Division of Biometrics I, Office of Biostatistics A Regulatory Perspective on Design and Analysis of Combination Drug Trial* H.M. James Hung Division of Biometrics I, Office of Biostatistics OPaSS, CDER, FDA Presented in FDA/Industry Workshop, Bethesda, Maryland, September 16, 2005 *The views expressed here are not necessarily of the U.S. Food and Drug Administration

J.Hung, 2005 FDA/Industry Wkshop Two Topics Combination of two drugs for the same therapeutic indication Combination of two drugs for different therapeutic indications J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop The U.S. FDA’s policy (21 CFR 300.50) regarding the use of a fixed-dose combination agent requires: Each component must make a contribution to the claimed effect of the combination. J.Hung, 2005 FDA/Industry Wkshop

Combination of two drugs for the same therapeutic indication At specific component doses, the combination drug must be superior to its components at the same respective doses. Example Combination of ACE inhibitor and HCTZ for treating hypertension J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop 22 factorial design trial Drugs A, B, AB at some fixed dose Goal: Show that AB more effective than A alone and B alone ( AB > A and AB > B ) P B A AB J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Sample mean Yi  N( i , 2/n ), i = A, B, AB n = sample size per treatment group (balanced design is assumed for simplicity). H0: AB  A or AB  B H1: AB > A and AB > B Min test and critical region: Min( TAB:A , TAB:B ) > C J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop For sufficiently large n, the pooled-group estimate in the distribution of Min test. Distribution of Min test involves the primary Parameter   AB - max(A , B) , which quantifies the least gain from AB relative to A and B, and the nuisance parameter  = n1/2(A - B)/. Power function of Min test Pr{ Min( TAB:A , TAB:B ) > C } 1)  in  2)  in || J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Note: H0:   0 H1:  > 0 maximum probability of type I error of Min test = max Pr{ Min( TAB:A , TAB:B ) > C |  = 0} = Pr{ Z > C }= (-C) Z = Z1 + (1- )Z2  = 1 if    or 0 if   - (Z1, Z2)  N( (0, 0) , [1, 1, =0.5] ) Thus, -level Min test has C = z . Lehmann (1952), Berger (1982), Snapinn (1987) Laska & Meisner (1989), Hung et al (1993, 1994) J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop -level rejection region for H0: The Z statistics of both pairwise comparisons are greater than z , regardless of sample size allocation. Equivalently, the nominal p-value of each pairwise comparison is less than  , that is, the larger p-value in the two pairwise comparisons, pmax, is less than . J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Sample size planning for 22 trial For any fixed , the power of Min test has the lowest level at  = 0 (i.e., A = B) Recommend conservative planning of n such that pr{ Min( TAB:A , TAB:B ) > z |  ,  = 0 } = 1- J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Most conservative sample size planning may substantially overpower the study because of making most pessimistic assumption about the . One remedial strategy is use of group sequential design that allows interim termination for futility or sufficient evidence of joint statistical significance of the two pairwise comparisons How? J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Perform repeated significance testing at information times t1, …, tm during the trial. Let Ei = [ min(TAB:A[i], TAB:B[i]) > Ci ] max type I error probability = max Pr{ Ei | H0 } = Pr{ [ Zi  Z1i + (1- )Z2i > Ci ] }. Zi is a standard Brownian process, thus, Ci can be generated using Lan-DeMets procedure. J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Summary With no restriction on the nuisance parameter space, the only valid test is the -level Min test which requires that the p-value of each pairwise comparison is no greater than . Sample size planning must take into account the difference between two components. Consider using group sequential design to allow for early trial termination for futility or for sufficient evidence of superiority. J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Summary If A >> B, then consider populating AB and A much more than B. May consider terminating B when using a group sequential design. Searching for an improved test by using estimate of the nuisance parameter seems futile. J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Multiple dose combinations trial In some disease areas (e.g., hypertension), multiple doses are studied. Often use the following factorial design (some of the cells may be empty). The subject of adaptation of design./analysis is closely related to “modification of design specifications…” The following are the most frequently seen modifications of design specifications in NDA/IND submissions. J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Study objectives 1) Assert that the combination drug is more effective than each component drug alone 2) Obtain useful and reliable DR information - identify a dose range where effect increases as a function of dose - identify a dose beyond which there is no appreciable increase of the effect or undesirable effects arise 3) ? Identify a (low) dose combination for first-line treatment, if each component drug has dose- dependent side effects at high dose(s) J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop ANOVA If the effects of two drugs are additive at every dose combination under study (note: this is very strong assumption), then the most efficient method is ANOVA without treatment by treatment interaction term. Use Main Effect to estimate the effect of each cell. But, ANOVA can be severely biased if the assumption of additivity is violated. Why? J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Ex. Blood pressure reductions (in mmHg) from baseline: P B P 2 8 A 7 9 Relative effect of AB versus A: AB – A = 2 Main effect estimate for B: {(AB-A)+(B-P)}/2 = 4 which overestimates the relative effect of AB versus A. J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop How to check whether the effects of two treatments are non-additive? 1) Use Lack-of-fit F test to reject “additive” ANOVA model ??? statistical power questionable? 2) Examine interaction pattern ? J.Hung, 2005 FDA/Industry Wkshop

