A general pharmacodynamic

interaction (GPDI) model

Sebastian Wicha, Chunli Chen, Oskar Clewe, Ulrika Simonsson

Pharmacometrics Research Group

Uppsala Universitet

PAGE Meeting, Lisbon, 2016-06-09

1

Combination therapy –

Drug interactions?

Combination therapy is prevalent in many therapeutic areas

– Anti-infectives

– Chemotherapy

– Antiepileptics

– Anaesthesia

What are our current modelling options and their limitations

for characterization of pharmacodynamic (PD) drug

interactions (DDI)?

2

PD DDI modelling

current options

Mechanistic approaches

• Receptor theory

– Competitive interaction models

– Noncompetitive/uncompetitive models

• Systems biology/pharmacology

Additivity-based empirical models

• Loewe Additivity

– Greco model, …

– Combination indices

• Bliss Independence

– Empiric Bliss model(s)

3

R

CA

CB

R*

R*

E

no E

Challenges with current

modelling options

Mechanistic approaches

• Lack of knowledge to parameterize mechanistic interaction models

Additivity-based empirical models

4

5

alpha = 0 Loewe Additivity

alpha > 0 Synergy

alpha < 0 Antagonism

W.R. Greco et al. Cancer Res., 50: 5318–27 (1990).

Greco model

1 =𝐶𝐴

𝐸𝐶50𝐴 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

1/𝐻𝐴+

𝐶𝐵

𝐸𝐶50𝐵 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

1/𝐻𝐵

+𝛼 × 𝐶𝐴 × 𝐶𝐵

𝐸𝐶50𝐴 × 𝐸𝐶50𝐵 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

12𝐻𝐴

+1

2𝐻𝐵

Loewe Additivity

Interaction

term

Challenges with current

modelling options

Mechanistic approaches

• Lack of knowledge to parameterize mechanistic interaction models

Additivity-based empirical models

• Interaction parameters are not quantitatively interpretable

• Single underlying additivity concept

• Mono-dimensional (‘symmetric’) interactions

• Limitation to two drugs

1 =𝐶𝐴

𝐸𝐶50𝐴 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

1/𝐻𝐴+

𝐶𝐵

𝐸𝐶50𝐵 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

1/𝐻𝐵

+𝛼 × 𝐶𝐴 × 𝐶𝐵

𝐸𝐶50𝐴 × 𝐸𝐶50𝐵 ×𝐸

𝐸𝑚𝑎𝑥 − 𝐸

12𝐻𝐴

+1

2𝐻𝐵

Greco model

W.R. Greco et al. Cancer Res., 50: 5318–27 (1990).

Towards a general PD

interaction model

• Receptor-based mechanistic approaches

– Competitive interaction models

– Noncompetitive/uncompetitive models

• Additivity-based empirical models

– Loewe Additivity

• Greco model

– Bliss Independence

• Empiric Bliss model(s)

7

General PD interaction

model

Basis: additivity criterion

Mechanistic elements

The Emax model for

quantification of drug effects

8

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Drug concentration C [fraction of EC50]

Dru

g effect

E [

frac

tion o

f Em

ax]

𝐸 =𝐸𝑚𝑎𝑥 × 𝐶𝐻

𝐸𝐶50𝐻 + 𝐶𝐻

GPDI model

implementation on EC50

• 𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴×𝐶

𝐴𝐻𝐴

𝐸𝐶50𝐴

× 1+𝐼𝑛𝑡

𝐴𝐵×𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇

,𝐴𝐵

+𝐶𝐵

𝐻𝐴+𝐶𝐴

𝐻𝐴

• 𝐸𝐵 =𝐸𝑚𝑎𝑥𝐵×𝐶

𝐵𝐻𝐵

𝐸𝐶50𝐵

× 1+𝐼𝑛𝑡

𝐵𝐴×𝐶𝐴

𝐸𝐶50𝐼𝑁𝑇

,𝐵𝐴

+𝐶𝐴

𝐻𝐵+𝐶𝐵

𝐻𝐵

• 4 parameter interaction model

– IntAB, IntBA (-1 < Int < Inf) (0: Additivity, <0: Synergy, >0: Antagonism)

– EC50INT,AB , EC50INT,BA

• Simplifications:

– IntAB = IntBA (joint INT parameter)

– EC50Int,AB = EC50B and EC50Int,BA = EC50A

9

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Drug concentration C [fraction of EC50]

Dru

g effect

E [

frac

tion o

f Em

ax]

