

for analyzing, presenting and 

storing drug development data. 

Consulting expertise in modelbased 

drug development and 

decision-making. 

Modeling-ready data sets 

complied by experts from public 

source medical & scientific 

literature. 

Training 

Reporting and 

Analysis Services 

Build your capabilities 

Regulatory Compliant 

Reporting and Analysis Services 

A variety of courses teaching 

Pharsight software tools and 

model-based drug development 

skills. 

High quality NCA and population 

PK/PD analysis and reporting. 

slide 6 


Who Are Pharsight Customers? 

This is a sample from Pharsight's customer base which includes all Top 50 

Pharmaceutical companies. 

slide 7 


Where Is Our Strategic Focus? 

We provide tools and services that help our customers increase drug 

development efficiency, with a particular focus on the decisions occurring 

within the FDA’s “critical path.” 

The Critical Path 

Average time and cost per approved compound:8 years and $524M 1,2 

slide 8 

5000 250 5 1 

Discovery Pre-Clinical Clinical Approval 

$23B 

1 Dimasi, et al, "The price of innovation: new estimates of drug development costs," Journal of Health Economics, 22:2, March 2003 

2 

2005 PAREXEL R&D Statistical Sourcebook from Bain and In Vivo 

3 

2002 Estimated Global Pharma and Biotech R&D Spending by Category: BioPharm International, March 2003 

4 

PhRMA 2003 Industry Profile, March 2003 

© Pharsight Corporation All Rights Reserved 

$48B 

except where noted all numbers are estimates for industry totals per year 3,4

Reporting and Analysis Services (RAS): Expertise, Workflow 

and Communication Plan 


What is RAS? 

Pharsight Reporting and Analysis Services (RAS) is a high quality resource for 

producing the clinical pharmacology study reports that are the basis of your 

regulatory submission document. 

Common Technical Document 

This is the RAS deliverable 

Module 5 

Clinical Study Reports 

RAS is a world class organization 

● Team experience on more than 400 client 

engagements 

● Experts with Pharsight's leading PK/PD analysis 

and reporting software including WinNonlin®, 

WinNonlin AutoPilot, and other tools (e.g., 

NONMEM) 

● Experienced in all major disease indications and 

development phases 

● Business representatives in the United States, 

Europe, and Japan to serve all major drug 

development geographies. 

Module 1 

Regional Info 

Module 4 

Non-clinical Study Reports 

Module 3 

Quality 

Module 2 

Common Technical Document Summaries 

Module 1 

Regional Info 

Module 1 

Regional Info 

slide 10 


RAS Value: High Quality Clinical Pharmacology Study Reports 

RAS Quality Assurance processes ensure the quality from data collection 

through final reporting. 

The quality of our reports is guaranteed through the following components: 

● 

● 

● 

● 

Standard Operating Procedures (SOPs) for PK/PD analysis and reporting. 

Registered quality assurance professional in GLPs (RQAP-GLP) 

Use of the latest validated software for our analyses 

Analysis and Reports are QC'd by an Authenticator (Scientist #1), a Reviewer (Scientist #2) and by 

the Vice-President of RAS (Approval). 

Analytic Lab 

QA 

Pharsight RAS 

Analytic Report 

SOPs 

SOPs 

SOPs 

Acceptance 

Analysis 

Reporting 

Clinic 

QA 

Clinical Deviations 

QA 

QA 

QA 

Final 

Clinical Report 

to Sponsor 

Protocol 

slide 11 


RAS Value: Timely Analysis with Pharsight Software 

RAS leverages Pharsight’s integrated software system for the analysis and 

storage of PK data to deliver timely, auditable and cost-effective results. 

