Statistics and modelisation for QbD

1

2eme Masters ISSBA 2010

Angers, the 3d of February 2010

Quality by Design

Statistics and Modelisation in Pharmaceutical Development

Alain Poncin

LFB Biotechnologies

Process Development Unit Manager

2

Introduction

3

Professional Experience

█ 1988 : MSc in Biochemistry, University of Liege

█ 1988 – 2008 : Eurogentec (Belgium)2 Business Units : Reagents and Tools for Research

Contract Research Organisation (CMO)

Development of more than 70 proteins in

Clinical trials (Phase I to IV)

█ 2008 - 2010 : LFB Biotechnologies (France)2 Companies : LFB Biomedicaments : Plasma fractionation

LFB Biotechnologies : mAbs and transgenic animals

Development of production process for TG

Introduction of QbD

█ March 2010 - : Protaffin (Austria)Small Biotech, production of recombinant proteins in e. Coli

4

Expertise in QbD

█ Implementation of QbD in Down Stream Proces for plasma derived recombinant proteins.

A.Poncin, P. Paolantanocci, M. Ollivier

Web Seminar PDA on Quality by Design, 3 March 2010.

█ Study of the anion Exchange chromatographic step operating conditions of the new IgG manufacturing process-Characterisation by Design of Experiment.

P. Paolantanocci, D Gachelin, S. Nakache, A.Poncin, A. Sauger, M. Ollivier

Plasma Product Biotechnology, 11-15 May 2009, Menorca, Spain.

█ Risk Assesment and DoE must be used in sinergy for Quality by Design succes. A. Poncin

PDA conference on Quality by Design, 7-8 October 2008, Frankfurt, Germany

█ Eurogentec current validation strategy A. Poncin

5th International conference on HIC/RPC chromatography, 2007 Interlaken

5

Pharmaceutical Development

Preclinical

From Drug discovery to animal testing

(Toxicology)

Phase I Phase II Phase III

Safety Safety

Efficacy

Efficacy

DoseIND/IMPD

(First in Man)

(e)CTD

(AMM)

Commercial

Process Development Production

Laboratory GMPValidation

3 Batches

Traditionnal Development

(Minimal Approach)

Phase IV

PharmacoVigilance

Process Design QualificationContinuous Verification

Enhanced Quality by Design Approach

6

Enhanced Quality by Design Approach

Preclinical Phase I Phase II Phase III Phase IV

Process Design QualificationContinuous Verification

Product Target Quality Profile

Potential Critical/Key Quality Attributes

Process

Design

Potential Critical/Key Parameters

Design SpacePrior Knowledge

ScienceDoE

Risk Management (wc)Critical/Key Parameters

Critical/Key Quality Attributes

Control Strategy

7

Statistics and Modelisation


Product Life Cycle

Process DevelopmentDoE : Factorial DesignIdentification of Critical Parameters

Design-Expert® SoftwareHCP peak

Error from replicates

Shapiro-Wilk testW-value = 0.992p-value = 0.968A: LoadB: Flow rateC: GradientD: pHE: Particle size

Positive Effects Negative Effects

Half-Normal Plot

X2: Half-Normal % ProbabilityX1: |Standardized Effect|

0.00 88.26 176.53 264.79 353.05

010

20

30

50

70

80

90

95

99

A

C

E

8



Product Life Cycle

Process OptimisationDoE : Response Surface ModelOptimisation and ModelisationIn silico modelisationTo establish Range and Specifications

Design-Expert® Software

YieldDesign points above predicted valueDesign points below predicted value96.8

0

X1 = A: Factor AX2 = B: Factor B

0.00

0.50

1.00

1.50

2.00

0.00

12.50

25.00

37.50

50.00

-20

15

50

85

120

Y

ield

A: Factor A B: Factor B

9



Product Life Cycle

Process CharacterisationScale Down ValidationDoE : Factorial DesignDemonstration of Range and Specifications Definition of Design Space

Sequential Model Sum of Squares [Type I]Sum of Mean F p-value

Source Squares df Square Value Prob > FMean vs Total 3,8571 1 3,8571 12,432 0.0021 SuggestedLinear vs Mean 12,6390 15 0,8426 8,3612 0.15022FI vs Linear 0,3256 2 0,1628 2,7393 0.2105Quadratic vs 2FI 0,0594 1 0,0594 1,0000 0.4226Cubic vs Quadratic 0,1189 2 0,0594 1,0000 0.4226

10



Product Life Cycle

Process Validation/characterisationMultivariate AnalysisDemonstration of scale up andreproducibility

1 2 3 4 5 6 7

50 kDa

30 kDa

20 kDa

15 kDa

1 L

350 L

Analysis of Variance for EFT - Type III Sums of Squares Source Sum of Squares Df Mean Square F-Ratio P-Value MAIN EFFECTS A:Scale 0,00666667 1 0,00666667 0,02 0,8842 RESIDUAL 1,10667 4 0,276667 TOTAL (CORRECTED) 1,11333 5

Analysis of Variance for Viable cells - Type III Sums of Squares Source Sum of Squares Df Mean Square F-Ratio P-Value MAIN EFFECTS A:Scale 0,0266667 1 0,0266667 0,18 0,6965 RESIDUAL 0,606667 4 0,151667 TOTAL (CORRECTED) 0,633333 5

Analysis of Variance for Expr level - Type III Sums of Squares Source Sum of Squares Df Mean Square F-Ratio P-Value MAIN EFFECTS A:Scale 0,00666667 1 0,00666667 0,40 0,5614 RESIDUAL 0,0666667 4 0,0166667 TOTAL (CORRECTED) 0,0733333 5

11



Product Life Cycle

Continued Process Verification Multivariate Analysis Graph Plot

X-bar Chart for Protéines-Rendement

0 20 40 60 80 100 120

Subgroup

-8

-4

0

4

8

12

16(X 10000,0)

X-b

ar

CTR = 26045,57UCL = 124007,09

LCL = -71915,95

12

UMFP - formulation


Product Life Cycle

Empirical development

Qualitative Justification (//Factorial)

Quantitative Justification (//RSM)

13

Analytics/Quality Control


Product Life Cycle

Development Validation Qualification (?) (including Robustness by DoE)

14

All that in a highly regulated environment

(EMA, FDA, ICH,…)

15

Regulation in the 20th Century : Reactivity

█ A long list of accidents linked to drugs1902 : Biologics Control Act, creation of CBER (US, 13 children dead))

1930 : Creation of the FDA agency (US, 107 adults dead)

1950 : First publication of FDA (Guidance for Industry)

1960 : Europe : thalidomide : 10,000 malformed children

Modern drugs are highly active, but also in a wrong way Initiation of regulation (EMA, FDA,…)

Acceleration (1960-1980)

Rationalisation (1980-1990), release of GMP guidelines

Harmonisation (199O, birth of ICH)

█ No Change

█ Still one of the most unsuccessfull industry Only 10 % of success between pre-clinical and market

16

Regulation in the 21th Century : science based

█ Bill Clinton‘s hobby horseSafe, effective and accessible drugs for all US citizen

Government responsibles for both regulation/accessibility

Complete reorganisation of FDA2002 : Pharmaceutical Industry for the 21th century

PAT 2004 Quality system, September 2006 OOS, October 2006…

█ ICH : Quality by Design (QbD) ICH Q8 : Pharmaceutical Development (2005), annex (2007), R1 (2007), R2 (2009) ICH Q9 : Quality Risk Management (2005) ICH Q10 : Pharmaceutical Quality System (2008) ICH Q11 : Development and Manufacture of Drug Substance (concept paper, 2008, draft expected

in 2010)

█ FDA : Process Validation : General Principle and Practices (draft 2008)

█ Freedom to operate in the Design Space

17

Regulatory and Science

18th century 1946 1985

(De Moivre) (Placket Burman) FMEA

Normal Law DoE

1944 1960 1988

Monte Carlo Simulation Bayesian Statistics (Harry)

Six Sigma

2000

Neuronal Network

2005 2006 2009(?)

