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In-Vitro Screening for Combination Drug Discovery

John J. Peterson GlaxoSmithKline Pharmaceuticals, R&D

2009 Midwest Biopharmaceutical Statistics Workshop

Cmpd A

Top conc.Cmpd A only

Cmpd B only

DMSO (pos. cntl.)

No cells (neg. cntl.)

Cmpd B Top conc. Top conc. Top conc.

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Outline of Talk

• Experimental design used

• What is “excess over highest single agent” (EOHSA)?

• Simultaneous testing for EOHSA across all combinations

• Some examples

• An Introduction to “nonlinear blending” synergy.

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Experimental design for screening pairs of compounds

Compound B Dose Levels

8 S C C C C C C C C

7 S C C C C C C C C

6 S C C C C C C C C

5 S C C C C C C C C

4 S C C C C C C C C

3 S C C C C C C C C

2 S C C C C C C C C

1 S C C C C C C C C

0 V S S S S S S S S

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

A kxk factorial. Here k = 9.

C = “combination”S = “single compound”V = “vehicle (control)”

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Excess over highest single agent (EOHSA)

• For a kxk factorial design let be the mean response for the combination ofcompound A at dose level i and compound B at dose level j.

• Let be the dose of compound A alone at dose level i.

• Let be the dose of compound B alone at dose level j.

• The compound combination at dose levels (i, j) exhibits EOHSA if

• EOHSA provides an easy-to-understand, low-level criterion for combination drug screening. - It is also an FDA criterion for (21 CRF 300.50) for combination drug approval. - Used by CombinatoRx Inc. for combination compound screening (Borisy et al, (2003) Proceedings of the National Academy of Science, 100, 7977–7982)

ij

i 0

j0

max ,ij i j 0 0

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Simultaneous testing for EOHSA across compound combinations

• Testing for EOHSA for one (i, j) compound combination can be accomplishedby use of the “min test” to test the null and alternative hypotheses below.

• The above hypothesis can he tested by doing two one-sided tests of the form

each at level for an overall false-positive error rate of (if both nulls are rejected)

• However since there are combinations, we need to adjust for multiple comparisons to control the family-wise error rate across all combinations.

• Hung (2000) and Westfall, Ho, and Prillaman (2001) have suggested procedures for conducting simultaneous min tests.

: vs. :ij i ij j ij i ij jH or H and 0 0 0 1 0 0

: vs. : and : vs. :ij i ij i ij j ij jH H H H 0 0 1 0 0 0 1 0

k 21

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Simultaneous testing for EOHSA across compound combinations

• Since there are combinations, we need to adjust for multiplecomparisons to control the family-wise error rate across all combinations.

• Hung (2000) and Westfall, Ho, and Prillaman (2001) suggested procedures for conducting simultaneous min tests.

• However since the kxk design involves increasing doses of both compounds,we can expect dose-response trends along each row and column of the design.

• These dose-response trends can be exploited to gain additional power to testfor EOHSA across the various compound combinations.

k 21

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Compound B Dose Levels

8 S C C C C C C C C

7 S C C C C C C C C

6 S C C C C C C C C

5 S C C C C C C C C

4 S C C C C C C C C

3 S C C C C C C C C

2 S C C C C C C C C

1 S C C C C C C C C

0 V S S S S S S S S

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

Simultaneous testing for EOHSA across compound combinations

C = “combination”S = “single compound”V = “vehicle (control)”

• Suppose there is a trend forcompound A (for dose levels 0 to 5)at dose level 4 of compound B.

• Suppose also there is a trend forcompound B (for dose levels 0 to 4)at dose level 5 of compound A.

• It follows then that the compoundcombination (5,4) has EOHSA.

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Compound B Dose Levels

8 S C C C C C C C C

7 S C C C C C C C C

6 S C C C C C C C C

5 S C C C C C C C C

4 S C C C C C C C C

3 S C C C C C C C C

2 S C C C C C C C C

1 S C C C C C C C C

0 V S S S S S S S S

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

Simultaneous testing for EOHSA across compound combinations

C = “combination”S = “single compound”V = “vehicle (control)”

• So intersecting trends can be used test for EOHSA.

• Since there are k dose levels of eachcompound there are 2(k-1) simultaneoustrend tests involving exactly l dose levels.

• At each dose level, l, we can do 2(k-1)Bonferroni-adjusted trend tests.

• The Tukey step-down trend test can be used as we step from level l=(k-1) to l=1.

• The Tukey step-down test requires noadjustment of the (Bonferroni-adjusted) -level.

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Compound B Dose Levels

8 S C C C C C C C C

7 S C C C C C C C C

6 S C C C C C C C C

5 S C C C C C C C C

4 S C C C C C C C C

3 S C C C C C C C C

2 S C C C C C C C C

1 S C C C C C C C C

0 V S S S S S S S S

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

Simultaneous testing for EOHSA across compound combinations

C = “combination”S = “single compound”V = “vehicle (control)”

PROPOSED TESTING PROCEDURE

1. At each dose level, l, do 2(k-1)Bonferroni-adjusted trend tests.

2. Use the Tukey step-down trend test as you step from level l=(k-1) to l=1.

Note:• The Tukey step-down test requires noadjustment of the (Bonferroni-adjusted) -level.