GPDI model

implementation on Emax

• 𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴× 1+

𝐼𝑛𝑡𝐴𝐵

×𝐶𝐵𝐸𝐶50

𝐼𝑁𝑇,𝐴𝐵

+𝐶𝐵×𝐶

𝐴𝐻𝐴

𝐸𝐶50𝐴𝐻𝐴+𝐶𝐴

𝐻𝐴

• 𝐸𝐵 =𝐸𝑚𝑎𝑥𝐵× 1+

𝐼𝑛𝑡𝐵𝐴

×𝐶𝐴𝐸𝐶50

𝐼𝑁𝑇,𝐵𝐴

+𝐶𝐴×𝐶

𝐵𝐻𝐵

𝐸𝐶50𝐵𝐻𝐵+𝐶𝐵

𝐻𝐵

• 4 parameter interaction model

– IntAB, IntBA

– EC50INT,AB , EC50INT,BA

• Simplifications:

– IntAB = IntBA (joint INT parameter)

– EC50Int,AB = EC50B and EC50Int,BA = EC50A

10

0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Drug concentration C [fraction of EC50]

Dru

g effect

E [

frac

tion o

f Em

ax]

The GPDI model is compatible with

several additivity criteria

11

𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴 × 𝐶𝐴

𝐻𝐴

𝐸𝐶50𝐴 × 1 +𝐼𝑛𝑡𝐴𝐵 × 𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇, 𝐴𝐵 + 𝐶𝐵

𝐻𝐴

+ 𝐶𝐴𝐻𝐴

𝐸𝐵 =𝐸𝑚𝑎𝑥𝐵 × 𝐶𝐵

𝐻𝐵

𝐸𝐶50𝐵 × 1 +𝐼𝑛𝑡𝐵𝐴 × 𝐶𝐴

𝐸𝐶50𝐼𝑁𝑇, 𝐵𝐴 + 𝐶𝐴

𝐻𝐵

+ 𝐶𝐵𝐻𝐵

Loewe Additivity

Bliss Independence

Effect summation

Highest single agent

…

GPDI Model on EC50

Two Drugs

12

Bliss Independence

Bidirectional Synergy

Joint decrease in EC50

Bidirectional Antagonism

Joint increase in EC50

Asymmetric interaction

A increases EC50 of B

B decreases EC50 of A

GPDI Model

Three Drugs

Bidirectional interactions between three drugs A, B and C:

• 𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴×𝐶𝐴

𝐻𝐴

𝐸𝐶50𝐴 × 1+𝐼𝑁𝑇𝐴𝐵×𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇,𝐴𝐵+𝐶𝐵× 1+

𝐼𝑁𝑇𝐴𝐶×𝐶𝐶𝐸𝐶50𝐼𝑁𝑇,𝐴𝐶+𝐶𝐶

𝐻𝐴+𝐶𝐴𝐻𝐴

Drug C modulates interaction between A and B:

• 𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴×𝐶𝐴

𝐻𝐴

𝐸𝐶50𝐴 × 1+𝐼𝑁𝑇𝐴𝐵× 1+

𝐼𝑁𝑇𝐴𝐵|𝐶×𝐶𝐶𝐸𝐶50𝐼𝑁𝑇,𝐴𝐵|𝐶+𝐶𝐶

×𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇,𝐴𝐵+𝐶𝐵× 1+

𝐼𝑁𝑇𝐴𝐶×𝐶𝐶𝐸𝐶50𝐼𝑁𝑇,𝐴𝐶+𝐶𝐶

𝐻𝐴

+𝐶𝐴𝐻𝐴

13

Application of the GPDI Model

• Dataset:

Cokol et al. Mol Syst Biol, 7: 544 (2011).

– Target organism:

S. cerevisiae BY4741

– 200 combinations of anti-fungal and

non-antifungal drugs.

• Inhibition of growth model

• GPDI model

– Loewe additivity

– Bliss Independence

• Comparison to Greco model

14

200x

Mono A

Mono B

Fungal lo

ad (

OD

)

Time (h)

Ind. Prediction of Loewe Additivity

15

Observation

Prediction

Ax Bx (fold MIC)

Individual predictions using

Greco (left) or GPDI model (right)

16

Observation Prediction Ax Bx (fold MIC)

INT values at EC50

17

SYN

ANT

AN

T +

SY

N

ANT + SYN

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

INT values at EC50 of

sham combinations

18

SYN

ANT

AN

T +

SY

N

ANT + SYN

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

INT values at EC50 of

sham combinations

19

SYN

ANT

AN

T +

SY

N

ANT + SYN

ADD

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

188/200 PD DDI supported

estimation of full GPDI model*

20

SYN

ANT

AN

T +

SY

N

ANT + SYN

ADD

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

* i.e. significant separate INT

value for each drug vs.

joint INT parameter

PD DDI are often misclassified

by conventional analyses!