ICH Q8 ICH Q9 FDA

validation

QbD In Place in LFB Training

(SOP, training)

To be extended

Regulatory

Phamaceutical development becomes a modern Science

18

In other industries : Quality is a long story

█ Starting in the 13TH century (craftsmen and guilds)

█ 1750-1900 : industrial revolutionFrom guilds copy to supervisor and engineersTarget : increase productivity with stable employmentCreation of Inspection DepartmentWhen a faulty product reached a customer :

Why did we let this product get out? Why did we make it this way?

19

Quality in the 20th centuries (1/2)

█ 1900 – 1920 : notion of Input Process Output

█ 1940 : World war II Bullets manufactured in one state must fit with Rifles assembled in other states

Manual inspection of all products Statistical analysis of samples

█ 1945 : end of WWII, reconstruction of Japan economyVery disappointing results

Japonese product = poor quality = gadget

Deming/Juran (US citizen) build new Quality Systems (Total Quality Management) Quality results from organisational process Successfully used for automobile, electronic,…

█ Success of Japanese industry became a serious threat for US Economy If Japanese can, why can’t we ?

20

Quality in the 20th centuries (2/2)

█ 1986 : Methodology Six Sigma (Motorola) : DMAICBased on customer’s satisfaction

< 3.4 defect/1 000 000

█ 1987 : Release of Iso 9000 Reaction against Japanese success

Reviewed in 2000 (Iso9000:2000)

█ 1987- Evolution of Six Sigma and ISO (alone or combined)DFSS, Lean Six Sigma, Toyota Way,, …to Process Ninja

Avoid Muri (overworked men or overstrechted equipment) Due to Mura (inconsistency, irregular production) To decrease Muda (waste, wrong product) In a Kaizen (continuous improvement) spirit

21

Cost of Low Quality

█ real cost of low quality = 10 x cost of known defects/failures

2006 2007 2008 2009

Cost of Quality History

0

400

800

1200

1600

CO

Q

PreventionAppraisalInt. FailureTotal COQTotal Failure

22

Six Sigma (6several methodologies

█ DMAIC (existing Product/Process)Define

Mesure

Analyse

Improve

Control

█ DFSS (Design For Six Sigma)DCOV : Define, Characterize, Optimize, Verify

IDOV : Identify, Design, Optimize, Validate/verify

IDDOV : Identify, Define, Develop, Optimize, Verify

DFSS : Software

█ Lean Six Sigma : ‘’Lean’’ manufacturing and Six Sigma

Will be used to organize this presentation

23

Six Sigma organisation

█ Six Sigma training is certifiedYellow Belt : Technical Staff

Green Belt : Project Manager

Black Belt : Head of Department (Operational Excellence,…)

Master Black Belt : Trainers

█ Expensive (5000 – 10 000 $/ level) and time consumming (1 – 2 weeks/level)

█ Main difficulty : statistical part

24

Statistics

Normal Law and basic tests

25

Normal law

█ A long story :

DeMoivre, 1667-1754 : description of games of chance (money)

Laplace, 1749-1827 and Gauss, 177-1855 : errors in astronomical calculations

Quetelet, 1796-1874 : biological and social data

Galton, 1822-1911 : psychological data

█ Reasons of success :

Easy (as compared to other laws or non parametric analysis)

Law of large number (central limit theorem)

random error distributed following a normal law

26

Normal law presentation

█ Normal law :

defined by 2 parameters average (mean), m or standard deviation, s.d or

█ several graphical illustrations :

non cumulative

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0 5 10 15 20 25 30

X

Pro

bab

ility

cumulative

0

0,2

0,4

0,6

0,8

1

0 5 10 15 20 25 30

X

Cum

ulat

ive

prob

abili

ty

22/2.

2.

1)(

xexf

0,00%10,00%20,00%30,00%40,00%50,00%60,00%70,00%80,00%90,00%

100,00%

0 5 10 15 20 25

X

Pro

babi

lity

-6

-4

-2

0

2

4

6

Log

it(p

roba

bili

ty)

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Normal law : average and s.d

Normal law

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

-10 0 10 20 30 40 50

X

Prob

abili

ty

Average : x position s.d : width

Normal law

0

0,1

0,2

0,3

0,4

0,5

0,6

0 5 10 15 20 25 30 35

X

pro

bab

ility

s.d=2,8 s.d=1,4 s.d=0,7

Area under the curve = 1

28

Standard/studentised Normal law

Standard normal law :

0

0,1

0,2

0,3

0,4

0,5

-10 -5 0 5 10 15 20 25 30 35

X

prob

abili

ty

Normal distribution standard normal distribution

average = 0

s.d. = 1 = varianceTable : probability versus z

29

Outliers

0

0,01

0,02

0,03

0,04

0,05

0,06

0,07

0,08

0,09

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

pro

bab

ility

99 %1 s.d. : 64 %

2 s.d. : 95 %

3 s.d. : 99 %

…….

6 s.d. : 99.99996%

6defects/millions

30

Outliers

█ Outliers : soundly studied

allowed detection of Mars’ satellites

economic (stock exchange, speculation,…..)

military (radioactivity,…)

never delete outliers without careful studies (can mask unexpected effect)

31

t test

█ Comparison of two groupsCalculation of average and s.d. of group values

Intersection of P9X confidence interval

00,020,040,060,080,1

0,120,140,16

0 5 10 15 20 25 30 35 X1 X20

0,2

0,4

0,6

0,8

1

0 5 10 15 20 25 30 35 X1 X2

32

ANOVA

█ Comparison of several groups

several presentations : values

Bar graph (Nested)

Line (DOE)

TableTable

33

Define

34

Define : 6

█ Define : ‘’The Customer’s Voice’’Your customer (internal or external)

General customers (‘’supermarket’’), Head of Production,…

Your target (if the market is segmented) Male 40-50 years old, teenagers,…

Their requirements to be satisfied (and encourage them to buy your product, your project,..)

Quality, Price, Special requirements,…

Your objectives, your goals, the product characteristics Memory > 4 mb, autonomy > 48h, productivity > 20%...