• It can be proven that this procedurecontrols the FWER strongly at level .

• The proposed procedure is more efficientthan doing (k-1)2 multiple comparisons,even with correlation adjusted p-values.

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Example

Compound B DoseLevel Numbers

8 7 3 10 15 8 31 58 68 72

7 0 3 2 3 4 23 56 66 68

6 5 2 -2 -1 5 18 54 63 68

5 -4 -3 -7 -3 2 20 56 63 68

4 -7 -6 3 -1 2 17 53 63 65

3 -9 -6 -4 -2 -1 14 51 66 68

2 -10 -9 -10 -2 1 23 54 63 66

1 -2 -11 -11 -5 2 20 52 60 64

0 0 -5 -1 0 -2 14 52 64 69

0 1 2 3 4 5 6 7 8

5’FU (Compound A) Dose Level Numbers

• Mean percent reduction in living cancer cells for 9x9 factorial experiment (n = 2)replications per treatment group) for compound A and compound B (A549 cell line).

• Means with boldface-italic font (inthe highlighted cells) are associatedwith combinations having statisticallysignificant EOHSA.

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Simultaneous testing for EOHSA across compound combinations

• Proposed Bonferroni testing procedure:

1. At each dose level, l, do 2(k-1)Bonferroni-adjusted trend tests.

2. Use the Tukey step-down trend test as you step down from level l=(k-1) to l=1.

• Proposed Modified Adjusted p-value testing procedure.In step 1 above replace the Bonferroni adjustment with a more efficient bootstrap adjusted p-value.

- This modification can be easily executed using SAS® PROC MULTTEST. - Simulations indicate that this procedure is more powerful than the Bonferroni adjusted version while still keeping the FWER to at most .

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It is possible to have many trends but no combinations with EOHSA

Compound B Dose Levels

8 8 8 8 8 8 8 8 8 8

7 7 7 7 7 7 7 7 7 8

6 6 6 6 6 6 6 6 7 8

5 5 5 5 5 5 5 6 7 8

4 4 4 4 4 4 5 6 7 8

3 3 3 3 3 4 5 6 7 8

2 2 2 2 3 4 5 6 7 8

1 1 1 2 3 4 5 6 7 8

0 0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

So the null space ofthis testing procedureis complex.

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If the 5 above were replaced by the (circled) 6 then thecombination highlighted in yellow would have EOHSA.

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Simulations to assess overall Type I error rate

• Consider the following three null hypothesis situations:

: all ' equal to zeroijH s10

: for all ( , )ijH j i j 20

: ' have the values in the table :ijH s30

Compound B Dose Levels

8 8 8 8 8 8 8 8 8 8

7 7 7 7 7 7 7 7 7 8

6 6 6 6 6 6 6 6 7 8

5 5 5 5 5 5 5 6 7 8

4 4 4 4 4 4 5 6 7 8

3 3 3 3 3 4 5 6 7 8

2 2 2 2 3 4 5 6 7 8

1 1 1 2 3 4 5 6 7 8

0 0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8

Compound A Dose Levels

• 1,000 (normally distributed) data setswere simulated under each of the threenull hypotheses (with n=2 per cell and= 1). Nominal = 0.05.

• The false-positive error rates were:

% . % . %

H H H1 2 30 0 0

0 48 09

Compound B only has a strong trend

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Comparisons with some other testing procedures

MATBOOT=“multiplicity adjusted Tukey step-down trend test (Bootstrap)”MATBON=“multiplicity adjusted Tukey step-down trend test (Bonferroni)”SHUIIUT=Simes-Hommel Union-Intersection-Intersection-Union TrendSHUIIU=Simes-Hommel Union-Intersection-Intersection-UnionMAPC=“multiplicity adjusted (bootstrap) p-values for (pairwise) contrasts.

Four drug combinations were tested in each of four cell lines resulting in 16 experiments

MATBOOT MATBON SHUIIUT SHUIIU MAPC

Average no. of cells with EOHSA reported

5.25 2.94 1.81 1.06 0.69

Median no. of cells with EOHSA reported

5 3 1.5 0 0

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Summary for Screening for EOHSA

• Using the Bonferroni procedure to adjust Tukey’s step-down trend test resultsin adjustments across only 2(k-1) groups rather than (k-1)2 groups. - This provides improved power, even over Monte Carol adjusted procedures, when their adjustment is over (k-1)2 groups (at least for k=9).

• The power of this adjustment of Tukey’s trend test can be improved by using PROC MULTTEST, which is easy to implement.

• It can be proven that the Bonferroni procedure to adjust Tukey’s step-down trend test strongly controls the FWER. - The more powerful bootstrap adjusted modification appears to strongly control the FWER as well. • It may be useful to follow up this “low level” screening with a criterion that providesa higher “drug synergy hurdle”. One possibility is to use the concept of “nonlinear blending” found in mixture experiments.

