P1253037223bnBCX

1
Some Statistical Issues in Developing a
Combination Drug Product John Peterson,
Ph.D. GlaxoSmithKline Pharmaceuticals, RD
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Some Statistical Issues in Developing a
Combination Drug Product
Outline

• 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 developingstrategies 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 - AB, 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 synergyVenditti et al (1956),
  Journal of the National Cancer InstituteMantel
  (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
  - FDAs 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 weretoo inflexible (e.g. one
  parameter to model synergy)
• 2. Some researchers have tried nonparametric and
  semi-parametericregression 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
• Different pharmacodynamic endpoints can result
  in different assessmentsof 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 (Hungs AVE and
  MAX tests) - Tricky statistical inference area
  (Perlman Wu, 1999 Statistical Science)
• Multiple inference for identifying combinations
  with EOHSA - ANOVA models (Hungs
  alternative MAX test, Hung (2000) Statistics
  inMedicine , 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
toDesign and Analysis for Combination Drug
Studies

• Need to find efficient designs and clearly show
  how much data is neededfor the best design.
• Need to know the concepts and definitions of
  synergybut
• 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 manydefinitions of
  synergy.
• Combination drug studies offer a variety of
  interesting challengingproblems 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, RD
Acknowledgements Bart Laurijssens Cathy
Barrows Steven Novick Philip Overend Yuehui Wu