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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Two Topics

• Combination of two drugs for the same therapeutic indication

• Combination of two drugs for different therapeutic indications

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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.

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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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22 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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Sample mean Yi N( i , 2/n ), i = A, B, ABn = sample size per treatment group (balanceddesign is assumed for simplicity).

H0: AB A or AB B

H1: AB > A and AB > B

BAjYYn

T jABjAB ,,

ˆ2:

Min test and critical region:

Min( TAB:A , TAB:B ) > C

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For sufficiently large n, the pooled-group estimate in the distribution of Min test. ˆ

Distribution of Min test involves the primaryParameter AB - max(A , B) ,which quantifies the least gain from AB relativeto 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 ||

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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)

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-level rejection region for H0:

The Z statistics of both pairwise comparisonsare 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 .

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Sample size planning for 22 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-

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Most conservative sample size planning maysubstantially overpower the study because ofmaking most pessimistic assumption about the .

One remedial strategy is use of group sequentialdesign that allows interim termination forfutility or sufficient evidence of joint statisticalsignificance of the two pairwise comparisonsHow?

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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.

m

i 1

m

i 1

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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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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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A0 A1 A2 A3

B0 A0B0 A1B0 A2B0 A3B0

B1 A0B1 A1B1 A2B1 A3B1

B2 A0B2 A1B2 A2B2 A3B2

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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Study objectives1) Assert that the combination drug is more effective than each component drug alone2) 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 arise3) ? 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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ANOVA

If the effects of two drugs are additive at everydose combination under study (note: this is verystrong 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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Ex. Blood pressure reductions (in mmHg) from baseline:

2

7

8

9

P B

P

A

Relative effect of AB versus A: AB – A = 2Main effect estimate for B:{(AB-A)+(B-P)}/2 = 4 which overestimatesthe relative effect of AB versus A.

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How to check whether the effects of twotreatments 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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An Example of Potential Interactions

Mean effect (placebo subtracted) in changeof SiDBP (in mmHg) from baseline at Week 8

E

A0 A1 A2 A3

B0 0

4

5

3

B1 5 9

7

8

B2 5 6

6

7

n= 25/cell

Potential interaction at A2B1: A2B1 – (A2+B1) = 7 – (5+5) = -3

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Estimate drug-drug interactions (from the last table):

A1 A2 A3

B1 0

-3

0

B2 -3 -4

-1

Negative interactionseems to occur

ANOVA will likelyoverestimate effect of each nonzero dose combinationLack-of-fit test for

ANOVA: p > 0.80

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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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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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Is strong control always necessary?

To identify the dose combinations that are moreeffective than their respective components, strong control is usually recommended from statistical perspective, but highly debatable, depending on application areas

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“Explore” dose-response

Response Surface Method:Use regression analysis to build a D-R model.

1) biological model (is there one?) - need a shape parameter2) quadratic polynomial model - this is only an approximation, has no biological relevance - contains ‘slope’ and ‘shape’ parameters

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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 +

11DADA + 22DBDB +

12DADB

DA: dose level of Treatment A DB: dose level of Treatment B

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Sample size planning for multi-level factorialclinical trial

Simulation is perhaps the only solution forplanning sample size per cell, depending on thestudy objectives.

May use some kind of adaptive designs toadjust sample size plan during the course of thetrial (Need research)

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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

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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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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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Selected ReferencesSnapinn (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.)

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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)