WinNonlin® AutoPilot enables Pharsight’s analysts to deliver results 80% faster than other manual 

NCA reporting methods 

IVIVC Toolkit for WinNonlin® enables Pharsight’s analyst to minimize manipulation and speed-up 

analysis and delivery of report 

Grid computing facility enables Pharsight’s analyst to use CPU intensive methods (e.g. bootstrap) 

Sponsor Data 

Final 

Clinical Report 

to Sponsor 

WinNonlin AutoPilot 

WinNonlin IVIVC Toolkit 

Mixed effects : NONMEM VI 

PKS Connector 

PKS Reporter 

Pharsight Knowledgebase Suite 

& GLP Server 

slide 12 


RAS Offers Three Analytic Competencies 

RAS scientists work collaboratively with your organization using the latest 

technology to produce and deliver timely, high quality analytic reports. 

Sponsor Data 

Pharsight RAS 

Analysis 

1. NCA 

•Preclinical 

•Phase I 

•Phase II 

2. IVIVC Formulation 

3. Regulatory Pop PK- 

PD Analysis 

Results 

Reporting 

1. Writing 

•Scientific 

•Pharmacological 

•Medical 

2. Quality Assurance 

3. Formatting 

Clinical Study 

Reports 

slide 13 


PK/PD PK/PD Expertise Expertise in in Early Early Drug Drug Development 

1) Non-Compartmental PK/PD analysis using WinNonlin ® and AutoPilot 

● PK and PD analyses and creation of Tables, Figures and Listings 

● Statistical analyses (ANOVAs, Dose-Proportionality, Steady-State Analysis) 

● Draft and Final ICHE3 Clinical Study Reports 

● PK/PD Analysis and Report 100% QC’d by two scientists (Authenticator and Reviewer) 

● QA inspection performed by a Registered Quality Assurance Professional in GLPs (RQAP-GLP). 

Plasma Concentration (ng/mL) 

1.2 

0.6 

0 

Preclinical 

• TK and PK analysis in animals 

• Allometric Scaling 

Cmax 

Phase I 

• Maximum Tolerated Dose (MTD) 

• SAD, MAD studies 

• Bioequivalence/Bioavailability 

• Food Effect Studies 

• Drug-Drug Interactions 

• Studies in Special Populations 

(renal/liver impaired) 

• QT Prolongation Studies 

Phase II 

• Dosing Requirements Studies (IIa) 

• Efficacy Studies (IIb) 

Total drug exposure (AUC 0-inf 

) CL = Dose / AUCinf IV 

CL/F = Dose / AUCinf PO 

Vss = CL x MRT IV 

Varea/F = Dose / AUCinf x λ z 

PO 

0 24 48 

Time (h) 

slide 14 


PK/PD Expertise in Early Drug Development 

2) IVIVC analysis using WinNonlin ® Toolkit to Perform Efficient Analyses 

● Modified-release formulations & super generics [505(b)2] 

● Fixed-Dose Combination Products 

● Drug Delivery systems (Transdermal, parenteral, microsphere, liposomes) 

Correlation 

1 

Cp (ug/ml) 

1.2 

0.6 

0 

0 30 60 

time (hr) 

In Vivo Release (%) 

Fastest 

Fast 

0 

Medium 

Slow 0 0.5 1 

In Vitro Release (%) 

0.5 

Percent Dissolved 

100% 

50% 

0 

Fastest 

Fast 

Medium 

Slow 

0 150 300 

time (min) 

In Vivo 

In Vitro 

slide 15 


PK/PD Expertise to Support Drug Development 

3) Population PK/PD Analysis 

● 

● 

● 

Modeling and Simulation Analysis Plan 

PK/PD Analysis using NONMEM and Supporting Figures with S-Plus 

• Model build-up Process 

• Covariate Analysis and Model Validation (bootstrap, case-deletion diagnostic, predictive check) 

• 100% QC’d (Dataset, Programs, & Outputs) by two scientists (Auth. and Reviewer) 

Population PK Report or ICHE3 Clinical Study Report 

Model Build-Up 

Covariate Analysis 

and Model Validation 

Simulations 

slide 16 


Communication Model: Single-Point Contact 

Pharsight Client 

Lead Scientist & Director of Pharmacology 

Maintain Scientific integrity 

Maintain Regulatory Compliance 

Project Manager 

Frequent status update 

Determine Priorities 

Maintain Timelines 

VP and 

Lead Scientist, RAS 

Team Leader 

Scientist #1 Scientist #2 … Scientist #3 

slide 17 


RAS: Regulatory Population Pharmacokinetics Workflow 


RAS Regulatory PK-PD Modeling 

RAS scientists use state of the art software and methods to perform 

regulatory-oriented population PK-PD data analysis. 

