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 multivariate
More than one variable at a time is considered.
The practice of holding the world constant while only considering onefactor-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 Interaction
AB Interaction Effect
70
60
50
40
30
20
10
0
0.5
1 1.5
2
B Low B High
2.5
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
?

1.
Critical Cause and Effect
3.
5.
4.
Multiple Causes
Independent
Factors
6.
Effects
R=
Dependent
Responses
2.

Design Space
Independent
Factor
Space
?
Dependent
Response
Space

Design Space
FACTOR SPACE
N dimension X’s
X
4
X
5
X
N
X
1
X
2
X
3
RESPONSE SPACE
M dimension Y’s
Y
4
Y
5
Y
M
Y
1
Y
2
Y
3

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 manufacturing
Optimal Conditions or Control Space

Conceptual Design Space
Design
Space Opt
Region of Interest
Uncertain space
Region of operability

Tablet Process Example
Filler


Lactose
Mannitol
Lubricant


Steraric Acid
Mag Stearate
Disintegrant


Maze Starch
Microcrystalline Cell
Binder


PVP
Gelatine
Intact drug %
Content uniformity
Impurities
Moisture
Disintegration
Dissolution
Weight
Hardness
Friability
Stability

Chemical Process Example
Catalyst

10-15 lbs
Temperature

220-240 degrees
Pressure

50-80 lbs
Concentration

10-12%
Yield
Percent converted
Impurity pH
Color
Turbidity
Viscosity
Stability

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. Box
Empirical Models:


Simple linear, y = a + bx
Quadric equation, y = a + bx + cx 2
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
SPO's
Management
Culture
Facilities People
S upplier
S upplier
S upplier
I nput
I nput
I nput
P rocess
O utput
O utput
O utput
C ustomer
C ustomer
C ustomer
Equipment
Regulations
Systems
Environment
Measurement

The Whole New Product Development Cycle
Controllable
Factors
Concomitant
Unknown
Product
Process
Design
Uncontrollable
Factors
Controlled
Responses
Uncontrolled
Responses
Macro View

Mid-Level View
Pre-formulation / formulation studies
Pharmacology / toxicology
Animal studies
Product development
Process development
Clinical trials
Validation and process improvement

Micro Level View:
Design Space
Independent
Factor
Space
Dependent
Response space

Existing Products
Design Space can be inferred by using existing information and historical data .
Retrospective process capability studies.
Annual Product Review analysis
Comparison of historical data to specs
Risk 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 criteria
The criteria for impurity 1 was NMT
1.0%
Four factors studied.
Four responses.

Quick Dry Example
FACTOR SPACE
Drying time

3-9 mins
Drying Temperature

40-100
Excipients Moisture

1.2-5 %
%Solvent

1-14 %
RESPONSE SPACE
Impurity-1 %
Impurity-2 %
Intact drug %
Final moisture %

Factor Space
B
+1
1.90
3.80
5.20
15.50
5.20
B
+1
1.30
20.70
6.10
0.80
C +1
-1 0.70
-1
-1
0.50
Left Cube Is D = LOW
0.80
A
0.60
C +1
-1 1.00
-1
-1 q62
Right Cube is D = HIGH
1.00
A
+1

Design Space
Independent
Factor
Space f(x)=?
Dependent
Response 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 Interaction
Effects to Consider
Time * Temperature
Time * Moisture
Time * Solvent
Temperature * Moisture
Temperature * Solvent
Moisture * Solvent

Time*Temp Interaction Plot
Interaction Graph
B: T em perature
DESIGN-EXPERT Plot
Impurity -1
X = A: Time
Y = B: Temperature
B- 40.000
B+ 100.000
Actual Factors
C: Moisture = 3.10
D: Solv ent = 7.50
20.7
15.2894
9.87889
4.46834
-0.94222
3.00
4.50
6.00
A: T i m e
7.50
9.00

Time* Moisture Interaction Plot
DESIGN-EXPERT Plot
Impurity -1
X = A: Time
Y = C: Moisture
20.7
C- 1.200
C+ 5.000
15.4312
Actual Factors
B: Temperature = 70.00
D: Solv ent = 7.50
10.1624
Interaction Graph
C: M oi sture
4.89364
-0.37515
3.00
4.50
6.00
A: T i m e
7.50
9.00