The way you will quantify the success of the product, of the project

█ In Pharmaceutical Industry : QbD : ICH Q8(R2)Quality Target Profile (intended use, route of administration, dosage strength,…)Drug Product Quality CriteriaPotential Critical Quality AttributesControl Strategy

35

Define : examples of tools

█ 1- Process Map

Preculture Fermentation Harvest Filtration Chromatography 1 Viral inactivation

Chromatography 2UltrafiltrationNano filtration Chromatography 3Vialing 0.22 µm filtration

Process Flow Chart

36


█ 2- Ishikawa fishbone

37


█ 3- Quality Function Deployment

InteractionsStrong PositivePositiveNegativeStrong Negative

Viru

s

Bio

burd

en/

End

otox

ins

Re

sidu

al D

NA

HC

P

Oxy

dise

d/d

eam

idat

ed

form

s

Mu

ltim

ers/

aggr

egat

es

Pos

t Tra

duct

ionn

al M

odifi

catio

ns

Re

sidu

al S

/D

Re

sidu

al P

rote

in A

De

grad

atio

n

Yie

ld

Re

prod

uci

bilit

y

Prio

rity

Safety 10

Efficacy 8

Low cost 6

Absolute weight 19 11 11 13 15 19 19 11 13 13 15 9 24

Relative weight 152 104 104 120 132 168 168 104 120 116 108 72 120

Fre

e

Ste

rile

an

d a

pyr

ogen

< 1

00 p

g/do

se

< 1

00 p

pm

< 1

%

Co

mpe

titor

Sta

y eq

uiv

alen

t

TB

D

< L

OD

No

vose

ven

> 1

g/L

Re

prod

uci

ble

Design requirements

Cus

tom

er

De

man

ds

Relationship :

Strong = 9.0 Medium = 3,0 Weak = 1,0

Development Target :

Decrease

Maintain

Increase

38

‘’Define’’ in QbD

█ Define the Target Product Profile (TPP)Based on prior knowledge, literature (including patents), the expected dosage,

way of administration,….establish the Target Product Profile

Example :

Protein X is a recombinant coagulation factor produced in the milk of transgenic animals to treat bleeding episodes in Hemophilia patients with inhibitors. It will be administrated by IV injection at 100 µg/kg.

█ From TPP identify potential Critical Quality Attributes (CQA) and the way to analyse/quantify them.

█ Rank the potential CQA (Risk Assesment for Product)

39

Potential CQA

Potential Quality Attribute

Product related Process related

Bioactive contaminants Contaminants without

Biological activity

Criticality Determination Safety assesment

Control Strategy and provisional Specifications

40

Potential CQA : example

Type Impurities Potential effect Analytical Tool Provisional specifications CommentsGlycosylation variants Modification of half life MS-HPLS must stay comparable

ImmunogenicityDes-Gla variants Lower activity MS-HPLC > 9 Gla domainsDeamidation Not known IEX-HPLC must stay comparableAggregates Immunogenicity SE-HPLC < 3 %Degradation Lower activity SE-HPLC Comparable to competitor

SDS-PAGEVirus Contamination / Free validation of viral clearanceBacteria Contamination Sterility SterileEndotoxins Fever to anaphylactic LAL < 5 EU/mgHCP Immunogenicity ELISA < 5 ppmanimal related protein Immunogenicity ELISA < LODDNA ? qPCR < 100 pg/doseresidual solvent stability/tolerance specific test < 0,5 mg/Lresidual detergent stability/tolerance specific test < 50 mg/Lparticles stability/tolerance Visual Free

Product related

Bioactive Process Related

Process without bioactivity

41

Classification of potential Quality attributes

A-Mab : a Case Study in BioProcess Development, CMC Biotech Working Group, 30th October 2009.

█ Tool 1 : criticality is evaluated using a risk ranking approach (ICHQ9) which assesses the possible impact of each potential attribute on safety and efficacy.

The ranking is determined by the IMPACT and the UNCERTAINTY

█ Tool 2 : criticality is also evaluated using a risk ranking approach (ICHQ9) which assesses the possible impact of each potential attribute on safety and efficacy.

The ranking is determined by the SEVERITY and the LIKELIHOOD

█ Tool 3 : Impurity Safety Factor (ISF)

ISF = LD50 (or MRL) / Level in product dose

LD50 : Lethal Dose for 50 % of animals

MRL : Maximum Residue Limit

42

Tool 1 : IMPACT and UNCERTAINTY

Impact (Score) Efficacy PK/PD Immunogenicity Safety

Very High = 20 Very significant change

Significant change on PK

ATA detected and confers limits on safety

Irrevesible AES

High = 16 Significant change

Moderate change with impact on PD

ATA detected and confers limits on efficacy

Reversible AES

Moderate = 12 Moderate change

Moderate change with no impact on PD

ATA detected with in vivo manageable effect

Manageable AES

Low = 4 Acceptable change

Acceptable change with no impact on PD

ATA detected with minimal in vivo effect

Minor AES

None = 2 No change No impact on PK/PD

ATA not detected No AES

AES : Adverses Events, ATA : Anti Therapeutic Antibody

43

Tool 1 : IMPACT and UNCERTAINTY

Uncertainty Description (variants and HCP)

Description (Process Raw Material)

Very High = 7 No information (new variant) No information (new impurity)

High = 5 Published external literature for variant in related molecule

---

Moderate = 3 Non clinical or in vitro data with this variant, (data in vitro, non clinical or clinical from similar class

Component used in previous process

Low = 2 Variant present at same level in batches used in clinical trials

---

Very low = 1 No impact of specific variant present at higher level in batches used in clinical trials

GRAS or studied in clinical trials

GRAS : generally recognised as safe

44

Tool 1 : example

█ Potential CQA : glycosylation variantsThe potential biological affect depends of the variation of glycosylation

Immunogenic variants : high mannose and 1-3 gal-gal Modified half life mono-sialic < di sialic terminal glycans

Impact score Biological efficacy : moderate change = 12 PK/PD : significant change on pK =20 Immunogenicity : ATA detected and confer limits on safety =20 Safety : Irreversible AES = 2 Highest Impact score = 20

Uncertainty Published external literature : High = 50

Criticality (Risk score) = 20 x 5 = 100

45

Tool 2 : SEVERITY AND LIKELIHOOD

Severity score

Severity (impact to Product Efficacy and Patient Safety)

9 Very High-death, microbiology related infections, hypersensitivity immune reaction

7 Bleeding not stopped due to lower efficacy or serious immune response

5 Moderate immunogenicity or reduction in efficacy

3 Low immunogenicity potential or small reduction in efficacy

1 Very Low – no mesurable impact

46


Likelihood score

Likelyhood of severity

9 Very High

7 High

5 Moderate

3 Low

1 Very Low or never observed

47

Tool 2 : example

█ Potential CQA : glycosylation variantsThe potential biological affect depends of the variation of glycosylation

Immunogenic variants : high mannose and 1-3 gal-gal Modified half life mono-sialic < di sialic terminal glycans

Severity Bleeding not stopped due to lower efficacy or serious immune response = 7

Likelihood Initial : High = 7

Criticality (Risk Priority Number) = 7 x 7 = 49

48


Likelihood score

Likelyhood of severity

9 Very High

7 High

5 Moderate

3 Low

1 Very Low or never observed

49

Tool 3 : Impurity Safety Factor

█ Example : residual Solvent : MRL < 0.5 mg/L1 dose : 7 mg = 7 ml.