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Nonlinear Blending Compared to FDA’s EOHSA.

total dose (molar)

Total dose(molar)

solid gray line of constant total dose (molar)

• Nonlinear blending is: “excess over highest single agent at total dose” as opposed to “excess over highest single agent (at component dose)”

• Therefore nonlinear blending is a stronger form of “synergy”.

drug A

drug B

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Why classical synergy indices do not generally work well for screening for combination drug synergy.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1 1.2

Drug 1 dose

Dru

g 2

do

se

Loewe synergy

Loewe anatagonism

Loewe additivity

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1 1.2

Drug 1 dose

Dru

g 2

do

se

Loewe synergy

Loewe anatagonism

Loewe additivityAB

C

AB

C

Drug 1

Dru

g 2

Isobologram (e.g. 50%)

d1+d2=A

Point of 50% response

d d

ED ED 1 2

1 250 50

1

We have Loewe synergy at thecombination (d1,d2) if

0.4 10.733 1

1 3

But what if one or both of theED50’s (or ED60’s, etc.) do notexist?

18log( Conc )

Re

spo

nse

0

20

40

60

80

100

-4 -2 0 2

Monotherapy 1

-4 -2 0 2

Monotherapy 2

-4 -2 0 2

50:50 Ratio

Problems with the Interaction Index

Cannot always compute the interaction index!

Monotherapies do not achieveY = 50%

Yet, excellent synergy existsAt a 50:50 ratio!

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Nonlinear Blending.• If the response increases as we move away from the single agent compounds, then we have “optimal nonlinear blending”.

• Optimal nonlinear blending can exist no matter what the shape of the dose response curves for the single agent compounds.

• This type of synergy is much stronger than “excess over highest single agent”.

Compound A

Compound B

total amount, T3

Total amount, T3

line of constant total amount, T3

total amount, T2

total amount, T1

Combined compound response

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Nonlinear Blending: Weak and Strong Nonlinear Blending

0 50 100 0 50 100

Percent of drug 1 Percent of drug 1

Response(percent)

Response(percent)

Weak nonlinear blending Strong nonlinear blending

0

100

50

0

50

100

25

75

25

75

Blending profiles for two different pairs of drugs at a given total (molar) dose

For details see: Peterson, J. and Novick, S., “Nonlinear Blending: A Useful,General Concept for the Assessment of Combination Drug Synergy”, Journalof Receptors and Signal Transduction, vol.27, pp125-146.

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2187Y 243X+2187Y

0.5

729Y 0.5 1/3

243Y 0.5 1/3 1/9

81Y 1X+81Y 0.5 1/3 1/9 1/27

27Y 1X+27Y 0.5 1/3 1/9 1/27

9Y 8/9

1X+9Y

0.5 1/3 1/9 1/27

3Y 2/3

1X+3Y

0.5 1/3 1/9 1/27

1Y 0.5

1X+1Y

1/3

3x+1Y

1/9

9X+1Y

1/27

27X+1Y

1/81

81X+1Y

0 1X 3X 9X 27X 81X 243X 729X 2187X

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The testing process for strong nonlinear blending.

drug A (nM)

drug B(nM)

7 Rays (diagonals) of constant dose ratio.

= actual data point

= interpolated data point

Plate APercent of drug A

Interpolatedresponse

0 10050

Interpolated datapoints from platesA and B.

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50%

Drug A

Drug B Ten ‘Total (Molar) Dose’ SlicesThrough the Combination Drug Region

1%

50%

99%

7 diagonals (rays)

This line only cutsacross 4 true rays

Percent of drug A

Interpolatedresponse

0 10050

Imputed valuesin blue

plate A

plate B

0%

0% 50% 99%

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The testing process for strong nonlinear blending.

Percent of drug A

Interpolatedresponse

0 10050

Interpolated datapoints from platesA and B.

1. For each total dose (molar) amount, fit a cubic polynomial curve to the data. (For robustness sake, we fit the data using a rank transformation of the percent drug A levels.)

2. Using gridding, find the maximum mean response.

3. Using the ‘min’ test, test to see if the maximum mean response is greater than both mean responses associated with 0% and 100% of drug A. If so, then we have strongnonlinear blending at that total (molar) amount.

4. Adjust the min test p-values (e.g. using the Hommel adjustment) across the various total dose levels used.

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Summary for Screening for Strong Nonlinear Blending• Strong nonlinear blending can, in a practical sense, address any situation that might come up in the screening of drug combinations.

• The classical synergy indices such as Loewe synergy index, Chou & Talalay, Bliss, etc. all have serious flaws with regard to computation or interpretation ofsynergy.

• If Loewe synergy can exist (e.g. both ED50’s exist) then the existence of strong nonlinear blending implies the existence of Loewe synergy.

• It may be possible to improve screening for ‘strong nonlinear blending’by use of generalized additive models to automate fitting of response surfacesto 9x9 factorial plate designs. This is work for the future!

For further details on Nonlinear Blending see: Peterson, J. and Novick, S., “Nonlinear Blending: A Useful,General Concept for the Assessment of Combination Drug Synergy”, Journalof Receptors and Signal Transduction, vol.27, pp125-146.

Send e-mail to john.peterson@gsk.com for a copy.