1. Experimental Design in the Pharmaceutical Industry
Brad Evans, Pfizer

2. Introduction Scope: Drug development process:
small scale lab experiments up to commercial supply,
including product formulation and long term storage
Out of Scope: Clinical trials, Drug Safety
Illustrative, not necessarily exhaustive
Focus on appropriate design (not models / analysis)

3. Standard Designs
Two-level factorial (more often continuous inputs, but categorical too)
Goal: screening, understanding, establish operating ranges, typically not optimization
Generally expect that all runs will be successful
Goal: operational window, expect to run at center condition
Example: Thawing cells from long term storage
How quickly to thaw?
How long can we allow?
Ambient or controlled thaw?
Due diligence type

4. Standard Design
Bioreactor: what makes the cells grow: acceptable, consistent?
(every biological product contains this step, as does beer and breadmaking)
Hardware limitation: Bank of 10 Reactors
23 + two center runs
24 + four center runs in two blocks of 10
four center runs in two blocks of 10
2500 L
15 mL

5. Standard Design
Purification chromatography: what cleans the material sufficiently?
Expect “enough clearance” under typical conditions
But how much might be needed if material is not typical?
Too harsh conditions: “good gets removed with the bad”
Run order effects typically present (more so with more runs)
23 + two center runs,
24 + four center runs
Run order is very important:
we need designs that are “robust against trend”

6. Standard, with a twist
Formulate multiple strengths and/or packages, test over time
Bracketing
Test low and high strength (large and small container)
Assume linearity across strength (or container size)
Matrixing
Typical time points (0,1, 3, 6, 9, 12, 18, 24, 36) months
Test 1/2 or 2/3 of the time points and every 12 months

7. Standard, with a twist
Formulate the final product five ways … based on five inputs
Not changing product or process, just store and test over time:
supply chain flexibility
ensure safety throughout shelf life
meet requirements
No ability to estimate individual effects
Idea is to test worst cases and thus ensure robustness
Far less analytical testing required
Subject matter experience / past experience “determines” groupings and worst case
Typically no modeling (other than “all pass”) X1 X2 X3 X4 X5 + -

8. Response Surface Designs
Central Composite is most frequently used (next talk)
Two – five inputs typically (full CCD gets big with 6+)
Might be “face centered” in one or more inputs,
Often that input has low precision and / or narrow range
May go straight to RSM based on our historical experience:
We will have a high % of “active factors”, expect curvature
We measure lots of responses: harder for factors to drop out
We may not have time for “round two”

9. Response Surface Designs
Definitive Screening Design (DSD)
Used with 5-8 factors
Analysis more complex since full model is saturated
multiple models with very similar fits
backward selection not an option
Works best when:
some factors drop out
few responses
(it is a *screening* design after all!)
Our use case: (likely) inactive factors not studied
most factors are active
many responses

10. Response Surface Designs
Doehlert Design has some unique properties
(less runs than CCD) ID X1 X2 1
0.5
0.866 2 3
-0.866 4
-0.5 5 -1 6 7
5 levels levels
Note X1 is tested at +/- 1,
but X2 only at +/
Choice of x1, x2 matters

11. Doehlert Design, k=3
Note that runs 1-7 are the same as the two-factor design (with x3 = 0) X1 X2 X3 #
0.5
0.866 1 2
-0.866 3
-0.5 4 -1 5 6 7
0.577
0.816 8
-0.289 9 10
0.289
-0.816 11 12
-0.577 13
Runs 8-13 are “inside” the first six for x1, x2
X1: same five levels
X2: five levels (was three)
X3: three levels (no +/- 1)

12. Doehlert Designs, k  k + 1 A factor can be added so long as:
it was involved in the first round (but not varied)
it can be both higher and lower than in the first round
i.e. it was set to “coded zero” in the first round
First round: k=2 inputs, concentration set at 10 for all runs
Second round:
Concentration = 10 + delta (runs 8, 9, 10)
Concentration = delta (runs 11, 12, 13)

13. Optimal designs (A/G/I/D)
Concerns:
Do we know the model?
Do we know the model for every response?
May require many factor levels, so not as operationally friendly
In simpler cases often pushes factor levels to extremes, so can end up very similar to standard designs
Can be (very) useful when fixed # of runs is not a power of two
Can be useful in augmenting a set of existing runs
Fits any “N”

14. 4 – factor Hybrid designs A, B, C (n=16) (CCD in 3 factors)
Coded levels of X4 A
0.6444
1.7844 B
0.6045
1.7317 C
0.5675
1.7658
x1, x2, x3
Design Axial A B C
A B C have different Axial levels and different X4 levels
X1 X2 X3 five levels, X4 has four levels

15. Summary Experimental design is very powerful tool
Goal is to find a design that fits the purpose and the setting
Standard designs
Standard, with case specific modifications
Novel / contemporary designs
Variations of the above
Thank you!

16. References
Roquemore KG (1976). “Hybrid Designs for Quadratic Response Surfaces.”Technometrics,18(4), 419–423
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