Regulatory Population PK-PD Modeling & Simulation Activities 

● 

Dataset construction including QC and QA activities 

● 

● 

Model Build-Up and Discrimination for Regulatory Population PK/PD Analysis 

Covariate Analysis 

● 

Model Validation (Bootstrap, Predictive Checks, Case-Deletion Diagnostics…) 

● 

Population PK Report & ICHE3 Clinical Study Report 

• Compliant with Population PK Guidances (FDA and EMEA) 

• Quality Controlled and Quality Assured 

slide 19 


RAS Typical Population Pharmacokinetics Workflow 

Sponsor Data 

Analytic Lab 

QA 

Locked SAS Dataset(s) (CDISC) 

Analytic Report 

dm.sas7bdat 

cm.sas7bdat 

RAS 

Protocol 

Sponsor 

ra.sas7bdat 

QA 

ex.sas7bdat 

Clinic 

pp.sas7bdat 

Clinical Deviations 

………….. 

………….. 

………….. 

………….. 

………….. 

Work Plan 

Protocol 

Import Data 

Merge 

Transform 

….. 

Exploratory graphs 

Detect outliers 

… 

Analysis 

1. NCA 

•Preclinical 

•Phase I 

•Phase II 

Reporting 

1. Writing 

•Scientific 

•Pharmacological 

•Medical 

2. IVIVC Formulation 

2. Quality Assurance 

Dataset 

construction 

3. Regulatory Pop PK- 

PD Analysis 

Results 

3. Formatting 

Clinical Study 

Reports 

slide 20 


Workflow: Population PK Analysis Part I (Dataset) 

SAS Dataset(s) from 

Locked Clinical Database 

NONMEM 

Dataset Construction 

QC 

Double-Coding 

or 

Construction/ 

Deconstruction 

QA 

NONMEM Dataset 

Ready for Pop PK/PD 

Analysis 

slide 21 


Different Steps to Generate an Analysis Ready Dataset 

Understand the design 

Protocol 

Read and understand 

the timeline of the 

protocol 

Schedule of Visits 

Schedule of Doses 

Schedule of PK/PD observations 

Administration data 

PK observations data 

Demographic and lab data 

(time independent) 

Randomization data 

Demographic and lab data 

(time dependent) 

These files are merged to create an analysis dataset 

slide 22 


QC/QA of the Analysis Dataset 

SAS Dataset(s) from 

Locked Clinical Database 

Import Data 

Merge 

Transform 

….. 

Exploratory graphs 

Detect outliers 

… 

dm.sas7bdat 

cm.sas7bdat 

ra.sas7bdat 

……………. 

Locked Dataset 

Ready for Pop PK 

Analysis 

Dataset 

construction 

Pharsight 

Scientist 1 

Construction 

of Dataset 1 

Authenticator 

Print and sign 

scripts verify … 

slide 23 


Scientist 2 

Deconstruction 

of Dataset 1 

Construction of 

Dataset 2 

QC 

Quality Control 

(Comparison) 

QA 

• Comparison of deconstructed 

Verification of Quality 

Dataset with source SAS files 

Control, Comparison 

• Comparison of the two datasets 

and Reconciliation 

and reconciliation 

QA 

Reviewer 

Comments QC QA 

QA 

Comments 

© Pharsight Corporation All Rights Reserved 

Quality 

Assurance

Workflow: PK/PD Modeling Part II (Analysis & Reporting) 

Stage I : Dataset 

FINAL FINAL QC’ed QC’ed 

PK/PD PK/PD Dataset 

QA 

NLME Engine 

e.g.: Phoenix NLME, NONMEM 

Stage II : Analysis 

QC 

Grid to enhance time 

of analysis 

Advanced scripting to 

ensure reproducibility 

QC 

QC QC QC 

Tables, Figures & Listings 

(Appendix and In-Text) 

