An Introduction to Design of Experiments (DOE) and Applications to Pharmaceutical Development W. Heath Rushing Adsurgo LLC
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An Introduction to Design of Experiments (DOE)
and Applications to Pharmaceutical Development
W. Heath Rushing
Adsurgo LLC
2
Outline
Introduction to DOE
Concepts
Screening Designs
Response Surface Designs
Summary
2
3
INTRODUCTION
3
4
Quality System – Product Lifecycle
Set Specifications
Measurement System
CQAs and Input Parameters
Pharmaceutical Development
Control or Risk Management Plan
Validate the Process
Commercial Manufacturing
Product Discontinuation
4
5
Set Specifications
Measurement System
CQAs and Input Parameters
Pharmaceutical Development
Control or Risk Management Plan
Validate the Process
Commercial Manufacturing
Product Discontinuation
5
DOE for Pharmaceutical Development
6
Design of Experiments (DOE)
Systematically chosen group of experiments where the
levels of (chosen) process parameters are varied
together to measure an effect on a critical quality
attribute (CQA).
Some factors are controlled while others are held constant.
Basic metrics:
– Number of factors
– Number of runs
– Confidence and power.
Isolate effects including interactions and quadratic effects.
6
7
1. State the objective.
2. Select the responses.
3. Choose factors, levels, and ranges.
4. Choose an appropriate design.
5. Run the experiments.
6. Analyze the results.
7. Conduct confirmation runs.
7
Steps to DOE
8
Steps to DOE
1. State the objective.
2. Select the responses.
3. Choose factors, levels, and ranges.
4. Choose an appropriate design.
5. Run the experiments.
6. Analyze the results.
7. Conduct confirmation runs.
8
9
Quality by Design (QbD) Using DOE
“An enhanced, quality by design approach to product
development would additionally include the following
elements:”
A systematic understanding that includes
– identifying, through experimentation and risk
assessment, the material attributes and process
parameters that have an effect on product CQAs
– a determination of the functional relationships that
link material attributes and process parameters to
product CQAs.
Using this understanding in combination with quality
risk management to establish an appropriate control
strategy
9
Reference: Guidance for Industry Q8(R2) Pharmaceutical Development. Nov 2007.
10
Purpose of Experiments
Establish significant process parameters.
Optimize the operating conditions of the process.
11
Classic versus Custom Design
11
Classic Custom
Screening Factorial
Fractional Factorial
D-optimal
Response
Surface
Central Composite Design (CCD)
Box-Behnken
I-optimal
12
CONCEPTS
12
13
Case Study 1
A pharmaceutical
manufacturer wants to
compare two tablet
press machines within
the same facility. They
sample a total of 16
tablets from the two
press machines.
13
The design/analysis of this is known as a two-sample t-test.
14
Two-Sample t Test
H0: µA = µB The means are equal.
Ha: µA ≠ µB The means are different.
14
µA = µB µA µB
15
H0: µA = µB The means are equal.
Ha: µA ≠ µB The means are different.
15
µA = µB
Type I error
or
α error
Confidence = 1- α
Two-Sample t Test
16
H0: µA = µB The means are equal.
Ha: µA ≠ µB The means are different.
16
µA µB
Type II error
or
β error
Power = 1- β
Two-Sample t Test
17
H0: µA = µB The means are equal.
Ha: µA ≠ µB The means are different.
α = 0.05 95% confidence
t stat = -5.655
p-value = <0.0001
17
Two-Sample t Test
18
t statistic and Power
18
0
19
Power - Smallest Standard Error
19
Option A
n A= 4
nB = 12
Option B
nA = 8
nB = 8
Number of experiments = 16
Balance wins!
20
Power - Smallest Standard Error
20
Option A
n A= 4
nB = 12
Option B
nA = 8
nB = 8
Number of experiments = 16
Balance wins!
21
SCREENING DESIGNS
21
22
Screening Designs
Establish significant process parameters.
Optimize the operating conditions of the process.
