Experimental Design in the Pharmaceutical Industry Brad Evans, Pfizer Brad.Evans@Pfizer.com

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)

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

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 25-1 + four center runs in two blocks of 10 2500 L 15 mL

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”

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

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 + -

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”

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

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 3 levels Note X1 is tested at +/- 1, but X2 only at +/- 0.866 Choice of x1, x2 matters

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)

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 = 10 - delta (runs 11, 12, 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”

4 – factor Hybrid designs A, B, C (n=16) (CCD in 3 factors) Coded levels of X4 A -0.9075 0.6444 -1.4945 1.7844 B -1.0498 0.6045 -0.2692 1.7317 C -1.0509 0.5675 1.7658 https://www.tandfonline.com/doi/abs/10.1080/00401706.1976.10489473 x1, x2, x3 Design Axial A 1.6853 B 1.5177 C 1.4697 A B C have different Axial levels and different X4 levels X1 X2 X3 five levels, X4 has four levels

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!

References Roquemore KG (1976). “Hybrid Designs for Quadratic Response Surfaces.”Technometrics,18(4), 419–423 http://www.hrpub.org/download/20170228/MS2- 13408044.pdf http://designcomputing.net/gendex/rat/