Giornata di Studio

Disegno Sperimentale (DoE) come strumento per QbD

Università degli Studi di Milano Dipartimento di Scienze Farmaceutiche

Milano, 22 aprile 2013

Dr. Lorenza Broccardo

Introduction

Quality by Design is

systematic approach to development that begins with predefined objectives and emphasizes product and process understanding

and process control, based on sound science and quality risk management

--ICH Q8 (R), Step 2

Nowadays, product quality cannot be tested into the finished product but it must be “designed” and built into a product and its manufacturing process The International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use provides a guide for pharmaceuticals process developers that introduce the QbD concept:

Design of Experiments (DOE) is

an statistical methodology useful to plan a set of experiments in order to obtain

the maximum amount of information with the minimum amount of experiments

Tools to achieve QbD: • Design by Experiments (DoE) • Risk Assessment • Multivariate data Analysis (MVA)

Which applications? • process • products

When is it useful? • development (new process-new product) • optimisation (process/product-performance) • minimization (cost-discard-pollution) • robustness testing (method-instrument) • selection of influencing variables • understand the relation between responses and variables • define the set point • define the design space

About DoE

Examples pharmaceutical problems well handled by DoE • define factors influencing a reaction yield

• optimization of a chromatographic separation • optimization of a mixture (mixture: blend which components cannot be

manipulated independently of one another)

• production of active substance as powder: define the design space, that is, the experimental conditions assuring a production inside specifications

Definitions

Factors

independent variables, X, controlled by the experimenter

Range

[Xmin; Xmax]

Experimental domain

the numbers of factors and their ranges of variability define the experimental domain

Responses

dependent variables, Y, measured

Objective

The experimentation purpose:

• screening (preliminary information)

• optimization (detailed information)

• robustness testing (evaluate the process robustness)

X

factors

Y

responses

MODEL

Why an experimental planning ? To obtain new information about the system, the experimenter causes a controlled variation of factors and measure the corresponding modification of the responses • information are “located” in the factors setting (X matrices): a careful

planning of experiments increases the amount of information • an appropriate experiments planning allow to connect matrix X and Y by a

mathematical equation (model) which enable prediction

Classical

1. incomplete sampling of the X space

2. gives different implications with different starting points

3. no quantification of interactions

4. does not lead to the real optimum

5. leads to many experiments and poor information

6. what about: X=3 and Y=2?

Classical vs DOE approach

10 11 12 13 14 15

-2

0

2

4

6

8

10

X1

X2

DOE

1. homogeneous sampling of the X space

2. result independent from the starting point

3. quantification of interactions

4. experimental results are interpreted by a regression model

- system description by a surface

- predictive power

- information about the real optimum

5. requires few experiments to obtain al lot of information

6. handles complex systems

10

10 11 12 13 14 15 -2 0 2 4 6 8

X1

X2

DoE make use of “design” Design: organized distribution of experiments within the experimental domain

Full Factorial Composit Box-Behnken

Doehlert x2=1 x3=1

x1=1

Simplex

The design generates the worksheet

Experiments are analyze and interpret by a model

11

The model is a mathematical relation between ∆X (set) and ∆Y (measured)

ƒ(x) = b0 + b1x + b2x2 + … bnx

n + e

Three main types of polynomial models

linear: y = b0 + b1x1 + b2x2 +...+ e

interaction: y = b0 + b1x1 + b2x2 + b12x1x2 +...+ e

quadratic: y = b0 + b1x1 + b2x2 + b11x12 + b22x2

2 + b12x1x2 +...+

The model graphical representation

It is a m dimensional surface representing Y

as a function of all Xi

(m = ∑i Xi + 1)

Y = f (Xi)

It is used for Y prediction

design

2 factors 3 factors > 3

Hyper cube

Balanced fraction

of hyper cube

Hyper cube + axial

points

Objectives, Design and Model are linked

12

objective

Screening (factors<4)

Screening (factors>4) Rob. testing

Optimization

response surface

Linear

Linear Interactions

Quadratic

model

Identification of influencing input process parameters

Early stage of system study (screening)

Find out which factors are the dominating ones

Many factors are investigated in few runs

List of supposed influencing factors is

proposed on the bases of:

• previous knowledge on the system

• fishbone (cause-and-effect) diagram

• risk assessment (FMEA)

Factors effect is tested by a

screening design

• outcome:

QbD steps that achieve benefit from DoE application

Definition of appropriate experimental domain

Early stage of system study (screening)

Find out which factors ranges include the experimental condition corresponding to the required response(s) value