22
23
Screening Designs
Screening designs are typically used to establish
significant process parameters:
Factorial design
Fractional factorial design
D-optimal design
23
24
Case Study 2
A biopharmaceutical manufacturer evaluated the effect of
process parameters on cell productivity.
From the assessment of quality risk, it was determined to
focus on the effect of temperature, pH, time, and rate on
cell productivity? The design/analysis of this is known as a
screening design.
24
25
DOE for 2-Level Process Parameters
When a DOE includes all combinations of the parameters and
their settings, the design is known as a 2k factorial.
Settings for factors in designs are coded with -1 and +1. This
is done to make the effects scale invariant (relative effects).
25
Temp pH
1
2
3
4
- 1
+1
- 1
+1
- 1
- 1
+1
+1
Temp pH
1
2
3
4
34
38
34
38
6.8
6.8
7.2
7.2
26
Single Replicate of a 2k Factorial Design
DOE enables you to detect the significance of main
effects, as well as their interactions.
26
Temp pH
1
2
3
4
- 1
+1
- 1
+1
- 1
- 1
+1
+1
+1
- 1
- 1
+1
Temp*pH Productivity
234
54
238
257
+
_ _
pH +
Temp
27
23 Factorial Design
Three factors: pH, Temp, and Time.
+
_ Time _ _
+
Temp +
pH Temp Time
1
2
3
4
5
6
7
8
- 1
+1
+1
- 1
+1
- 1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
- 1
+1
+1
- 1
- 1
+1
+1
pH
28
24 Factorial Design
The benefits of designed experiments increases as the
number of significant process parameters are added to
the design. Add Rate to the design.
28
pH
+
_ Time _
_
+
Temp +
Rate +
+
_ _
_
+
Temp +
29
24 Factorial Design
The benefits of designed experiments increases as the
number of significant process parameters are added to
the design. Add Rate to the design.
29
30
Number of Runs – 2k Factorial Designs
30
22 = 4 runs
23 = 8 runs
24 = 16 runs
25 = 32 runs
26 = 64 runs
27 = 128 runs
1. Prescription number of runs.
2. Increasing number of factors? 5, 6, 7…
31
Number of Runs – 2k Factorial Designs
31
22 = 4 runs
23 = 8 runs
24 = 16 runs
25 = 32 runs
26 = 64 runs
27 = 128 runs
1. Prescription number of runs.
2. Increasing number of factors? 5, 6, 7…
32
Screening Designs
Screening designs are typically used to establish
significant process parameters:
Factorial design
Fractional factorial design
D-optimal design
32
33
Fractional Factorial Design
Fractional factorial experiments give up information about
some of interactions in favor of examining more
parameters. For this process, you might want to know
whether Temperature, pH, or Time has a significant
effect on Productivity. A 23 full-factorial design has eight
runs. A half-fractional factorial has four runs.
33
Temp Time 1
2
3
4
5
6
7
8
- 1
+1
+1
- 1
+1
- 1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
- 1
+1
+1
- 1
- 1
+1
+1
pH
34
Aliasing – Resolution 3
Notice that the Temp*pH*Time (three-factor) interaction
is always positive. Each main effect is identical to a two-
factor interaction. When certain interaction effects are
identical to other effects, this is called aliasing.
34
Temp Time 1
2
3
4
+1
- 1
- 1
+1
- 1
+1
- 1
+1
- 1
- 1
+1
+1
pH
35
DOE for 2-Level Process Parameters
The benefits of designed experiments increases as the
number of significant process parameters are added to
the design. Add Rate to the design.
35
pH
+
_ Time _
_
+
Temp +
Rate +
+
_ _
_
+
Temp +
36
Aliasing – Resolution 4
For this process, you might want to know whether
Temperature, pH, Time, or Rate has a significant effect
on Productivity. A 24 full-factorial design has 16 runs.
A half-fractional factorial has eight runs. Notice that the
four-factor interaction is always positive.
