1. 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

2. 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

3. J.Hung, 2005 FDA/Industry Wkshop
The U.S. FDA’s 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.
J.Hung, 2005 FDA/Industry Wkshop

4. 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

5. 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
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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
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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 ||
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Note: H0:   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

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-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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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.
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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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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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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

19. 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

20. 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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21. 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
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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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24. 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
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25. 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
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26. 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
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27. 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

28. 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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29. 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
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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 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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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., )
J.Hung, 2005 FDA/Industry Wkshop