Transcript Global Data Management

Equivalence Tests in Clinical Trials
Chunqin Deng, PhD
PPD Development
Research Triangle Park, NC 27560
Traditional Hypothesis Test
Test for Difference:
H0: T=R
HA: TR
or
H0: T/R=1
HA: T/R1
or
H0: T-R=0
HA: T-R0
Issue with traditional hypothesis
test
Inconsistent result between a significant statistical
difference and a clinically meaningful difference
 A statistically significant difference is referred to a
difference that is unlikely to occur by chance alone.
 A clinically significant difference is a difference that is
considered clinically meaningful and important to the
investigators.
Issue with traditional hypothesis
test
When our purpose is to test for the indifference
(equivalence), the traditional approach is not
appropriate
 Failure to reject the null hypothesis is not enough to
prove that the two treatment methods are equivalent
 Failure to reject the null hypothesis only indicates that
the evidence is insufficient to conclude the difference
 No evidence of difference  evidence of no difference
Equivalence Test
Test for Equivalence (indifference):
H0: T -R  L or T -R  U
HA: L < T -R < U
H0: T /R  L or T / R  U
HA: L < T / R < U
L ,U, L, U are pre-specified limits - Equivalence margin.
H0 assumes the difference, if H0 is rejected, we accept the
alternative hypothesis Ha and claim equivalence.
Equivalence Test
H0 (no difference)
Fail to reject
True
No error
False
Type II error
Reject
Type I error
Power
H0 (difference)
True
False
(Inequivalent)
(Equivalent)
Fail to reject
(Inequivalent)
Reject
(Equivalent)
No error
Type II error
Type I error
Power
Application of Equivalence Test
Equivalence test in the analysis of bioavailability
(or PK/PD)
 Bioequivalence
Equivalence test in therapeutic efficacy comparison


Equivalence or Non-inferiority test
In Active Control Trials
Bioequivalence & Bioavailability
Bioequivalence & Bioavailability
Clinical trials for drug development
PreClinical
IND
Phase I
Phase II
Phase III
Phase IV
NDA
After the experiment (brand name) drug is
approved and is marketed, there is a patent
protection for certain period
Bioequivalence & Bioavailability
When the patent for a brand name drug expires, the
generic drug can be manufactured and marketed
No need for trials to demonstrate the therapeutic
equivalence for generic drugs
Assumption:
Therapeutical
Equivalence
Same amount of
Drug at the
site of drug action
Same
bioavailability
profile
Bioequivalence & Bioavailability
Bioavailability means the rate and extent to which the
active ingredient or active moiety is absorbed from a drug
product and becomes available at the site of action.
Bioequivalence means that two products are equivalent
in terms of the bioavailability endpoints when
administered at the same molar dose under similar
conditions in an appropriately designed study
Bioavailability
Bioequivalence & Bioavailability
Bioequivalence: Test for equivalence In
terms of bioavailability endpoints
 Two products are bioequivalent
Two products are therapeutically equivalent
 Generic Copies = Brand Name Drug
Examples of BE/BA Clinical Trial
 Generic drug application (demonstrate that the generic
product is bioequivalent to the brand-name drug) – ANDA
 Drug-drug interaction studies
 Food-drug interaction studies
 Formulation studies
 Special population studies (Hepatic or renal impaired
patients vs healthy; pediatric, elderly subjects vs
healthy adults)
Bioequivalence test
Test for equivalence (indifference):
H0: T -R  L or T -R  U
HA: L < T -R < U
Two one-sided test procedure:
and
H01: T -R  L
HA1: T -R > L
H02: T -R  U
HA2: T -R < U
Two One-Side Test (TOST)
( X T  X R )  L
t1 
 t1 ( v )
s 2/ n
t2 
U  ( X T  X R )
s 2/ n
 t1 ( v )
Identical to the procedure of declaring equivalence
only if the ordinary 1-2 confidence interval for
T-R is completely contained in the equivalence
interval [L,U]
Bioequivalence test
In practice:
 Log-normal distribution is assumed for bioavailability endpoints
H01: T /R  L
and
H02: T / R  U
HA1: T / R > L
HA2: T / R < U
 Equivalence Margin: 20 rule, 80/125 rule (0.8 – 1.25 for
ratio)
 90% confidence interval is used.
