how to define design space

How to Define Design Space

Lynn Torbeck

Overview

• Why is a definition important?• Definitions of Design Space.• Deconstructing Q8 Definition.• Basic science, Cause and Effect• SIPOC Process Analysis• Three Levels of Application.• Case Study with Example.

Why is this Important?

ICH Q8 is in its final version.Design Space is defined in Q8.Many presenters are using the term.All are repeating the same definition.Many presenters don’t understand the statistical implications of the issue.Need for a detailed ‘Operational Definition’

Regulatory Impact“Design space is proposed by the applicant and is subject to regulatory assessment and approval.”“Working within the design space is not considered a change.”“Movement out of the design space is considered to be a change and would normally initiate a regulatory post approval change process.”This is a big deal, it needs to be done correctly !The economic impact of this can be huge.

Potential Benefits

Real process understanding and knowledge, not just tables of raw data.Reduced rejects, deviations, discrepancies, lost time, scrap and rework.Fewer 483 citations and warning letters.Fewer investigations and CAPA.Freedom to operate with design space

ICH Q8 Definition

“The multidimensional combination and interaction of input variables and process parameters that have been demonstrated to provide assurance of quality.”This is not universally understood by all parties involved. We need to harmonize several viewpoints, statistical, scientific, engineering and regulatory.

Deconstructing the Definition

Need to deconstruct the definition to get to a day to day working Operational Definition that can be implemented.Need enough detail to write a Standard Operating Procedure or SOP.Need to see an example of what it looks like.

Multidimensional

Also called multivariable or multivariateMore than one variable at a time is considered.The practice of holding the world constant while only considering one-factor-at-a-time has been shown to be grossly inefficient and ineffective.

Interaction

Defined in the PAT guidance“Interactions essentially are the inability of one factor to produce the same effect on the response at different levels of another factor.”Interactions are the joint action of two or more factors working together.

Example InteractionAB Interaction Effect

0

10

20

30

40

50

60

70

0.5 1 1.5 2 2.5

B Low B High

Av

era

ge

Eff

ect

A Low

A High

“Input” Variables

Input Variables: The “cause” Independent variable Factor

Output Variables The “effect” Dependent variable Responses

Assurance of Quality

Assurance is a high probability of meeting: Safety Strength Quality Identity Purity

For all measured quality characteristics.

Basic Science

Cause Effect

?

Critical Cause and Effect

R=

1.

2.

3.

4.

5.

6.

Effects

Dependent

Multiple Causes

Independent

FactorsResponses

Design Space

IndependentFactorSpace

?DependentResponse

Space

Design Space

FACTOR SPACEN dimension X’sX1

X2

X3

X4

X5

XN

RESPONSE SPACEM dimension Y’sY1

Y2

Y3

Y4

Y5

YM

Factor Space

“Potential Space” Areas that could be investigated“Uncertain Space” Insufficient data for a decision.“Unacceptable Space” Factors and ranges have been shown to not provide assurance of SSQuIP.“Acceptable Space” Data to demonstrate assurance of SSQuIP.“Production Space” Factors and ranges that are selected for routine use.

Response Space

“Potential space” or “Region of Interest”“Uncertain Space”, unknown responses“Unacceptable Space” unacceptable responses“Region of Operability,” acceptable responses“Production Space” for manufacturingOptimal Conditions or Control Space

Conceptual Design Space

Uncertain space

Region of operability

Design Space Opt

Region of Interest

Tablet Process Example

Filler Lactose Mannitol

Lubricant Steraric Acid Mag Stearate

Disintegrant Maze Starch Microcrystalline Cell

Binder PVP Gelatine

Intact drug %Content uniformityImpuritiesMoistureDisintegrationDissolutionWeightHardnessFriabilityStability

Chemical Process Example

Catalyst 10-15 lbs

Temperature 220-240 degrees

Pressure 50-80 lbs

Concentration 10-12%

YieldPercent convertedImpuritypHColorTurbidityViscosityStability

Statistical Design Space

“The mathematically and statistically defined combination of Factor Space and Response Space that results in a system, product or process that consistently meets its quality characteristics, SSQuIP, with a high degree of assurance.” LDT

Modeling the World

“All Models are wrong, but some are useful.” G. E. P. BoxEmpirical Models: Simple linear, y = a + bx Quadric equation, y = a + bx + cx2

Mechanistic Models: A physical or chemical equation.

