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Some Statistical Issues in Developing a Combination Drug Product John Peterson, Ph.D. GlaxoSmithKline Pharmaceuticals, R&D 1 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 2 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) 3 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 4 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 5 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. 6 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. 7 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.) 8 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 2 3 4 5 Time (hours) 6 7 8 • 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. 9 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 10 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. 11 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. 12 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 13