21

SYN

ANT

AN

T +

SY

N

ANT + SYN

Result of Greco analysis:

• Antagonism

• Additivity

• Synergy

ADD

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

The choice of additivity criterion

affects the determined interaction

22

0 2 4 6 8 10

0

2

4

6

8

10

INTAB at EC50A

INT

BA a

t EC

50

B

0 2 4 6 8 10

0

2

4

6

8

10

GPDI – Loewe Additivity GPDI – Bliss Independence

76

35 35

54

27

88

27

58

Conclusions

• The GPDI model combined elements from mechanism-based

interaction models with empirical additivity concepts.

• Advantages of the GPDI model over conventional

approaches are:

– interpretable parameters

– Applicability for > 2 interacting drugs

– Compatibility with multiple additivity criteria

– More-dimensional interactions

– Scalability to adapt to complexity of the data

– Applicability in both concentration-effect and longitudinal

modelling

23

GPDI model application studies

at PAGE 2016

24

II-50 II-44

In vitro and in vivo (acute mouse infection model) drug effects of

rifampicin, isoniazid, ethambutol and pyrazinamide against

M. tuberculosis

Acknowledgements

PMx research group at Uppsala University

• Elin Svensson

• Anders Kristofferson

PreDiCT-TB consortium

25

The research leading to these results has received funding from the Innovative

Medicines Initiative Joint Undertaking (www.imi.europe.eu) under grant agreement

n°115337, resources of which are composed of financial contribution from the

European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA

companies’ in kind contribution.

Appendix

26

Implementation of Combined

Effects on Inhibition of Growth

GPDI within Bliss Independence:

𝐸 = 𝐸𝐴 + 𝐸𝐵 − 𝐸𝐴 × 𝐸𝐵

• 𝐸𝐴 =𝐸𝑚𝑎𝑥𝐴×𝐶𝐴

𝐻𝐴

𝐸𝐶50𝐴 × 1+𝐼𝑛𝑡

𝐴𝐵×𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇

,𝐴𝐵

+𝐶𝐵

𝐻𝐴+𝐶𝐴

𝐻𝐴

• 𝐸𝐵 =𝐸𝑚𝑎𝑥𝐵×𝐶𝐵

𝐻𝐵

𝐸𝐶50𝐵 × 1+𝐼𝑛𝑡

𝐵𝐴×𝐶𝐴

𝐸𝐶50𝐼𝑁𝑇

,𝐵𝐴

+𝐶𝐴

𝐻𝐵+𝐶𝐵

𝐻𝐵

GPDI within Loewe additivity:

27

𝐸𝐶50𝐴 = 𝐸𝐶50𝐴 × 1 +𝐼𝑛𝑡𝐴𝐵 × 𝐶𝐵

𝐸𝐶50𝐼𝑁𝑇, 𝐴𝐵 + 𝐶𝐵

𝐸𝐶50𝐵 = 𝐸𝐶50𝐵 × 1 +𝐼𝑛𝑡𝐵𝐴 × 𝐶𝐴

𝐸𝐶50𝐼𝑁𝑇, 𝐵𝐴 + 𝐶𝐴

*

*

* *

N

kgrowth·(1-E)

[1] W.J. Jusko, J. Pharm. Sci. 60 (1971).

[1]

The full GPDI Model is identifiable

on standard checkerboard designs

28

8x8 checkerboard

• 1000 scenarios assessed

• n=3 replicates per scenario

• max. growth: 10 log10 CFU/mL

• 𝜎add = 0.3 log10 CFU/mL

Emax ∈ {0.5,1}

EC50 ∈ {0. 5, 2}

H ∈ {1, 4}

Int ∈ {-0.9, -0.2} ∪ {2, 20}

EC50_Int ∈ {0.1, 1}

Em

ax

A

EC

50

A

HA

Em

ax

B

EC

50

B

HB

Int A

B

Int B

A

EC

50

Int,

AB

EC

50

Int,

BA

0.5

1.0

2.0

5.0

10.0

20.0

50.0

100.0

200.0

exp

ecte

d R

SE

%