Maximum detergent = 0.0035 mg = 3.5 µg/dose

[solvent] for S/D viral clerance = 1 % = 10 g/L = 106 µg/L

At this step : 10 L of product for 10 00 doses = 107 µg/10 000 dose

• if no clearance (copurification) : 103 µg/dose

• ISF = 3.5/103 = 10-2.45

50

Product Quality Risk Assesment Summary

pCQA Tool #1 Tool #2 Tool #3 Potential process step

Control strategy

Glycosylation variants

100 49 / / Pooling strategy MS-HPLC

Des-Gla variants 36 12 / IEX, Ca elution

a/Ag, SDS

Virus free 100 49 / 2 viral clearance

Validation of viral clearance

… … … …

Detergent / / 10-2.45 AEX Quantification of detergent

51

Product Quality Risk Assesment Summary

█ Continuum of risk scoreFrom high risks which require a priority evaluation to low risk which may be

adressed later on.

Needs to establish internal policy : what is acceptable, what is not

█ Not fixedEvolution due to better understanding (clearance studies), better control

█ Allow to draw basic requirements for process and early justification of the steps to investigate

52

From pCQA to process development

Preculture Fermentation Harvest Filtration Chromatography 1 Viral inactivation

Chromatography 2UltrafiltrationNano filtration Chromatography 3Vialing 0.22 µm filtration

Figure 1 : Process Flow Chart

53

And justification of steps to develop

█ Simplified QFD Matrix (from EMeA Mock Dossier Examplain)

54

Early Process Risk Assesment

█ Several tools/methodologyFood : HACCP (Hazard Analysis and Critical Control Point)

Automobile : FMEA (Failure Mode Effect Analysis, AMDEC in French)

Medical Device : FMEA

Pharmaceutical : mainly FMEA but not regulated

…

█ Used for years in industry, new and difficult for Pharmaceutical Implementation usually with consultancy (1 year, 90 000 €)

55

FMEA principle

█ For Each process Step/Substep :

█ Identify Potential Failure Mode (5 M, Ishikawa, Prior Knowledge)

█ Describe the possible effects of the failure and its possible cause

█ Quantify the Severity (S) and the Probability (P) of the potential failure

█ (Quantify the Detectability (D) of the potential failure)

█ Calculate the Risk Priority Number (RPN) of the potential failure

RPN = S x P (x D)

█ Identify Measures, Controls,… to reduce the failure

█ Recalculate the Risk Priority Number (RPN)

56

FMEA easy but…

█ How many levels for quantification?1 – 3

1 – 5

1 -10

█ RPN : what is acceptable, what is not

█ Easy to draw the initial FMEA analysis but usually non homogeneous, > 300 sheets, a nightmare to update.

57

FMEA : possible strategy : RPN and Policy

S : 1 -10

P : 1 -10

D : 1 -10

RPN : 1 - 1000

o 1 to 100 : broadly acceptable region o 101 to 150 : as low as reasonable practicable region (ALARP), part I o 151 to 250 : as low as reasonable practicable region (ALARP), par II

o 251 to 1000 : intolerable region

58

FMEA : possible strategy : Homogeneity

█ Define the various failure modes (5M) :Human error

Material deficiency

…

█ Describe the various levels for S, P and DP : 1 never,…, 5 sometimes,…, 10 always

P might also be based on Process Capability Indices

█ Describe the Controls and Measures of Risk ReductionHuman error : staff training, double check, detailled Standard Operating Procedures,…

Material deficiency : trained staff, qualified equipment, preventive maintenance,…

59

FMEA : possible strategy : Size

█ Other initial Risk Assessment tools(HACCP, initial Risk assessment, FMEA only on critical failure)

First FMEA based only on Probability, all failure with Low Probability Indice not treated

3 D Risk Assessment Model (J Olivier, Journal of Validation Technology, 2008) Distance along product stream (effect of bacterial contamination from fermentation to F&F) Distance from product (WFI, HVAC, GMP area, Product Tank,…) System complexity

Use of generic FMEA : from 300 to only 30 sheets containing the same information Containers preparation Buffers/reagents preparation General Equipment assembly and calibration … For each Process Unit/Subunit : identify only specific failures

60

FMEA : example

247

30

30

RPN

7

3

3

D

7

5

5

S

5

2

2

P

Identification of critical factors

Trained staff

WrittenSOP/method of production

Automation

Description/QC of raw material

Approvedsuppliers

Risk Control, Measures of Risk reduction, Tests

To be determinedContamination of Drug Product

Ineffective purification

Purification5.5.6

Human errorContamination of Drug product

Wrongbuffer (pH, conductivity)

Purification5.5.1

Reagentsidentity/Quality

Purification failure,

Production stopped

Wrongpreparation(saltaddition, …

Samplepreparation

5.4.5

Possible causePossible effect(harm) of the hazard/failure

Possible hazard/

failure

Product, Part, System, Function, Process

N#

247

30

30

RPN

7

3

3

D

7

5

5

S

5

2

2

P


Trained staff

WrittenSOP/method of production

Automation

Description/QC of raw material

Approvedsuppliers

Risk Control, Measures of Risk reduction, Tests

To be determinedContamination of Drug Product

Ineffective purification

Purification5.5.6

Human errorContamination of Drug product

Wrongbuffer (pH, conductivity)

Purification5.5.1

Reagentsidentity/Quality

Purification failure,

Production stopped

Wrongpreparation(saltaddition, …

Samplepreparation

5.4.5

Possible causePossible effect(harm) of the hazard/failure

Possible hazard/

failure

Product, Part, System, Function, Process

N#

61

If improvment of existing process

6 : Measure(Only for existing Products/Process)

62

Measure

█ Make sure you have data in accordance with ‘’Define’’

█ process input (parameter)

█ process output (results)

█ Link graphically (Matrix Plot) Inputs and Outputs

█ Example : yield of precipitation of proteins related topH

Temperature

Conductivity

%alcool

Initial proteins

Historical data, 106 productions

63

Measure : Temperature variation

0 20 40 60 80 100 120

Row

-5,5

-5

-4,5

-4

-3,5

-3

-2,5

Tem

pera

ture

Time Sequence Plot

Useful to detect shift

64

Measure : output (yield x-bar Chart)

X-bar Chart for Yield

51 53 55 57 59 61

Subgroup

0,31

0,33

0,35

0,37

0,39

X-b

ar

CTR = 0,33UCL = 0,35

LCL = 0,31

65

Measure : Radar/Spider Plot

Radar/Spider Plot

Scale: (-6,0-74,0)pH

Temperature

ConductivityAlcool

Proteins

Yield0,3168550,3109310,3190790,3110270,3107070,325940,3087450,2998860,3307450,3362780,3222890,3195420,3188260,3110370,3322780,335541

