Transcript How to Define Design Space

How to Define Design Space
Lynn Torbeck
Overview
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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
Average Effect
50
40
A Low
A High
30
20
10
0
0.5
1
B Low
1.5
2
B High
2.5
“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
1.
3.
5.
Multiple Causes
Effects
R=
Independent
Factors
2.
4.
6.
Dependent
Responses
Design Space
Independent
Factor
Space
?
Dependent
Response
Space
Design Space
FACTOR SPACE
N dimension X’s
X1
X2
X3
X4
X5
XN
RESPONSE SPACE
M dimension Y’s
Y1
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 manufacturing
Optimal Conditions or Control Space
Conceptual Design Space
Design
Space
Opt
Region of Interest
Region of operability
Uncertain space
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 + 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
Culture
Management
Supplier
Input
Supplier
Input
Supplier
Input
SPO's
Facilities
People
Process
Equipment
Systems
Regulations
Measurement
Environment
Output
Cus tom er
Output
Cus tom er
Output
Cus tom er
The Whole New Product Development Cycle
Unknown
Controllable
Factors
Concomitant
Uncontrollable
Factors
Product
Process
Design
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
B
+1
+1
1.90
3.80
5.20
1.30
15.50
-1
0.70
5.20
0.80
A
20.70
-1
1.00
-1
C
1.00
-1
-1
0.80
6.10
-1
0.50
+1
0.60
C
Left Cube Is D = LOW
q62
+1
Right Cube is D = HIGH
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
DESIGN-EXPERT Plot
Impurity -1
B: T em perature
20.7
X = A: Time
Y = B: Temperature
15.2894
Impurity-1
B- 40.000
B+ 100.000
Actual Factors
C: Moisture = 3.10
D: Solv ent = 7.50
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
Interaction Graph
DESIGN-EXPERT Plot
Impurity -1
C: M oi sture
20.7
X = A: Time
Y = C: Moisture
Impurity-1
C- 1.200
15.4312
C+ 5.000
Actual Factors
B: Temperature = 70.00
D: Solv ent = 7.50
10.1624
4.89364
-0.37515
3.00
4.50
6.00
A: T i m e
7.50
9.00
Temp*Moisture Interaction Plot
Interaction Graph
DESIGN-EXPERT Plot
Impurity -1
C: M oi sture
20.7
X = B: Temperature
Y = C: Moisture
C- 1.200
C+ 5.000
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
15.2697
Impurity-1
Design Points
9.8395
4.40925
2
-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
100.00
Impurity -1
20.7
8
0.1
85.00
Actual Factors
C: Moisture = 3.10
D: Solv ent = 7.50
Temp
B: Temperature
X1 = A: Time
X2 = B: Temperature
6
4
70.00
2
55.00
1
40.00
3.00
4.50
Time
6.00
A: T i m e
7.50
9.00
Time*Moisture Contour Plot
Impurity-1
Design-Expert® Sof tware
5.00
Impurity -1
20.7
8
0.1
C: Moisture
Moisture
Actual Factors
B: Temperature = 70.00
D: Solv ent = 7.50
6
4.05
X1 = A: Time
X2 = C: Moisture
4
3.10
2
2.15
1
1.20
3.00
4.50
6.00
Time
A: T i m e
7.50
9.00
Temp*Moisture Contour Plot
Impurity-1
Design-Expert® Sof tware
5.00
Impurity -1
Design Points
20.7
8
0.1
Moisture
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
6
C: Moisture
X1 = B: Temperature
X2 = C: Moisture
4.05
3.10
1
3
4
2
2.15
1.20
40.00
55.00
70.00
Temp
B: T em perature
85.00
100.00
Time*Temp Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
12
X1 = A: Time
X2 = B: Temperature
9
Impurity-1
Actual Factors
C: Moisture = 3.10
D: Solv ent = 7.50
6
3
0
100.00
9.00
85.00
7.50
70.00
B: Temperature
6.00
55.00
4.50
40.00
3.00
A: Time
Time*Moisture Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
9.1
X1 = A: Time
X2 = C: Moisture
7.025
Impurity-1
Actual Factors
B: Temperature = 70.00
D: Solv ent = 7.50
4.95
2.875
0.8
5.00
9.00
4.05
7.50
3.10
C: Moisture
6.00
2.15
4.50
1.20
3.00
A: Time
Temp*Moisture Surface
Design-Expert® Sof tware
Impurity -1
20.7
0.1
12
X1 = B: Temperature
X2 = C: Moisture
9
Impurity-1
Actual Factors
A: Time = 6.00
D: Solv ent = 7.50
6
3
0
5.00
100.00
4.05
85.00
3.10
C: Moisture
70.00
2.15
55.00
1.20
40.00
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%
R2 = 0.95
f(Xi) Design Space
Impurity =
+0.6079
+Time
*
+Temperature *
+Moisture
*
+Time*Temp *
+Time*Moist *
+Temp*Moist *
+T*T*M
*
-0.0057
-0.0058
+0.1994
+0.00061
-0.29386
-0.00502
+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
Intercept
A-Time
B-Temperature
C-Moisture
AB
AC
BC
ABC
Coefficient Factor Level
0.607940
-0.005702
4
-0.005813
70
0.199410
1
0.000614
280
-0.293860
4
-0.005018
70
0.007127
280
Impurity
1.0
Predictive Equation
Factor
Intercept
A-Time
B-Temperature
C-Moisture
AB
AC
BC
ABC
Coefficient Factor Level
0.607940
-0.005702
9
-0.005813
43
0.199410
5
0.000614
387
-0.293860
45
-0.005018
215
0.007127
1935
Impurity
1.0
Design Space
Overlay Plot
Design-Expert® Sof tware
100.00
Ov erlay Plot
Impurity -1
X1 = A: Time
X2 = B: Temperature
B: Temperature
Actual Factors
C: Moisture = 5.00
D: Solv ent = 7.50
85.00
70.00
55.00
Impurity-1: 1
40.00
3.00
4.50
6.00
A: T ime
7.50
9.00
Design Space
Overlay Plot
Design-Expert® Sof tware
100.00
Ov erlay Plot
Impurity -1
X1 = A: Time
X2 = B: Temperature
B: Temperature
Actual Factors
C: Moisture = 1.20
D: Solv ent = 7.50
85.00
70.00
Impurity-1: 1
55.00
40.00
3.00
4.50
6.00
A: T im 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.