Model Prediction

Equations for critical factors and the mechanistic connection with the critical responses allow for the prediction of the quality characteristics in quantitative terms.Multidimensional in factors and responses.

S.I.P.O.C. Model

P rocess

Management Facilities People

Culture SPO's

Input

Input

Input

S upplier

S upplier

S upplier

Equipment Systems

Environment

Measurement

Regulations

O utput

O utput

O utput

C ustomer

C ustomer

C ustomer

Macro View

ProductProcessDesign

ControllableFactors

Concomitant

UncontrollableFactors

ControlledResponses

UncontrolledResponses

Unknown

The Whole New Product Development Cycle

Mid-Level View

Pre-formulation / formulation studiesPharmacology / toxicologyAnimal studiesProduct developmentProcess developmentClinical trialsValidation and process improvement

Micro Level View:Design Space


DependentResponse

space

Existing Products

Design Space can be inferred by using existing information and historical data .Retrospective process capability studies.Annual Product Review analysisComparison of historical data to specsRisk management and assessment, Q9

Factor Space

ASTM E1325-2002“That portion of the experiment space restricted to the range of levels of the factors to be studied in the experiment …”

AKA, “Design Regions” The Cambridge Dictionary of Statistics.

B. S. Everitt, Cambridge University Press

Quick Dry Example

Five batches of product had been lost to an impurity exceeding the criteriaThe criteria for impurity 1 was NMT 1.0%Four factors studied.Four responses.

Quick Dry Example

FACTOR SPACEDrying time 3-9 mins

Drying Temperature 40-100

Excipients Moisture 1.2-5 %

%Solvent 1-14 %

RESPONSE SPACEImpurity-1 %Impurity-2 %Intact drug %Final moisture %

Factor SpaceB B

+1 +1

1.90 3.80 1.30 6.10

5.20 15.50 5.20 20.70

-1 0.70 0.80 A -1 1.00 1.00 A-1 -1 +1

-1 -1

0.80 0.50 0.60 q62

C +1 C +1

Right Cube is D = HIGHLeft Cube Is D = LOW

Design Space


f(x)=?DependentResponse

space

Process understanding is cause and effect quantitated. We find a mathematical and statistical formula that describes the relationship between factor space and response space.

2 Factor InteractionEffects to Consider

Time * TemperatureTime * MoistureTime * SolventTemperature * MoistureTemperature * SolventMoisture * Solvent

Time*Temp Interaction Plot

DESIGN-EXPERT Plot

Impurity -1

X = A: TimeY = B: Temperature

B- 40.000B+ 100.000

Actual FactorsC: Moisture = 3.10D: Solv ent = 7.50

B: TemperatureInteraction Graph

Impurity

-1

A: T ime

3.00 4.50 6.00 7.50 9.00

-0.94222

4.46834

9.87889

15.2894

20.7

Time* Moisture Interaction Plot

DESIGN-EXPERT Plot

Impurity -1

X = A: TimeY = C: Moisture

C- 1.200C+ 5.000

Actual FactorsB: Temperature = 70.00D: Solv ent = 7.50

C: MoistureInteraction Graph

Impu

rity-

1

A: T ime

3.00 4.50 6.00 7.50 9.00

-0.37515

4.89364

10.1624

15.4312

20.7

Temp*Moisture Interaction Plot

DESIGN-EXPERT Plot

Impurity -1

X = B: TemperatureY = C: Moisture

Design Points

C- 1.200C+ 5.000

Actual FactorsA: Time = 6.00D: Solv ent = 7.50

C: MoistureInteraction Graph

Impurity

-1

B: Temperature

40.00 55.00 70.00 85.00 100.00

-1.021

4.40925

9.8395

15.2697

20.7

22

Time*Temp Contour Plot

Time

Temp

Design-Expert® Sof tware

Impurity -120.7

0.1

X1 = A: TimeX2 = B: Temperature


3.00 4.50 6.00 7.50 9.00

40.00

55.00

70.00

85.00

100.00Impurity-1

A: T ime

B:

Tem

pera

ture

2

4

6

8

1

Time*Moisture Contour Plot

Time

Moisture


Impurity -120.7

0.1

X1 = A: TimeX2 = C: Moisture


3.00 4.50 6.00 7.50 9.00

1.20

2.15

3.10

4.05

5.00Impurity-1

A: T ime

C:

Mois

ture

2

4

6

8

1

Temp*Moisture Contour Plot

Temp

Moisture


Impurity -1Design Points20.7

0.1

X1 = B: TemperatureX2 = C: Moisture


40.00 55.00 70.00 85.00 100.00

1.20

2.15

3.10

4.05

5.00Impurity-1

B: Temperature

C:

Mois

ture

2

4

6

8

1 333

Time*Temp SurfaceDesign-Expert® Sof tware

Impurity -120.7

0.1



3.00

4.50

6.00

7.50

9.00

40.00

55.00

70.00

85.00

100.00

0

3

6

9

12 Im

pu

rity

-1

A: Time B: Temperature

Time*Moisture SurfaceDesign-Expert® Sof tware

Impurity -120.7

0.1

X1 = A: TimeX2 = C: Moisture


3.00

4.50

6.00

7.50

9.00

1.20

2.15

3.10

4.05

5.00

0.8

2.875

4.95

7.025

9.1 I

mp

uri

ty-1

A: Time C: Moisture

Temp*Moisture Surface


Impurity -120.7

0.1

X1 = B: TemperatureX2 = C: Moisture


40.00

55.00

70.00

85.00

100.00

1.20

2.15

3.10

4.05

5.00

0

3

6

9

12 Im

pu

rity

-1

B: Temperature C: Moisture

Quick Dry Example

FACTOR SPACEDrying time 3-9 mins

Drying Temperature 40-100

Excipients Moisture 1.2-5 %

%Solvent 1-14 %

RESPONSE SPACEImpurity-1 %Impurity-2 %Intact drug %Final moisture %

Conclusions

FACTOR SPACESolvent, no effectTime, decreaseTemp, decreaseMoisture, decrease

RESPONSE SPACEImpurity 1 Less than 1%

R2 = 0.95

f(Xi) Design Space

Impurity =+0.6079 +Time *-0.0057+Temperature * -0.0058+Moisture * +0.1994+Time*Temp * +0.00061+Time*Moist * -0.29386+Temp*Moist * -0.00502+T*T*M * +0.00713

Goal

Find a set of levels for Time, Temperature, and Moisture that will predict impurity of less than 1 percent. (Solvent doesn’t matter.)The combination of levels is the design space for impurity 1.

Predictive EquationFactor Coefficient Factor Level Impurity

Intercept 0.607940 1.0A-Time -0.005702 4

B-Temperature -0.005813 70C-Moisture 0.199410 1

AB 0.000614 280AC -0.293860 4BC -0.005018 70

ABC 0.007127 280

Predictive Equation

Factor Coefficient Factor Level ImpurityIntercept 0.607940 1.0A-Time -0.005702 9

B-Temperature -0.005813 43C-Moisture 0.199410 5

AB 0.000614 387AC -0.293860 45BC -0.005018 215

ABC 0.007127 1935

Design SpaceDesign-Expert® Sof tware

Ov erlay Plot

Impurity -1



3.00 4.50 6.00 7.50 9.00

40.00

55.00

70.00

85.00

100.00Overlay Plot

A: Time

B:

Tem

pera

ture

Impurity-1: 1

Design SpaceDesign-Expert® Sof tware

Ov erlay Plot

Impurity -1



3.00 4.50 6.00 7.50 9.00

40.00

55.00

70.00

85.00

100.00Overlay Plot

A: T ime

B:

Tem

pera

ture

Impurity-1: 1

Multidimensional Specifications

Specifications should not be set one factor at a time.We need to consider all responses together.We need to do the same analysis for impurity 2, intact drug and final moisture and then overlay the four solutions to find the design space that will meet all of the criteria at the same time.

Scale-Up

Scale-up may not be linearAssume that the basic equations will applyAssume the design space will be somewhat robust and rugged.Need to do confirmation experiments to confirm assumptions.Or reestablish the design space.

Design Space Conclusions

ICH Q8 and the FDA are asking for designed experiments and predictive equations for each aspect of a new product.Descriptions need to be mathematical and statistical equations.Empirical equations are the most common, but a few mechanistic equations may be possible.

Design Space Conclusions

This is a new and perhaps confusing issue for the pharmaceutical industry.To implement this approach will require designed experiments with overlays of multiple responses for each new product.Sometimes retrospective studies of existing products can be done with historical data.

how to define design space

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