66

Measure : Matrix Plot

67

6 : Analyse

68

Analyse : Capability indices for Inputs

█ Capability indices indicated how well you master/control your process

█ Pc, Pck, Cc, Cck,,…P : initial analysis

C : when the process is under control

c : when symetric (upper and lower) results

ck : lower value of c upper/c lower

Upper specifications

Lower specifications Low Control High Control

69

Capability indices and statistics

NormalMean=6,0667Std. Dev.=0,0342462

Cp = 0,94Pp = 0,97Cpk = 0,63Ppk = 0,65K = -0,33

Process Capability for pH

LSL = 6,0; Nominal = 6,1; USL = 6,2

5,9 5,95 6 6,05 6,1 6,15 6,2

pH

0

10

20

30

40

50

freq

uenc

y

Observed Estimated Defects Specifications Beyond Spec. Z-Score Beyond Spec. Per Million USL = 6,2 0,000000% 3,89 0,004964% 49,64 Nominal = 6,1 0,97 LSL = 6,0 0,943396% -1,95 2,573095% 25730,95 Total 0,943396% 2,578058% 25780,58

70

Analyse : multivariate analysis

Input 1 (pH)

Monovariate

Outp

u

t

Input 2 (°C)

multivariateInput 1 (pH)

Multivariate

71

What is DoE

Classical approach DoE Process understanding

72

DoE : nearly a century

73

For me, only 20 years

74

DoEDoE

- interactions

- real optimum

- quality of information

X Interaction Optimum

75

From simple (fractionnal) design to RSM

X1X2

X3

Factorial Box Behnken Doehlert

76

From linear to Surface Response Model (non linear)


ConversionDesign points above predicted valueDesign points below predicted value97

51

X1 = A: TimeX2 = B: Temperature

Actual FactorC: Catalyst = 2.50

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A: Time B: Temperature

77

█ Several familiesn = number of Factor tested and L : level/factor Semi Factorial Design : the lowest number of experiments required : 2n-k

Used for a first screening of mains factors and at least single interactions Used for demonstration of a Proven Acceptable Range (PAR) or Design Space Don’t be afraid by the number of factor.

Factorial Design : higher number of experiments : 2n

For both Design, only two levels (L = 2) + eventual central point(s), Models will always be linear.

Response Surface Model : higher number of experiments : Ln. Non linear models.The number of experiments can be decreased by historical methods or by computer optimisation (D Optimal).

Used for optimisation/modeling of a process Used for searching the ‘’edge of failure’’

Mixture : RSM + constraint (sum of component = fixed value) Used in chemistry, formulation,…

Combined : Mixture + (semi) Factorial or RSM Used for combines mixture/process such as formulation (excipents) and freeze drying

conditions.

78

DoE, an other spirit

█ The kind of question to answer must be understood :Critical parameters

Interactions

Optimisation

Demonstration of Proven Acceptable Range

Modeling

█ The experiments are planned before starting

█ Apparently a high number of experiments, more work, more time, more money.

█ In reality, far less experiments (semi factorial or reduction for RSM) to obtain far less valuables results. Allow a better planning of experiments including Analytical.

79

How to build a Design Space

█ Factorial design

█ Semi factorial design

STD Factor A Factor B Factor C ALEA1 -1 -1 -1 32 1 -1 -1 53 -1 1 -1 74 1 1 -1 85 -1 -1 1 26 1 -1 1 17 -1 1 1 48 1 1 1 6

STD Factor A Factor B Factor C ALEA1 -1 -1 1 32 1 -1 -1 53 -1 1 -1 74 1 1 1 85 -1 -1 1 26 1 -1 1 17 -1 1 1 48 1 1 1 6

C = A x B

Lack of orthogonality

Introduction of ‘’aliase’’

Usefull to know to detect made up/false results

80

High collinearity : regression by least square not efficient

Ridge parameter Factor 1 Factor 2 Factor 3

0.0 (classical regression) 4.2637 -1.5614 -2.9287

0.01 (ridge regression) 0.6741 -0.1870 -0.2684

Use of Ridge statistics allows to analyse non

orthogonal Design

Lack of Orthogonality is not a problem

81


OLS8.7538

-8.7538

X1 = A: pHX2 = B: Conductivity

Actual FactorC: Load = 0.00

-1

-0.5

0

0.5

1

-1.00

-0.50

0.00

0.50

1.00

-6

-3

0

3

6

O

LS

A: pH B: Conductivity


Ridge1.1295

-1.1295

X1 = A: pHX2 = B: Conductivity

Actual FactorC: Load = 0.00

-1

-0.5

0

0.5

1

-1.00

-0.50

0.00

0.50

1.00

-0.9

-0.45

0

0.45

0.9

R

idg

e

A: pH B: Conductivity

OLS Ridge

Same overall topology, but completely different precision of the model (Monte Carlo simulation…)

82

DoE : number of experiments

83

DoE : Number of experiments

█ With n experiments, you can calculate the coefficients for n-1 factors and interactions

For 2 factors, Factorial design requires 22 = 4 experiments, you can calculate the coefficients for 3 factors and interactions : A, B and interaction AB (green color), it’s not interesting to erase 1 experiment and loose informations on possible interaction between A and B.

For 3 factors, Factorial design requires 23 = 8 experiments, you can calculate the coefficients for 7 factors and interactions : A, B, C and interactions AB, AC, BC and ABC. Using semi Factorial design (22 = 4 experiments) informations on possible interaction are also lost (red color).

For more than 3 factors, the number of experiments should be limited to the number of factors tested + the number of single interactions. I never found (up to now) significant triple interactions (ABC), Why loose time, money for a large number of such interactions ABC…F, ABD…F, ACD…F, AED…F…(yellow color)

84

Center points are useful to estimate

Reproducibility Linearity Extension of Design

Center points

- +

Factor A

- +

Factor A

- +

Factor A

85

Example of semi factorial design

86

Représentations :For each factor (and each response), estimation of the slope

between the average at low and high value of the factor or interaction.