WinNonlin Table Wizard 

Autopilot 

QC 

Stage III : Reporting 

ICHE3 Report 

Highly customized 

scripted graphics 

QC 

Stage IV: Finalize 

QC Report 

QA QA 

Sr. Review 

(Approval) 

slide 24 


Regulatory and Timely POP PK/PD 

Pharsight Tools and Facilities to ensure quality and speed 

Multi-disciplinary Team 

Clinical 

Pharmacology 

(FCP, MD, 

PharmD,…) 

Math & Stats 

100 % QC 

on all aspects of modeling 

Data, models and reporting 

Registered 

RQAP-GLP 

Advanced scripted 

graphics 

Reg. Affairs 

Advanced scripted 

dataset assembly (S-Plus) 

QA QA 

 

WinNonlin Table Wizard 

and Autopilot 

Computing Facility 

(Grid) 

Timely analysis and reliable reporting 

Stage V: Archive and Share 


Knowledgebase 

Server 

Model and data storage 

Secure Warehouse and 

convenient sharing with 

Regulatory agencies 

slide 25 


Case Study : Population PK/PD to Support NDA Submission 


PK Data 

PK from PHASE I, II and III studies 

Phase I 

Phase II 

Phase III 

Single/Multiple Dose Single/Multiple Dose Multiple Dose 

Time of exposure 

Richness in PK samples 

slide 27 


PD Data 

Efficacy and Safety from PHASE II/III studies 

Phase I 

Phase II 

Phase III 

Multiple Dose 

Sparse PK 

Three Efficacy endpoints 

Two Safety endpoints 

slide 28 


Typical POP PK Model Development Workflow 

Developing the Base PK Model 

Structural Model 

How many compartments 

are needed for disposition ? 

What input function can 

describe the absorption ? 

Statistical Model 

Deterministic 

Component 

⎡θ 

⎤ 

1 

Θ= 

⎢ 

θ 

⎥ 

⎢ 

2 ⎥ 

⎢θ 

⎥ 

3 

⎣ 

⎦ 

Disposition function 

One-Two-or Three-compartments 

Non-linearities, target-mediated… 

Input function 

What random effects on 

parameters are needed or 

supported by the data ? 

What residual variability 

model to use ? 

Stochastic 

Component 

Between subject variability (BSV) matrix 

Distributional assumption (Log-normal) 

Full Block 

Full Diagonal 

Reduced 

Residual variability model 

Additive, proportional, combined 

⎡Ω11 

Ω= 

⎢ 

⎢ 

Ω Ω 

⎢⎣ 

0 0 

⎡σ 

12 22 

⎤ 

11 

Σ= ⎢ 

0 σ ⎥ 

22 

⎣ 

⎦ 

⎤ 

⎥ 

⎥ 

Ω ⎥ 

33 ⎦ 

slide 29 


Examples of GOF Plots 

Note the smooth predictions at times with no observations 

Phoenix NLME generates these very efficiently 

slide 30 



Covariance needed between Eta’s ? (Plot from run with diagonal Omega) 