36
Temp Time
1
2
3
4
5
6
7
8
- 1
+1
+1
- 1
+1
- 1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
+1
- 1
- 1
+1
+1
- 1
- 1
+1
+1
pH Rate
- 1
- 1
- 1
- 1
+1
+1
+1
+1
37
Aliasing – Resolution 5
The benefits of designed experiments increases as the
number of significant process parameters are added to
the design. Add Amount to the design. A 25 full-factorial
design would have 32 runs. A half-fractional factorial
design would have 16 runs and have no main effects or
two-factor interactions aliased with other main effects or
two-factor interactions.
37
38
Number of Runs – 2k Factorial Designs
38
22 = 4 runs
23 = 8 runs
24 = 16 runs
25 = 32 runs
26 = 64 runs
27 = 128 runs
1. Prescription number of runs.
2. Increasing number of factors? 5, 6, 7…
39
Purpose of Experiments
Establish significant process parameters.
Optimize the operating conditions of the process.
39
40 40
Correlation of Estimates - Spectrum
0 1
2k factorial design Fractional factorial design
41
D-Optimal Design
D-optimal designs seek to minimize the variance associated
with parameter estimates. This design is appropriate when
the goal is to establish significant process parameters.
User-specified number of runs.
Allows:
– Hard-to-change factors
– Constraints
– Quadratic effects.
Spreads experimental runs across the design region as
evenly as possible.
Much more flexible!
41
42 42
0 1
D-Optimal Design
43
Case Study 2
43
44
RESPONSE SURFACE DESIGNS
44
45
The purpose of the experiments is to do the following:
establish significant process parameters
optimize the operating conditions of the process
Response Surface Designs
46
Case Study 3
A pharmaceutical
manufacturer has
developed a control
strategy for a milling
process for the amount of
water, mill rate, and drying
temperature for two critical
quality attributes: moisture
content and amount of API.
46
However, they would like to optimize the process; find the
optimal settings for the amount of water, mill rate, and
drying temperature that minimize the moisture content
while matching a target amount of API. The design/analysis
of this is known as a response surface design.
47
Response Surface Designs
Response surface designs are typically used to optimize
the operating conditions of the process.
Central Composite Designs (CCDs)
Box-Behnken Designs
I-optimal design
47
48
DOE for 2-Level Process Parameters
The benefits of designed experiments increases as the
number of significant process parameters are added to
the design.
48
+
_ Rate _ _
+
Temp +
Water
49
Central Composite Design
A central composite design (CCD) is a widely used
response surface design.
The CCD adds axial runs to the initial design.
Each factor in the design has five levels (factorial,
center, axial).
Each (added) experimental run has one factor
at its axial value and all others at its center.
+
_ Rate _
_
+
Temp +
Water
50
CCD: Face-Centered
A face-centered central composite design is also a widely
used response surface design.
uses a pre-existing screening design.
usually, used when augmenting original design; often
called sequential experimentation.
places points on the face of the cube. Therefore, it
requires only three levels of factor settings with no
settings outside the original design region.
+
_ Rate _ _
+
Temp +
Water
51
Box-Behnken Designs
A Box-Behnken design is also a widely used response
surface design.
Each factor in the design has three levels.
This design avoids extreme design points.
Each (added) experimental run has one factor at its center and all others at its axial value.
+
_ Rate _
_
+
Temp +
Water
52
I-Optimal Design
An I-optimal design seeks to minimize the average
prediction variance over the design region. This design is
appropriate when the goal is to optimize the operating
conditions of the process.
User-specified number of runs.
Allows:
– Hard-to-change factors
– Constraints
– Quadratic effects.
The design focuses design points near the center of
the design region.
Flexible response surface design option.
53
Case Study 3
53
55
SUMMARY
55
56
Quality System – Product Lifecycle
Set Specifications
Measurement System
CQAs and Input Parameters
Pharmaceutical Development
Control or Risk Management Plan
Validate the Process
Commercial Manufacturing
Product Discontinuation
56
57
Classic versus Custom Design
57
Classic Custom
Screening Factorial
Fractional Factorial
D-optimal
Response
Surface
Central Composite Design (CCD)
Box-Behnken
I-optimal
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