Standard order Factor A Factor B Factor C AB AC BC ABC Response-1 -1 -1 1 1 1 -1 221 -1 -1 -1 -1 1 1 28-1 1 -1 -1 1 -1 1 261 1 -1 1 -1 -1 -1 84-1 -1 1 1 -1 -1 1 921 -1 1 -1 1 -1 -1 86-1 1 1 -1 -1 1 -1 101 1 1 1 1 1 1 56

Average Low 37,5 57,0 40,0 52,0 53,5 70,5 50,5Average High 63,5 44,0 61,0 63,5 47,5 29,0 50,5Slope 26,0 -13,0 21,0 11,5 -6,0 -41,5 0,0Effect 13,0 -6,5 10,5 5,8 -3,0 -20,8 0,0

87

3D View of critical factors and interactions

C A

B

A B C

AB AC BC

ABC

88

Design-Expert® SoftwareFVIIam capacity


Shapiro-Wilk testW-value = 0.997p-value = 0.992A: Contact TimeB: pH loadC: Column VolumeD: ConductivityE: Elution temperature


Half-Normal Plot

Ha

lf-N

orm

al

% P

rob

ab

ilit

y

|Standardized Effect|

0.00 142.38 284.75 427.13 569.50

010

20

30

50

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80

90

95

99

C

E

CE

Identification of Critical Factors and interaction

Identification of critical factors and interactions

Critical factorsPlace for

improvement

Reproducibility

Half Normal Plot

89

Design-Expert® SoftwareFVIIam capacity

A: Contact TimeB: pH loadC: Column VolumeD: ConductivityE: Elution temperature


Pareto Chart

t-V

alu

e o

f |E

ffe

ct|

Rank

0.00

1.21

2.41

3.62

4.82

Bonf erroni Limit 4.38176

t-Value Limit 2.57058

1 2 3 4 5 6 7

E

CE

C

Identification of Critical Factors and interaction

Pareto Chart

90

Factorial - semi factorial Design

pH Temperature Stability6 4 604 4 306 37 204 37 154 4 286 4 756 37 154 37 17

Factorial

pH Temperature Stability4 4 306 37 204 37 154 4 28

Semi factorial

91

Factorial analysis - semi factorial

DESIGN-EXPERT PlotStability

A: pHB: temperature

Half Normal plotHa

lf No

rmal

% p

roba

bility

|Effect|

0.00 7.88 15.75 23.63 31.50

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DESIGN-EXPERT PlotStability

A: pHB: temperature

Half Normal plot

Half

Norm

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pro

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|Effect|

0.00 4.04 8.08 12.12 16.17

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A

B

Term AliasesRequire Intercept ABModel A ABModel B ABAliased AB

92

Factorial - semi factorial Design

2 3 4 5 6 7 8

4 Full 1/28 Full 1/2 1/4 1/8 1/16

16 Full 1/2 1/4 1/8 1/1632 Full 1/2 1/4 1/864 Full 1/2 1/4

128 Full 1/2256 Full

Num

ber of experiments

Number of factor

Factorial analysis : NL

Semi Factorial analysis : N(L-X)

Loss of resolution (aliase)

93

But how many factors to select?

Design-Expert® SoftwareFT


Shapiro-Wilk testW-value = 0.798p-value = 0.039A: LoadB: Flow rateC: GradientD: pHE: Particle size


Half-Normal Plot

Ha

lf-N

orm

al

% P

rob

ab

ilit

y


0.00 3.59 7.18 10.77 14.36

010

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95

99Warning! No terms are selected.

94

Recherche des paramètres critiques :

95

- +

Factor X

Are the factors selected significant ?

Analyse statistique :Ttest (P95)

Comparison of Alow –Ahigh 5%

Comparison of Blow –Bhigh 5%

Comparison of Clow –Chigh 5%

Comparison of ABlow –ABhigh 5%

…

Ttest not applicable

Anova

96

ANOVA (Table)

Analyse statistique :Analysis of variance table [Partial sum of squares - Type III]Sum of Mean F p-value

Source Squares df Square Value Prob > FModel 2502 3 834 24,75 0.0020 significant B-Conductivity sample722 1 722 21,42 0.0057 C-Load 722 1 722 21,42 0.0057 BC 1058 1 1058 31,39 0.0025Curvature 160 1 160 4,75 0.0812 not significantResidual 168,5 5 33,7Lack of Fit 156 4 39 3,12 0.3984 not significantPure Error 12,5 1 12,5Cor Total 2830,5 9

Factors Variation degree of SS/df MS/residual associated

selected associated freedom probability

97

Demonstration of PAR

Design-Expert® SoftwarePurity


Shapiro-Wilk testW-value = 0.847p-value = 0.116A: pH sampleB: Conductivity sampleC: LoadD: pH elutionE: Gradient


Half-Normal Plot

Ha

lf-N

orm

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% P

rob

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0.00 5.59 11.18 16.77 22.36

0

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99Warning! No terms are selected.

98

Analysis of variance table [Partial sum of squares - Type III]Sum of Mean F p-value

Source Squares df Square Value Prob > FModel 661,88 7 95 0,33 0.8755 not significant A-pH sample 210,13 1 210 0,73 0.5500 B-Conductivity sample45,13 1 45 0,16 0.7601 C-Load 66,13 1 66 0,23 0.7155 D-pH elution 15,13 1 15 0,05 0.8566 E-Gradient 15,13 1 15 0,05 0.8566 BC 10,13 1 10 0,04 0.8820 BE 300,13 1 300 1,04 0.4934Curvature 30,63 1 31 0,11 0.7993 not significantPure Error 288,00 1 288Cor Total 980,50 9

If a model is found significant, estimation of the impact on product quality can be studied by in silico simultation

99

Significant model found…

Final Equation in Terms of Coded Factors:

Specifc activity =77,59,5 * B9,5 * C

-11,5 * B * C

Final Equation in Terms of Actual Factors:

Specifc activity =4,338,67 * Conductivity sample2,87 * Load

-0,31 * Conductivity sample * Load

But what is its accuracy/validity ?

100

Accuracy/validity of the model : residuals

█ 1- Normal Plot of residuals


Color points by value ofHCP peak:

519.2

2.5

Internally Studentized Residuals

No

rma

l %

Pro

ba

bil

ity

Normal Plot of Residuals

-1.43 -0.71 0.00 0.71 1.43

1

5

10

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30

50

70

80

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95

99

Design-Expert® SoftwareRP cor pic 2

Color points by value ofRP cor pic 2:

97.4616

0

Internally Studentized Residuals

No

rma

l %

Pro

ba

bil

ity

Normal Plot of Residuals

-2.56 -1.03 0.50 2.03 3.56

1

5

10

20

30

50

70

80

90

95

99

If all factors affecting the process are identified, residuals are random and distributed according a normal law

101

█ 2- Distribution of residuals (homo/heterodiasticity)


Color points by value ofHCP peak:

519.2

2.5

Predicted

Inte

rna

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Stu

de

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d R

es

idu

als

Residuals vs. Predicted

-3.00

-1.50

0.00

1.50

3.00

3.10 128.59 254.08 379.56 505.05

Design-Expert® Softwareyield

Color points by value ofyield:

5769

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Predicted

Inte

rna

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Stu

de

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d R

es

idu

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Residuals vs. Predicted

-3.00

-1.50

0.00

1.50

3.00

568.13 1534.59 2501.06 3467.53 4434.00

OK Will require data transformation

102

Box – Cox Plot


LambdaCurrent = 1Best = 0.23Low C.I. = -0.31High C.I. = 0.84

Recommend transform:Log (Lambda = 0)

Lambda

Ln

(Re

sid

ua

lSS

)

Box-Cox Plot for Power Transforms

15.11

17.04

18.98

20.92

22.86

-3 -2 -1 0 1 2 3

If heterodiasticity, = f ()

