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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

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J.Hung, 2005 FDA/Industry Wkshop2 Two Topics Combination of two drugs for the same therapeutic indication Combination of two drugs for different therapeutic indications

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J.Hung, 2005 FDA/Industry Wkshop3 The U.S. FDAs policy (21 CFR ) regarding the use of a fixed-dose combination agent requires: Each component must make a contribution to the claimed effect of the combination.

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J.Hung, 2005 FDA/Industry Wkshop4 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

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J.Hung, 2005 FDA/Industry Wkshop5 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 A B AB

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J.Hung, 2005 FDA/Industry Wkshop6 Sample mean Y i N( i, 2 /n ), i = A, B, AB n = sample size per treatment group (balanced design is assumed for simplicity). H 0 : AB A or AB B H 1 : AB > A and AB > B Min test and critical region: Min( T AB:A, T AB:B ) > C

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J.Hung, 2005 FDA/Industry Wkshop7 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 = n 1/2 ( A - B )/. Power function of Min test Pr{ Min( T AB:A, T AB:B ) > C } 1) in 2) in | |

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J.Hung, 2005 FDA/Industry Wkshop8 Note: H 0 : 0 H 1 : > 0 maximum probability of type I error of Min test = max Pr{ Min( T AB:A, T AB:B ) > C | = 0} = Pr{ Z > C }= (-C) Z = Z 1 + (1- )Z 2 = 1 if or 0 if - (Z 1, Z 2 ) 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)

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J.Hung, 2005 FDA/Industry Wkshop9 -level rejection region for H 0 : 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, p max, is less than.

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J.Hung, 2005 FDA/Industry Wkshop10 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( T AB:A, T AB:B ) > z |, = 0 } = 1-

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J.Hung, 2005 FDA/Industry Wkshop11 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?

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J.Hung, 2005 FDA/Industry Wkshop12 Perform repeated significance testing at information times t 1, …, t m during the trial. Let E i = [ min(T AB:A[i], T AB:B[i] ) > C i ] max type I error probability = max Pr{ E i | H 0 } = Pr{ [ Z i Z 1i + (1- )Z 2i > C i ] }. Z i is a standard Brownian process, thus, C i can be generated using Lan-DeMets procedure.

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J.Hung, 2005 FDA/Industry Wkshop13 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.

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J.Hung, 2005 FDA/Industry Wkshop14 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.

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J.Hung, 2005 FDA/Industry Wkshop15 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).

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J.Hung, 2005 FDA/Industry Wkshop16 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)

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J.Hung, 2005 FDA/Industry Wkshop17 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?

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J.Hung, 2005 FDA/Industry Wkshop18 Ex. Blood pressure reductions (in mmHg) from baseline: P B P A 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.

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J.Hung, 2005 FDA/Industry Wkshop19 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 ?

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J.Hung, 2005 FDA/Industry Wkshop20 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

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J.Hung, 2005 FDA/Industry Wkshop21 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

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J.Hung, 2005 FDA/Industry Wkshop22 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)

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J.Hung, 2005 FDA/Industry Wkshop23 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

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J.Hung, 2005 FDA/Industry Wkshop24 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

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J.Hung, 2005 FDA/Industry Wkshop25 Explore dose-response Response Surface Method: Use regression analysis to build a D-R model. 1)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

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J.Hung, 2005 FDA/Industry Wkshop26 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) = D A + 2 D B + 11 D A D A + 22 D B D B + 12 D A D B D A : dose level of Treatment A D B : dose level of Treatment B

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J.Hung, 2005 FDA/Industry Wkshop27 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)

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J.Hung, 2005 FDA/Industry Wkshop28 Combination of two drugs for different therapeutic indications Example Combination of a BP lowering drug and a lipid lowering drug Goal: show that combination drug maintains the benefit of each component drug

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J.Hung, 2005 FDA/Industry Wkshop29 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 BP effect combo BP lipid lowering component on lipid effect ? Non-inferiority (NI) testing

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J.Hung, 2005 FDA/Industry Wkshop30 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

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J.Hung, 2005 FDA/Industry Wkshop31 Selected References Snapinn (1987, Stat in Med, ) Laska & Meisner (1989, Biometrics, ) Gibson & Overall (1989, Stat in Med, ) Hung (1993, Stat in Med, ) Hung, Ng, Chi, Lipicky (1990, Drug Info J, ) Hung (1992, Stat in Med, ) Hung, Chi, Lipicky (1993, Biometrics, 85-94) Hung, Chi, Lipicky (1994, Biometrics, ) Hung, Chi, Lipicky (1994, Comm in Stat-A, ) Hung (1996, Stat in Med, ) Wang, Hung (1997, Biometrics, ) Hung (2000, Stat in Med, ) Hung (2003, Encyclopedia of Biopharm. Statist.)

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J.Hung, 2005 FDA/Industry Wkshop32 Hung (2003, short course given to French Society of Statistics, Paris, France) Laska, Tang, Meisner (1992, J. of Amer. Stat. Assoc., ) Laska, Meisner, Siegel (1994, Biometrics, ) Laska, Meisner, Tang (1997, Stat. In Med., )

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