A Regulatory Perspective on Design and Analysis of Combination Drug Trial*

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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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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. FDAs 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 Goal Show that AB more
effective than A alone and B alone
( AB gt A and AB gt 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 gt ?A and ?AB
gt ?B
Min test and critical region Min( TABA ,
TABB ) gt 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(
TABA , TABB ) gt C 1) ? in ? 2)
? in ?
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Note H0 ? ? 0 H1 ? gt 0 maximum
probability of type I error of Min test max Pr
Min( TABA , TABB ) gt C ? 0 Pr Z gt 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( TABA ,
TABB ) gt 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(TABAi, TABBi) gt Ci
max type I error probability max Pr Ei
H0 Pr Zi ? ?Z1i (1- ?)Z2i gt Ci
. Zi is a standard Brownian process, thus, Ci
can be generated using Lan-DeMets 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 gtgt ?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).



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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
7
9
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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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

n 25/cell
Potential interaction at A2B1 A2B1
(A2B1) 7 (55) -3
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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 gt 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 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.
• 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
• lt mainly for convenience in use gt
• Goal show that combination drug maintains the
• benefit of each component drug

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Not sufficient to show combo gt lipid
lowering component on BP effect
combo gt 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)