The transformation = 1- will reduce that effect :

= -1 : inverse, = 0 : Log

= 0.5 : square root, = 1 : no transformation

103

█ 3- Distribution of residuals (vs Run or time)



5769

275

Run Number

Inte

rna

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Stu

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Residuals vs. Run

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3.00

1 2 3 4 5 6 7 8 9 10

104

Accuracy/validity of the model

105

Weight of runs on the model



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Ex

tern

all

y S

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lsExternally Studentized Residuals

-4.32

-2.16

0.00

2.16

4.32

1 2 3 4 5 6 7 8 9 10

106

DoE and Regulatory Agencies

█ EMA and FDA expect to find informations not dataLoad Flow rate Gradient pH Particle size

% cm/h CV µm ppm50 50 15 8 30 450 150 15 6 30 350 50 5 8 90 211

150 150 5 8 30 491150 50 5 6 30 519100 100 10 7 60 157150 150 15 8 90 43150 50 15 6 90 950 150 5 6 90 249

100 100 10 7 60 143

HCP contamination


HCP peakDesign points below predicted value519.2

2.5

X1 = A: LoadX2 = C: Gradient

Actual FactorsB: Flow rate = 100.00D: pH = 7.00E: Particle size = 60.00

50.00

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60

190

320

450

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CP

pe

ak

A: Load C: Gradient

107

Factorial analysis - semi factorial

█ Loss of resolution (aliase)

Lower detection of interaction

Main factors ‘’aliased’’ to interaction

108

Improve - DoE

109


AS

Design Points

X1 = D: Conductivity

Actual FactorsA: Contact Time = 90B: pH load = 7.5C: Column Volume = 8E: Elution temperature = 20

20 25 30 35 40

8

25.75

43.5

61.25

79

D: Conductivity

AS

One Factor

25 + 5 mS/cm

NOR

PAR

Edge of failure

?

Definition of Critical Factors

PAR/NOR

Access to CP

110

Optimisation of an affinity chromatography step

█ Define :Affinity chromatography step based on VHH ligand

Prior knowledge : 2 washes : 25 % compound A followed by 0.5 M compound B Elution : 0.5 M compound B in 25 % A

█ Mesure :Yield : 65 – 85 % (mainly affected by number of use and quality of the starting material)

HCP : Clearance : 2.9 – 3.1 Log

111

Optimisation of an affinity chromatography step

█ AnalyseDesign : RSM, 5 level/compound

Compound A : 0 – 25 % (not tested at higher % due to high viscosity)

Compound B : 0 – 1 M

Use of D optimal design : only 14 experiments including replicates

Chromatography in // by 96 well format (Atoll GmBh) in a single day

1 model for yield

1 model for HCP clearance

112

Model for yield and HCP clearance

113

Optimisation of washes

█ Optimised wash : minimize ‘’yield’’ (low loss of target protein) – maximize HCP

X

114

Optimisation of elution

█ Optimised wash : maximize ‘’yield’’ (low loss of target protein) – minimize HCP

X

X

115

Optimisation of chromatographic conditions

Current conditionsCurrent conditions Optimised conditionsOptimised conditions

Wash 1 : 25 % A 0.2 M B in 8 % A

Wash 2 : 0.5 M B

Elution : 0.5 M B in 25 % A 0.75 M B in 22.5 % A

Only a mathematical model, results must be controled (C in 6sigma)

Yield : 68 – 85 % 85 %

HCP Clearance : 2.9 – 3.1 Log 4.1 Log

116

Quality of results depends also of analytics

117

DoE is not anymore sufficient

█ Results of DoE expresses an average, not individual results

█ What about the robustness of the process?

█ ICH Q8(R2) requires to provide assurance of quality

█ Bayesian Statistical approch including Monte Carlo Simulation is able to add this assurance

118

Monte Carlo simulation

120

Monte Carlo theory

Y = f(a,b,c)

121

Example 1 : area calculation

Precision increased with number of shoots

Only valid if shoots randomized

122

Example 2 : NovoNordisk

137

Example 3 : specifications for optimized affinity chromatography

Optimized Wash : 0.2 M B in 8 % A

0.2 M + ? B

8 % + ? A

Clearance must be > 3.75 to reach a final contamination < 5 ppm HCP

Equation (by DoE) Initial specification tested

A : 8 + 2 %

B : 0.2 + 0.05 M

Final Equation in Terms of Actual Factors:HCP Clearance = 2,48

12,395,17 * Compound A 0

-0,91 * Compound B 01,40 * Compound A* Compound B

-25,83 * Compound A^20,04 * Compound B^2

-0,36 * Compound A^2 * Compound B-0,01 * Compound A* Compound B^210,15 * Compound A^3

0,00 * Compound B^3

138

Monte Carlo simulation for initial specifications

█ 10 000 calculations with A and B randomly chosen within initial specifications

█ Nearly 20 % of failure

139

How to improve the process?

A

B

A B

140

Optimized specifications

Initial specifications Optimized specification

A : 8 + 2 % A : 7.5 + 1 %

B : 0.2 + 0.05 M B : 0.2 + 0.05 M

20 % failure No Failure (< 3.4/106 : Six Sigma robust process)

141

Validation of optimal specifications

█ These theoretical specifications for Compound A and B have been confirmed/validated by DoE during Process characterisation studies

Sequential Model Sum of Squares [Type I]Sum of Mean F p-value

Source Squares df Square Value Prob > FMean vs Total 3,8571 1 3,8571 12,432 0.0021 SuggestedLinear vs Mean 12,6390 15 0,8426 8,3612 0.15022FI vs Linear 0,3256 2 0,1628 2,7393 0.2105Quadratic vs 2FI 0,0594 1 0,0594 1,0000 0.4226Cubic vs Quadratic 0,1189 2 0,0594 1,0000 0.4226

142

Mono/multi-dimensionnal specifications

█ Additionnal advantage of DoE : multidimensionnal

Monodimensionnal

Factor 1 : 45 -51

Factor 2 : 1 – 1.45

In case of Deviation

Factor 1 : 53

Factor 2 : 0.7

Both out of specifications but no impact

X

143

Conclusions

144

█ Statistic = math = truth

█ Presented as nice graphics

█ But…



51



40.00

42.50

45.00

47.50

50.00

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90.00

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145

█ Presentation

Experiment Results1 102 253 14 505 1006 257 508 109 110 20

Experiment Results1 10,052 25,13 1,00984 50,25 1006 25,5787 50,878 10,29 1,0059810 20,02