-0.8 -0.3 0.2 0.7 

1 

ETA1 

-0 

-1 

-2 

0.7 

-3 

0.2 

ETA2 

-0.3 

-0.8 

0.75 

0.50 

ETA3 

0.25 

0.00 

-0.25 

-3 -2 -1 -0 1 

-0.50 -0.25 0.00 0.25 0.50 0.75 

-0.50 

slide 31 



Cobs 

0 100 200 300 

IDENT 

LOESS 

Cobs 

0 100 200 300 

IDENT 

LOESS 

WRES 

-6 -4 -2 0 2 4 6 

ZERO 

LOESS 

WRES 

-6 -4 -2 0 2 4 6 

ZERO 

LOESS 

0 50 100 150 200 

0 50 100 150 200 250 300 

0 50 100 150 200 

0 20 40 60 

PRED 

IPRED 

PRED 

Time after dose 

Cobs 

0 100 200 300 

LOESS PRED 

LOESS Cobs 

WRES 

-6 -4 -2 0 2 4 6 

ZERO 

LOESS 

CWRES 

-6 -4 -2 0 2 4 6 

ZERO 

LOESS 

CWRES 

-6 -4 -2 0 2 4 6 

ZERO 

LOESS 

0 20 40 60 

0 500 1000 1500 2000 

0 50 100 150 200 

0 20 40 60 


TIME 

PRED 


slide 32 


Model Building : Adding Covariates 



Developing a Covariate Model : Examples of Covariates 

•Demographics 

● Sex, Race, Size (weight, height, BSA, IBW, BMI, …) 

•Lab values 

● Renal function : Serum creatinine 

● Liver: bilirubin, albumin, AST, ALT, … 

● pheno/genotype 

Disease severity, Co-medication, smoking etc. 

slide 34 


Summary of Model building 

Absorption Model 

Disposition Model 

⎡θ1 

⎤ 

⎢ 

θ 

⎥ 

Θ= ⎢ 

2 ⎥ 

⎢⎣ 

θ ⎥ 

3 ⎦ 

Deterministic 

Component 

⎡Ω11 

Ω= 

⎢ 

⎢ 

Ω Ω 

⎢⎣ 

0 0 

12 22 

⎡σ 

Ω 

33 

⎤ 

⎥ 

⎥ 

⎥⎦ 

⎤ 

11 

Σ= ⎢ 

0 σ ⎥ 

22 

⎣ 

Between subject variability Matrix 

⎦ 

Residual error model 

Stochastic 

Component 

Covariate Model Building 

Base Model 

slide 35 



Developing a Covariate Model : Stepwise Model Building 

Proceed with next step 

of covariate addition 

Important Covariates (GAM) 

Forward Stepwise Addition 

Graphs of WRES/CWRES and etas 

vs 

Covariates : Weight, Sex, CRCL 

Repeat until no 

covariate Covariate is Model significant Building 

Tentative Model 

With Covariates 

or 

Test each on PK parameters 

one by one : 

Weight and Sex on Vd 

Weight, Sex, CRCL on CL 

Keep the most 

Significant 


Model + Covariate 

slide 36 



Developing a Covariate Model : Backward Elimination 


Backward Deletion 

Remove covariates 

one by one by reverse order : 

Weight and Sex on Vd 

Weight, Sex, CRCL on CL 

Repeat until no 

covariate can be 

removed 

Proceed with Model 

Validation and Evaluation 

Final Model 

Tentative Final Model 


slide 37 



Developing a Covariate Model : Multiple Covariates on a Parameter 

0.75 

⎛WEIGHT 

⎞ 

SEX 

TVCL= θ 

CL 

⋅⎜ 

⎟ ⋅ 

L / h 

⎝ 75 ⎠ 

( θ 

CL, SEX ) { } 

Blue denotes population parameter 

Red is a patient specific covariate 

Black is a constant usually the mean or the median are used 

Usually a linear multiplicative model with no interactions is used. 

