Download “Excess over Highest Single Agent” Synergy

Some Statistical Issues in Developing a
Combination Drug Product
John Peterson, Ph.D.
GlaxoSmithKline Pharmaceuticals, R&D
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Some Statistical Issues in Developing a
Combination Drug Product
Outline
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Why is Combination Drug Product Development Potentially Useful?
•
Nonclinical Drug Discovery & Development
•
Phase I
• Phase II/III
• Some Statistical Consulting Issues with Regard to Design and Analysis
for Combination Drug Studies
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Why is Combination Drug Product Development
Potentially Useful?
•
There is growing interest in the pharmaceutical industry in the discovery
and development of combination drug products.
• This is due to the flexibility a combination drug product offers in developing
strategies to treat a disease.
•
For example
- A combination drug product (with low doses of each drug) may achieve a
desired level of efficacy with a low side effects profile if each compound
is associated with biologically different and independent side effects.
- A disease may have two biological pathways which each of which can be blocked
by a different drug compound (Keith et al, 2005, Nature Reviews - Drug Discovery).
- Improved kill rates for infectious agents such as bacteria and viruses.
- Improved kill rates for cancer cells.
- Treating multiple aspects of a disease
(e.g. bronchoconstriction and inflammation in asthma)
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Some Statistical Issues in Developing a
Combination Drug Product:
Nonclinical Drug Discovery & Development

•
Some Definitions of “synergy”
Loewe synergy (excess over dose-wise additivity).
- Based upon notion that two identical compounds would be additive.
- Two compounds that do better than dose-wise additivity are Loewe synergistic.
Loewe (1928) Ergeb. Physiol.
•
Bliss synergy (excess over Bliss independence or “additivity”).
- The Bliss independence combined response C for two single compounds with
effects A and B is C = A + B - A*B, where each effect is expressed as a
fractional inhibition between 0 and 1. (This idea is relevant for pairs of compounds
with different targets that have no mechanistic connection other than the outcome.)
Bliss (1939) Annals of Applied Biology
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Some Statistical Issues in Developing a
Combination Drug Product:
Nonclinical Drug Discovery & Development

Some Definitions of “synergy” (continued)
•
Therapeutic Synergy
- Two compounds are therapeutically synergistic if there exists a combination
that is superior to the best doses of either of the two compounds.
- I call this “global therapeutic synergy”
Venditti et al (1956), Journal of the National Cancer Institute
Mantel (1974), Cancer Chemotherapy Reports Part II
•
“Excess over Highest Single Agent” Synergy
- If a combination of fixed doses is such that it is superior to both of its
component doses then this is called “excess over highest single agent”.
- I call this “local therapeutic synergy”
- FDA’s policy (21 CRF 300.50) employs this notion for approval of combination
drug products.
Borisy et al (2003) Proceedings of the National Academy of Science
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Some Statistical Issues in Developing a
Combination Drug Product:
Nonclinical Drug Discovery & Development
 High-throughput Screening for combination compound pairs.
•
•
•
kxk factorial designs (k = 6 to 10) have been used (with few replications)
Borisy et al (2003) have used “excess over highest single agent” (EOHSA)
and Bliss independence as screening criteria.
Statistical inference:
- Hung AVE or MAX tests using an ANOVA model? (But few reps!)
- Inference from a response surface model? (But modeling issues?)
- GSK using trend-based tests as a compromise.
Peterson, J.J. (2005) “Multiplicity Adjusted Trend Tests with Application to
High-Throughput Screening for Compound Pairs”, GSK, BDS Working paper.
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Some Statistical Issues in Developing a
Combination Drug Product:
Nonclinical Drug Discovery & Development
 Fitting Monotone Dose-Response Surfaces for Combination
Drug Studies
1. Historically, many dose-response models for combination drugs were
too inflexible (e.g. one parameter to model synergy)
2. Some researchers have tried nonparametric and semi-parameteric
regression modeling.
3. White et al (2003) Current Drug Metabolism.
- They have proposed a hierarchical generalization of the three (or four)
parameter logistic regression model.
- Here, each of the 3 (or 4) parameters is a function a linear model in the
dose proportions.
- Use of ray designs helpful.
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Some Statistical Issues in Developing a
Combination Drug Product:
Phase I
 Dose escalation – balancing safety and tolerability in two dimensions
• Some kind of modeling and/or constraints needed to keep sample size
at a reasonable level.
1. Bayesian approach: Thall at al (2003) Biometrics
2. Order-restricted nonparameteric approach: Ivanova and Wang, (2004)
Statistics in Medicine.
3. Optimal design application: Dragalin (2005) JSM, Minneapolis
(Articles 1 and 2 above propose ad-hoc design strategies.)
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Some Statistical Issues in Developing a
Combination Drug Product:
Phase I
 Pharmacokinetics & pharmacodynamics for combination drug studies
• Pharmacokinetics for combination drugs is a more complex situation
- Drug ratios in the blood can change over time.
- More complex compartmental modeling
Plasma concentration
100
B
10
1
0
A
1
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Time (hours)
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Different pharmacodynamic endpoints can result in different assessments
of what is synergistic. A drug combination may show some type of synergy
(e.g. Loewe) for one endpoint but not for another.
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Some Statistical Issues in
Developing Combination Drug Product:
Phase II-III
• Testing for the existence Excess over Highest Single Agent (EOHSA)
- ‘Min’ (and related) tests (Laska & Meisner, 1989, Biometrics)
- Testing r xs factorial designs (Hung’s AVE and MAX tests)
- Tricky statistical inference area (Perlman & Wu, 1999 Statistical Science)
• Multiple inference for identifying combinations with EOHSA
- ANOVA models (Hung’s alternative MAX test, Hung (2000) Statistics in
Medicine , Hellmich & Lehmacher closed testing procedures (2005) Biometrics.)
- Response Surface models (Hung, 1992, Statistics in Medicine)
(Also approaches based upon simultaneous multiple comparisons within a RSM
can be done using Monte Carlo simulations to get critical values.
See Edwards & Berry, (1987), Biometrics, Hsu & Nelson (1992), and Hsu (1996).)
- ANOVA or RSM approaches? (“model bias” vs. “precision”)
See Hung, Chi, & Lipicky, 1994, Communications in Stats. Theory & Methods,
and Carter & Dornseif 1990, Drug Information Journal for some discussion.)
•
Design efficiency critical
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Some Statistical Consulting Issues with Regard to
Design and Analysis for Combination Drug Studies
• Need to find efficient designs and clearly show how much data is needed
for the best design.
•
•
Need to know the concepts and definitions of synergy…but
Do not allow yourself to get bogged down in building entire research
project around a specific concept of synergy…(e.g. Loewe, Bliss)
•
A possible exception is “excess over highest single agent” as a
baseline hurdle.
•
Therapeutic drug combinations should be “beneficial”.
Define “beneficial” and quantify it, preferably with a good
combination-dose-response model.
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Some Statistical Issues in
Developing Combination Drug Product:
Summary
• Efficient experimental designs are needed for many in-vivo studies, both
animal and human.
•
Response surface methodology may have much potential, but there is
a critical trade-off between “model bias” and “precision”.
• Consulting statisticians need to avoid getting bogged down with the many
definitions of “synergy”.
•
Combination drug studies offer a variety of interesting & challenging
problems for statisticians working in all phases of drug discovery &
development.
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Some Statistical Issues in Developing a
Combination Drug Product
John Peterson, Ph.D.
GlaxoSmithKline Pharmaceuticals, R&D
Acknowledgements:
Bart Laurijssens
Cathy Barrows
Steven Novick
Philip Overend
Yuehui Wu
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