146

█ Number of experiment

147

█ Scale

148

█ Design

0

2

4

6

8

10

12

0 2 4 6 8 10 12

X

Y

-200

0

200

400

600

800

1000

1200

0 100 200 300 400 500 600

X

Y

Y=0.113+0.981X

R = 0.9904

Y=-12.51+2.021X

R =0.9993

149

Design

Assays from world class company

150

Design-Expert® Sof tware

y ield5769

274.5

X1 = A: LoadX2 = B: Flow rate

Actual FactorsC: Gradient = 10.00D: pH = 7.00E: Particle size = 60.00

50

75

100

125

150

50.00

75.00

100.00

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150.00

500

1500

2500

3500

4500

yie

ld

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Design-Expert® Sof tware

Corrected HCP498

5

X1 = A: LoadX2 = B: Flow rate

Actual FactorsC: Gradient = 10.00D: pH = 7.00E: Particle size = 60.00

50

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50.00

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142

164.75

187.5

210.25

233

Co

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CP

A: Load

B: Flow rate

Graphical interpretation

151

Run Temperature Pressure Duration1 25 5 162 20 5 243 25 5 244 20 5 165 25 25 246 20 25 167 25 25 168 20 25 24



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Présentation d’un concurrent, QbD, Dusseldorf, Octobre 2008

Factorial Design

RSM

152

█ Transformation of Response

0

2

4

6

8

10

12

-200 0 200 400 600 800

days

mo

rtal

ity

non treated treated Linear (non treated) Linear (treated)

0

5

10

15

20

0 0,5 1 1,5 2 2,5 3 3,5

log(days)

mo

rtal

ity

non treated treated Linear (non treated) Linear (treated)

Drug commercialised 4 years

153

And in the future

154

QbD now and tomorrow

█ ICH meeting, Bruxelles; November 2008

155

Neuronal Network

█ DoE has been developped 100 years ago

█ DoE, despite serious improvment is now an ‘’old’’ technique and suffers from many disadvantages

Number of experiments may be further reduced

Model may be wrong in the real world

Difficulty to select the best model (complexity)

Predictability of model difficult to estimate

156


█ DoE : With n experiments, you can calculate the coefficients for SIGNIFICANT n-1 factors and interactions

█ Exemple : 5 factors tested : Factorial : 2^5 = 32 experiments

Half Factorial : 16 experiments

If only A, B and interaction AB are found significant, evaluation of their parameter would have required only 4 experiments

157


█ RSM model with interactions may required a lot of expirements.

█ Yi = naaa*A3+ nbbb*B3+ naab*A2B + nabb*AB2 + naa*A2+ nbb*B2+ nab*AB + na*A+ nb*B + ……..

█ 9 parameters for only 2 factors

158


█ 3 Factors : A, B, C, RSM

█ Real = 3A2 + 2 B2 + C + AB + AC

Run A B C Real Alea Real1 0,0 2,0 1,0 11,0 2,7 13,72 5,0 2,0 1,0 96,0 18,2 114,23 5,0 4,0 1,0 132,0 10,2 142,24 0,0 4,0 1,0 37,0 4,7 41,75 2,5 3,0 3,5 58,3 -14,3 43,96 2,5 3,0 -0,7 41,4 -17,4 24,07 2,5 3,0 3,5 58,3 17,1 75,38 2,5 1,3 3,5 33,6 2,0 35,79 2,5 3,0 3,5 58,3 -0,9 57,3

10 6,7 3,0 3,5 187,0 -4,5 182,511 2,5 3,0 3,5 58,3 -12,5 45,812 5,0 2,0 6,0 111,0 6,1 117,113 2,5 3,0 3,5 58,3 -13,0 45,314 2,5 3,0 3,5 58,3 -8,3 49,915 0,0 4,0 6,0 62,0 -7,0 55,016 2,5 4,7 3,5 94,2 -2,4 91,817 5,0 4,0 6,0 157,0 -18,9 138,118 -1,7 3,0 3,5 35,6 -6,7 28,919 0,0 2,0 6,0 26,0 11,2 37,220 2,5 3,0 7,7 75,1 8,3 83,4

Equation CoefficientFactor EstimateInterceptA-AB-BC-C 1 1,0AB 1 1,1AC 1 1,0BCA^2 3 3,1B^2 2 1,8C^2

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█ Real world + 20% (precision of the process / analytics)

Run A B C Real Alea Real1 0,0 2,0 1,0 11,0 2,7 13,72 5,0 2,0 1,0 96,0 18,2 114,23 5,0 4,0 1,0 132,0 10,2 142,24 0,0 4,0 1,0 37,0 4,7 41,75 2,5 3,0 3,5 58,3 -14,3 43,96 2,5 3,0 -0,7 41,4 -17,4 24,07 2,5 3,0 3,5 58,3 17,1 75,38 2,5 1,3 3,5 33,6 2,0 35,79 2,5 3,0 3,5 58,3 -0,9 57,3

10 6,7 3,0 3,5 187,0 -4,5 182,511 2,5 3,0 3,5 58,3 -12,5 45,812 5,0 2,0 6,0 111,0 6,1 117,113 2,5 3,0 3,5 58,3 -13,0 45,314 2,5 3,0 3,5 58,3 -8,3 49,915 0,0 4,0 6,0 62,0 -7,0 55,016 2,5 4,7 3,5 94,2 -2,4 91,817 5,0 4,0 6,0 157,0 -18,9 138,118 -1,7 3,0 3,5 35,6 -6,7 28,919 0,0 2,0 6,0 26,0 11,2 37,220 2,5 3,0 7,7 75,1 8,3 83,4

Equation CoefficientFactor EstimateIntercept 56,7A-A 44,1B-B 17,6C-C 1 11,0AB 1 3,8AC 1 -4,1BC 4,0A^2 3 20,0B^2 2 3,6C^2 -0,4

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Best Model and Predictibility

█ Real model : A, linear , tested at 4 levels

0123456789

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0 1 2 3 4 5

Theoretical Real Mean Linear cubic

0123456789

10

0 1 2 3 4 5

Real cubic Next time

If complexity of model increase, precision to data increase (diminution of Sum of Square) but predictibility to other results decrease (increase of bias)

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Bayes limit : Bias/variance dilemna

0

20

40

60

80

100

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0 2 4 6 8

Complexity of model

Sum of Square Bias Bayes Limit

Best Model

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DoE models : which is the best ?

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DoE / Neuronal Network

DoE Neuronal Network

Factors

Response

Constant Function

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Functions in Neuronal Network

█ Several types of fonctions, only two parameters/function

█ Reduced number of experiments for modeling (statistical learning)

█ If classical DoE require 36 experiments for modelisation, neuronal network may use this number of experiment to

Statistical learning (modelisation), ex : 12 experiments

+

Evaluation of the model on other data not used (validation), ex 12 experiments

+

Evaluation of the model on final data remaining (test), ex 12 experiments

█ Allow Bootstrap : instead of a single analysis, perform i.e 200 statistical modeling/validation/testing analysis using each time 12 random experiments for each step

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Neuronal neutwork

█ Modern statistical modelisation

█ Succesfully applied to learning ofQuantitative models (// to DoE)

Qualitative model : oral/picture recognition (classification)

█ Mathematical optimisation no more problematic and user-friendly

dedicated software on the market

█ Introduced in one of the next ICH ?

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QbD strongly requested by Authorities, lack of implementation may lead not only to a Dossier Assessment Refusal Report but to the discontinuation of

GMP authorisation for Manufacturing of Facility

Statistics and modelisation for QbD

Education

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