Many factors are investigated in few runs

10

10 11 12 13 14 15 -2 0 2 4 6 8

X1

X2

Define the set point conditions

As a result of the screening phase, the most important factors and their appropriate range of variability have been defined

Optimization:

• understand the relation between each factor and each response (linear, interaction, quadratic)

• plot the responses predicted value by the polynomial models

• predict the best set point conditions

Few factors are investigated in many runs

-100

1020

Sul

Mof

Tem

p

Sul*

Sul

Mof*

Mof

Tem

p*T

em

p

Sul*

Mof

Sul*

Tem

p

Mof*

Tem

p

%

Scaled & Centered Coefficients for Yield

Robustness testing

It is usually carried out before the release of a product or an analytical method as a latest test to assure quality.

The objective is to verify the process stability and define the design space

Responses specifications must be defined

Set point Factor combination which is currently used for running the process

Experimental domain “small” shift around the set point

Design Linear (many factors are investigated in few runs)

Outcome • the process is robust:

release the set point factor combination and the factors variability ranges that assure quality

• the process is not robust: identify factors responsible for the process high sensitivity and define how to reduce their impact

4000

5000

6000

1 2 3 4 5 6 7 8 9 10 11

Pla

teN

Replicate Index

12 3

4

5

6 7

8 910

1112

Min

Target

Nature of robustness

Are responses inside or outside specifications? Is regression model significant or not? Four limiting cases

1) Inside specification/Significant model • all the measured values are inside the specification • regression model significant • apply the model to predict maximum variation

the process is robust 2) Inside specification/Non-Significant model • ideal outcome • changes in parameters correspond to the experimental error

the process is robust

3) Outside specification/Significant model • discover which factors causes the outside of specification • apply the model to understand how factors’ ranges should be varied to achieve robustness the process is not robust

2,5

3,0

3,5

1 2 3 4 5 6 7 8 9 10 11

k2

Replicate Index

1

2

3

4

5

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7

8

910 1112Target

Max

-0,30-0,20-0,10-0,000,10

AcN

#

pH

#

Tem

p#

OS

A#

Co

l(A

)

Co

l(B

)

Scaled & Centered Coefficients for k2

4) Outside specification/Non-Significant model

Most complex limiting case ......

• replicated center-points have much higher response values (left) o might be possible to resolve by shrinking the design o at minimum an additional design

• one strong outlier (right) o risk for a process that is unstable and then gives strange results o cause of problem needs to be found and a new design performed

25

30

35

40

45

1 2 3 4 5 6 7 8 9

ve

tifi

c

Replicate Index

Plot of Replications for vetificwith Experiment Number labels

1 23

4

5 6 7 8 91011

Investigation: itdoe_roblimcases

MOD DE 7 - 2003-11-17 11:58:00

50

60

70

1 2 3 4 5 6 7 8 9

ve

tifi

c

Replicate Index

Plot of Replications for vetificwith Experiment Number labels

1 23 4 5 6 7 8

91011

Investigation: itdoe_roblimcases

MODDE 7 - 2003-11-17 11:59:51

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9

ve

tifi

c

Replicate Index

Plot of Replications for vetificwith Experiment Number labels

1 2

3

4 5 6 7 8 91011

Investigation: itdoe_roblimcases

MODDE 7 - 2003-11-17 12:01:59

Design Space

The Design Space correspond to the experimental domain centered on the set point and including only experimental conditions that assure quality according

with defined standard (y) and the accepted level of risk of failure (DPMO)

To define the Design Space, a robustness test is required

The design space is calculated on the bases of: • regression model • model error • Monte Carlo simulation • responses specifications • DPMO (Defect Per Million Opportunities) level accepted Outcome: experimental domain (design space) assuring that all responses are inside specifications according to the accepted level of failure

Monte Carlo simulation The Monte Carlo simulations are: • random factor settings according to • the selected distribution • around their optimum value but • within the Low and High limits • followed by predictions of the responses 1.000.000 predictions are performed DPMO (Defect Per Million Opportunities) shows how many response predictions are outside the response specifications based on one million simulations Indicates the sensitivity of the responses to the external perturbation applied to the factors settings Ideal outcome: DMPO = 0

Design Space outcome Identify critical factors (AcN, OSA) and define new range of variability

Identify critical responses (k2) Verify that the new factors range assure robustness

Design space outcome Probability contour plot

DoE

• is a tool to achieve QbD

• is an organized methodology useful to plan a set of experiments efficiently

• provides tools to analyze the data and make decision

• makes available a deep understanding of the process

• allows to save time and money

Conclusion

Acknowledgements

Scientific committee

Organizing committee All attendees