This parameterization is easily interpretable 

TVCL is the clearance for a subject with median weight with SEX=0 

It is always useful to have a realistic typical patient when we have multiple 

covariates on a single parameter 

slide 38 


Examples of Graphs to Aid Covariate Model Building 

Explore collinearity between covariates 

19 

17 

15 

13 

11 

70 

60 

50 

40 

30 

20 

0.45 

0.20 

-0.05 

-0.30 

-0.55 

-0.80 

CRCL 

0 50 100150200250 

11 13 15 17 19 

MTX 

HT 

150 160 170 180 

20 30 40 50 60 70 

AGE 

WT 

40 60 80 100 120 

-0.80 -0.55 -0.30 -0.050.20.45 

ETACL 

ETAKA 

-3 -2 -1 -0 1 

250 

200 

150 

100 

50 

0 

180 

170 

160 

150 

120 

100 

80 

60 

40 

1 

-0 

-1 

-2 

-3 

slide 39 


Summary of Model building 

Absorption Model 

Disposition Model 

⎡θ1 

⎤ 

⎢ 

θ 

⎥ 

Θ= ⎢ 

2 ⎥ 

⎢⎣ 

θ ⎥ 

3 ⎦ 

Deterministic 

Component 

⎡Ω11 

Ω= 

⎢ 

⎢ 

Ω Ω 

⎢⎣ 

0 0 

12 22 

⎡σ 

Ω 

33 

⎤ 

⎥ 

⎥ 

⎥⎦ 

⎤ 

11 

Σ= ⎢ 

0 σ ⎥ 

22 

⎣ 

Between subject variability Matrix 

⎦ 

Residual error model 

Stochastic 

Component 



Final Model 


Model Evaluation 

slide 40 


Model Discrimination, Evaluation and Diagnosis 


Model Evaluation/Diagnosis ? 

• Assumption Checking 

•Evaluation Methods 

• Parameters 

• Predictive Performance 

• Sensitivity Analysis 

slide 42 


What Can We Evaluate ? 

• The different parts of the model 

– Structural PK-PD model 

– Covariate-parameter relationships models 

– Random effect models 

- Residual variability model 

• The performance of model-based inferences 

– Parameter estimates & confidence intervals 

– Hypothesis tests 

• Explore the data (EDA) 

• Follow the objectives 

• Keep the model plausible 

• Understand and check the 

assumptions and limitations 

• Define useful decision making 

criteria 

•Diagnosis can include a set of 

plausible models 

– Predictions/simulations with model 

slide 43 


How Can We Evaluate ? 

• Assumption Checking 

● 

● 

Randomization tests for the p-values 

Graphics for distributional assumptions (Residuals, empirical Bayesian estimates, …) 

• Stability/precision of parameter estimates 

● 

● 

● 

● 

Validation through parameter prediction errors 

Log-Likelihood Profile 

Bootstrap (parametric & non-parametric) 

Cross-Validation/Leverage analysis 

• Assessment of model performance/properties 

● 

● 

● 

Prediction errors (from internal or external test set) 

Posterior Predictive Check/ Predictive Check/ Visual / Numerical / Quantitative 

Sensitivity Analysis 

Karlsson et al. Assumption testing in population pharmacokinetic models: illustrated with an 

analysis of moxonidine data from congestive heart failure patients. J PK B 26(2):207-46 1998. 

EI Ette. Population Model Stability and Performance. J Clin Pharmacol 37:486-495 (1997). 

slide 44 


When to use diagnostics ? 

● 

● 

● 

Basic 

• Confirm convergence : numerical checks 

• Check if we had some improvement (OFV lower, BSV on parameter lower, residual 

variability lower…) 

Key runs 

• Unusual covariate detected : confirm with randomization test 

• Depends on the importance of the run 

Final run 

• Extensive diagnostics 

• Check if we have influential individuals 

♦ Individual contributions to OFV + fits with and without the suspect individuals 

♦ Case deletion diagnostics, Jackknifing 

• Check if we have outliers ( data with |WRES| > 4) compare fit with and without outliers 

• Check if parameters are precise not on a boundary and plausible 

♦ Standard errors may be obtained 

- Asymptotically from covariance step: always symmetric may contain impossible 

values 

- From bootstrap: time consuming 

- From likelihood profiling : time consuming poor if LRT not applicable and if 

likelihood approximation is far from the true likelihood 

• Check if the model describe the observed data well (PPC) 

slide 45 


What to use in diagnostics ? 

● 

● 

● 

Residuals 

• RES = DV-PRED 

• IRES = DV-IPRED 

• IWRES=IRES/SD(residual variance) 

• WRES are based on FO approximation and fails when FO fails ( high non linearity, sparse 

data) 

• CWRES are based on FOCE approximation and have better properties 

Simulation Based Residuals or Prediction Discrepancies 

• Prediction discrepancies (PD) which are the quantile of each observation within its 

simulated distribution 

• Normalized Prediction distribution errors (NPDE) ( decorrelated, then normalized) 

Empirical Bayesian Estimates (EBE) 

• IWRES=IRES/SD(residual variance), residual variability diagnostics 

• IPRED are based on individual parameters, structural model diagnostics 

• Are used in the estimation process (FOCE) 

• Are used as initial support points for a non-parametric engine (Leary’s Method) 

• May suffer from shrinkage ( It is advisable to report shrinkage in plots and reports) 

slide 46 


What to use in diagnostics ? 

