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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
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
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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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22 factorial design trial
Drugs A, B, AB at some fixed dose
P
B
A
AB
Goal: Show that AB more effective than
A alone and B alone
( AB > A and AB > B )
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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
TAB: j
n  YAB  Y j 
,
 
2  ˆ 
j  A, B
Min test and critical region:
Min( TAB:A , TAB:B ) > C
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For sufficiently large n, the pooled-group
estimate ˆ   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:   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 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 .
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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-
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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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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 ] }.
m
i 1
m
i 1
Zi is a standard Brownian process, thus,
Ci can be generated using Lan-DeMets
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procedure.
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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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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).
A0
A1
A2
A3
B0
A0B0 A1B0 A2B0
A3B0
B1
A0B1 A1B1 A2B1
A3B1
B2
A0B2 A1B2 A2B2
A3B2
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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 dosedependent 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.
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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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An Example of Potential Interactions
Mean effect (placebo subtracted) in change
of 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):
Negative interaction
A1
A2
A3
seems to occur
B1
0
-3
0
B2
-3
-4
-1
Lack-of-fit test for
ANOVA: p > 0.80
ANOVA will likely
overestimate effect
of each nonzero
dose combination
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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 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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“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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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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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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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 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.)
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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)
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