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

2 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

3 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)

4 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

5 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 - FDAs policy (21 CRF ) employs this notion for approval of combination drug products. Borisy et al (2003) Proceedings of the National Academy of Science

6 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.

7 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.

8 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.)

9 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 assessments of what is synergistic. A drug combination may show some type of synergy (e.g. Loewe) for one endpoint but not for another Time (hours) Plasma concentration A B

10 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 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

11 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.

12 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.

13 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