● 

⎡Ω11 

Ω= 

⎢ 

⎢ 

Ω Ω 

⎢⎣ 

0 0 

Simulation Based Diagnostics 

• Posterior Predictive Checks 

1 

Θ= 

⎢ 

θ 

⎥ 

⎢ 

2 ⎥ 

⎢θ 

⎥ 

3 

12 22 

⎡σ 

♦ 

♦ 

♦ 

♦ 

♦ 

Ω 

33 

⎤ 

⎥ 

⎥ 

⎥⎦ 

⎤ 

11 

Σ= ⎢ 

0 σ ⎥ 

22 

⎣ 

⎡θ 

⎤ 

⎣ 

⎦ 

⎦ 

Select a statistic of interest that a good model should not miss (e.g. AUC, 

Cmax, etc) and that can be derived from the raw data 

Simulate many data sets from the model (with uncertainty, TS2.2) 

Calculate the statistic from the N simulated data and J Replicates 

Calculate the statistic from the observed data 

Compare the statistic from raw and simulated data 

⎡Var 

⎤ 

⎢ 

Cov Var 

⎥ 

VARCOV = ⎢ 

⎥ 

⎢ Cov Cov Var ⎥ 

⎢ 

⎥ 

⎣Cov Cov Cov Var⎦ 

Draw N Parameters form the 

final estimates and Variance 

Covariance Matrix 

Simulate Data according 

to the design of the study 

and compute the statistic 

Compare the statistic 

from raw and simulated 

data 

If we ignore parameter uncertainty this reduces to predictive check 

slide 47 


Example of a likelihood profile 

-200.000 

Llikelihood Likelihood profile Profile for for propafenone Covariate Effect effect 

-201.000 

-201.581 

-202.000 

OFV value 

-203.000 

-204.000 

Delta OFV= 3.84 

-205.000 

0.167 

-205.42 

0.422 

0.15 0.20 0.25 0.30 0.35 0.40 0.45 

Propafenone Covariate Effect effect 

slide 48 


Example of predictive check 

Drug ROP Men 1 Men Drug ROP 1 Women Drug BUP 2 

Concentrations and predictions in "mg/L" 

2.0 

1.5 

1.0 

0.5 

90 % PI 

Cobs 

PRED 

2.0 

1.5 

1.0 

0.5 

90 % PI 

Cobs 

PRED 

2.0 

1.5 

1.0 

0.5 

90 % PI 

Cobs 

PRED 

0.0 

Vd/F=366 L 

0.0 

Vd/F=208 L 

0.0 

0 5 10 15 20 25 30 

0 5 10 15 20 25 30 

0 5 10 15 20 25 30 

TIME "Hr" 

TIME "Hr" 

TIME "Hr" 

slide 49 


Contact and Follow-Up: Thank you! 

James Hayden 

Senior Vice President, Global Sales 

Email: jhayden@pharsight.com 

Telephone: +1-650-314-3760 

Internet Site (www.pharsight.com) 

slide 50 


Proprietary Notice 

● All contents Copyright © 2008 Pharsight Corporation. All rights reserved. The 

copyright for this document is owned by Pharsight Corporation. 

● No part of this document may be reproduced or transmitted in any form or by 

any means, electronic or mechanical, including photocopying, for any 

purpose, without the express written permission of Pharsight Corporation. 

● WinNonlin, WNL, WinNonMix, WNM, Trial Simulator, TS2, Pharsight 

Knowledgebase Server, PKS, Drug Model Explorer, DMX and Pharsight are 

trademarks or registered trademarks of Pharsight Corporation. 

● All other brand and product names are trademarks or registered trademarks 

of their respective holders. 

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Population PKPD Mode.. - Pharsight Corporation

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