An Example of Potential Interactions Mean effect (placebo subtracted) in change of SiDBP (in mmHg) from baseline at Week 8 n= 25/cell Potential interaction at A2B1: A2B1 – (A2+B1) = 7 – (5+5) = -3 J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Estimate drug-drug interactions (from the last table): Negative interaction seems to occur ANOVA will likely overestimate effect of each nonzero dose combination Lack-of-fit test for ANOVA: p > 0.80 J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop When negative interaction is suspected, at a minimum, perform a global test to show that at least one dose combination beats its components. AVE test (weak control of FWE type I error)* Average the least gains in effect over all the dose combinations (compared to their respective component doses). Determine whether this average gain is statistically significant. *Hung, Chi, Lipicky (1993, Biometrics) J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Strong control procedures: 1) Single-step MAX test (or adjusted p-value procedure using James approximation [1991], particularly for unequal cell sample size) 2) Stepwise testing strategies (using Hochberg SU or Holm SD) 3) Closed testing strategy using AVE test J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Is strong control always necessary? To identify the dose combinations that are more effective than their respective components, strong control is usually recommended from statistical perspective, but highly debatable, depending on application areas J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop “Explore” dose-response Response Surface Method: Use regression analysis to build a D-R model. biological model (is there one?) - need a shape parameter 2) quadratic polynomial model - this is only an approximation, has no biological relevance - contains ‘slope’ and ‘shape’ parameters J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Using quadratic polynomial model Often start with a first-degree polynomial model (plane) and then a quadratic polynomial model with treatment by treatment interaction. Y (response) = 0 + 1DA + 2DB + 11DADA + 22DBDB + 12DADB DA: dose level of Treatment A DB: dose level of Treatment B J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Sample size planning for multi-level factorial clinical trial Simulation is perhaps the only solution for planning sample size per cell, depending on the study objectives. May use some kind of adaptive designs to adjust sample size plan during the course of the trial (Need research) J.Hung, 2005 FDA/Industry Wkshop

Combination of two drugs for different therapeutic indications Example Combination of a BP lowering drug and a lipid lowering drug < mainly for convenience in use > Goal: show that combination drug maintains the benefit of each component drug J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Not sufficient to show: combo > lipid lowering component on BP effect combo > BP lowering component on lipid effect ? Need to show: combo  BP lowering component on combo  BP lipid lowering component on ? Non-inferiority (NI) testing J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Issues and questions Need a “clinical relevant” NI margin - demands much greater sample size per cell make sense (for showing convenience in use)? Is NI to be shown only at the combination of highest marketed doses? - studying low-dose combinations is also recommended for descriptive purpose? compare ED50? Need new statistical framework J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Selected References Snapinn (1987, Stat in Med, 657-665) Laska & Meisner (1989, Biometrics, 1139-1151) Gibson & Overall (1989, Stat in Med, 1479-1484) Hung (1993, Stat in Med, 645-660) Hung, Ng, Chi, Lipicky (1990, Drug Info J, 371-378) Hung (1992, Stat in Med, 703-711) Hung, Chi, Lipicky (1993, Biometrics, 85-94) Hung, Chi, Lipicky (1994, Biometrics, 307-308) Hung, Chi, Lipicky (1994, Comm in Stat-A, 361-376) Hung (1996, Stat in Med, 233-247) Wang, Hung (1997, Biometrics, 498-503) Hung (2000, Stat in Med, 2079-2087) Hung (2003, Encyclopedia of Biopharm. Statist.) J.Hung, 2005 FDA/Industry Wkshop

J.Hung, 2005 FDA/Industry Wkshop Hung (2003, short course given to French Society of Statistics, Paris, France) Laska, Tang, Meisner (1992, J. of Amer. Stat. Assoc., 825-831) Laska, Meisner, Siegel (1994, Biometrics, 834-841) Laska, Meisner, Tang (1997, Stat. In Med., 2211-2228) J.Hung, 2005 FDA/Industry Wkshop