Temp*Moisture Interaction Plot
DESIGN-EXPERT Plot
Impurity -1
X = B: Temperature
Y = C: Moisture
Design Points
C- 1.200
C+ 5.000
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
20.7
15.2697
9.8395
Interaction Graph
C: M oi sture
4.40925
-1.021
40.00
55.00
70.00
85.00
B: T em perature
100.00

Time*Temp Contour Plot
Impurity-1 Design-Expert® Sof tware
Impurity -1
20.7
0.1
X1 = A: Time
X2 = B: Temperature
Actual Factors
C: Moisture = 3.10
Temp
100.00
85.00
70.00
4
6
8
55.00
40.00
3.00
Time
4.50
2
1
6.00
A: T i m e
7.50
9.00

Time*Moisture Contour Plot
Impurity-1 Design-Expert® Sof tware
Impurity -1
20.7
0.1
X1 = A: Time
X2 = C: Moisture
B: Temperature = 70.00
D: Solv ent = 7.50
5.00
4.05
3.10
4
6
8
2
2.15
1
1.20
3.00
Time
4.50
6.00
A: T i m e
7.50
9.00

Temp*Moisture Contour Plot
Impurity-1 Design-Expert® Sof tware
Impurity -1
Design Points
20.7
0.1
X1 = B: Temperature
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
5.00
4.05
3.10
1
2
4
6
8
2.15
1.20
40.00
Temp
55.00
70.00
B: T em perature
85.00
100.00

Time*Temp Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
X1 = A: Time
X2 = B: Temperature
Actual Factors
C: Moisture = 3.10
D: Solv ent = 7.50
12
9
6
3
0
100.00
85.00
70.00
B: Tem perature
55.00
40.00 3.00
4.50
9.00
7.50
6.00
A: Tim e

Time*Moisture Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
X1 = A: Time
X2 = C: Moisture
Actual Factors
B: Temperature = 70.00
D: Solv ent = 7.50
9.1
7.025
4.95
2.875
0.8
5.00
4.05
3.10
C: Moisture
2.15
1.20 3.00
4.50
9.00
7.50
6.00
A: Time

Temp*Moisture Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
X1 = B: Temperature
X2 = C: Moisture
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
12
9
6
3
0
5.00
4.05
3.10
C: Moisture
2.15
100.00
85.00
1.20 40.00
70.00
55.00
B: Temperature

Quick Dry Example
FACTOR SPACE
Drying time

3-9 mins
Drying Temperature

40-100
Excipients Moisture

1.2-5 %
%Solvent

1-14 %
RESPONSE SPACE
Impurity-1 %
Impurity-2 %
Intact drug %
Final moisture %

Conclusions
FACTOR SPACE
Solvent, no effect
Time, decrease
Temp, decrease
Moisture, decrease
RESPONSE SPACE
Impurity 1

Less than 1%
R 2 = 0.95

f(X i
) 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 Equation
Factor Coefficient Factor Level Impurity
Intercept 0.607940
1.0
A-Time -0.005702
4
B-Temperature -0.005813
70
C-Moisture 0.199410
AB 0.000614
1
280
AC -0.293860
4
BC -0.005018
70
ABC 0.007127
280

Predictive Equation
Factor Coefficient Factor Level Impurity
Intercept 0.607940
1.0
A-Time -0.005702
9
B-Temperature -0.005813
43
C-Moisture 0.199410
AB 0.000614
5
387
AC
BC
-0.293860
-0.005018
45
215
ABC 0.007127
1935

Design Space
Design-Expert® Sof tware
Ov erlay Plot
Impurity -1
X1 = A: Time
X2 = B: Temperature
Actual Factors
C: Moisture = 5.00
D: Solv ent = 7.50
100.00
85.00
70.00
Overlay Plot
55.00
40.00
3.00
4.50
Impurity-1: 1
6.00
A: T i m e
7.50
9.00

Design Space
Design-Expert® Sof tware
Ov erlay Plot
Impurity -1
X1 = A: Time
X2 = B: Temperature
Actual Factors
C: Moisture = 1.20
D: Solv ent = 7.50
100.00
85.00
70.00
Overlay Plot
Impurity-1: 1
55.00
40.00
3.00
4.50
6.00
A: T i m e
7.50
9.00

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 linear
Assume that the basic equations will apply
Assume 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.