 Cross over design are usually used in bioequivalence studies
A
B
B
A
A 2x2x2 Cross-over Design
Period
II
Trt A
Trt B
Washout
Randomization
Subjects
Sequence 1
I
Sequence 2
Trt B
Trt A
Cross-over Design
yijkm    Si  bj (i )  pk  tm  ijkm
y is the response (AUC, Cmax…)
S is the effect due to sequence
b is the effect due to subject nested within sequence
p is the effect due to period
t is the effect due to treatment
 is the random error
Cross-over Design
proc mixed alpha=0.1;
class treat sequence period subject;
model lCmax = treat sequence period;
random sequence(subject);
lsmeans treat/pdiff cl alpha = 0.1 ;
run;
Bioequivalence test
Ratio of
Geometric Geometric 90% CI
Parameters Treatment N
mean
means
for ratio
-----------------------------------------------------------------AUC(0-t)
A
B
13
13
37693.44
44904.33
1.19
(1.12, 1.27)
AUC(0-inf)
A
B
13
13
37952.40
45340.64
1.19
(1.12, 1.27)
Cmax
A
13
8944.31
1.11
(0.98, 1.27)
B
13
9959.24
------------------------------------------------------------------
Confidence Interval vs P-value
Equivalence & Non-inferiority Test
Therapeutic Equivalence Test
When comparing two different drugs (or regimens),
direct comparison of the therapeutic endpoints
(efficacy endpoints) need to be performed.
Traditional approach:
 Test for Difference: Superiority test.
 Usually comparing with placebo
Equivalence approach:
 Equivalence test
 Non-inferiority test
Therapeutic Equivalence Test
 Superiority Test
To demonstrate superiority (or difference) by rejecting
the null hypothesis of no difference.
 Equivalence test
To show that the effects differ by no more than a specific
amount (the equivalence margin)
 Non-inferiority test
To show that an experimental treatment is not worse
than an active control by more than the equivalence margin.
Why equivalence and non-inferiority?
 Placebo-controlled trial is unethical when there
are existing drugs on the market
– Active control trial
 A new product or regimen may have better safety
profile (less adverse events, less side effects)
 Cost-effective
 Easy to administer
 Diversity
Placebo Control vs Active Control Trials
Placebo Control Trial
 Placebo as control arm
 To demonstrate the superiority of the new product
Active Control Trial
 Active drug as control arm
 To demonstrate the superiority/equivalence/noninferiority of the new product
Combination of Placebo and Active Control Trial
 Both Placebo and Active drug as control arms
Hypothesis pertaining to superiority
To demonstrate the superiority of the new product
(usually comparing to the placebo)
 H0: T<=P versus HA: T>P with bigger being better; T and P
could be rates or means
 H0: (T-P)<=0 versus HA: (T-P)>0
 H0: (T/P)<=1 versus HA: (T/P)>1
Hypothesis pertaining to equivalence
To demonstrate the new product is equivalent to the
comparator (within certain margin in both
directions)
 H0: {T <= (R - ) or T >= (R - ) } versus
HA: {(R - ) < T < (R + )} with  > 0
 H0: |T – R| >=  versus HA: |T – R| < 
 H0: {(T/R) <= (R - )/R or {(T/R) >= (R + )/R} versus
HA: {(R-  )/R ) < (T/R) < (R+  )/R}
Hypothesis pertaining to non-inferiority
To demonstrate the new product is not worse than
the comparator by certain margin
 H0: T <= (R - ) versus HA: T > (R - ) with  > 0
and bigger response being better
 H0: (T - R) <= -  versus HA: (T - R) > - 
 H0: (T/R) <= (R - )/R versus HA: (T/R) > (R-  )/R
Superiority of New Product
CPMP (2001) Points to consider on switching between superiority and non-inferiority. British Journal
of Clinical Pharmacology. 52(3):223, 2001
Equivalence of Two Products
Noninferiority of New Product
Equivalence Margin
 Clinically meaningful
 Pre-specified
 Often chosen with reference to the effect of
the active control in historical placebo-controlled
trials
 Margin could be expressed as mean, ratio...
Equivalence Margin
Assumption: the effect of the active control in the current
trial is similar to its effect in the historical trials.
Active Control Active control
vs
Placebo
is superior
New treatment
vs
Active control
New treatment is
equivalent or
non-inferior to
the active control,
therefore is
effective
Caveat: When this assumption does not hold,
a non-effective treatment may be claimed to be effective.
Switch between superiority and
noninferiority
It is always possible to choose a margin which leads to
a conclusion of equivalence or noninferiority if it is
chosen after the data have been inspected.
Interpreting a noninferiority trial as a superiority trial
Interpreting a superiority trial as a noninferiority trial
Summaries
 Equivalence tests are driven by the needs in clinical trials,
and are now gaining the popularity in clinical trials and
other areas
 Equivalence tests have major applications in
bioequivalence / bioavailability studies and
active control trials
References
Schuirmann DJ (1987) A comparison of the two one-sided tests
procedure and the power approach for assessing the equivalence
of average bioavailability. Journal of Pharmacokinetics and
Biopharmaceutics 15(6): 657-680
CPMP (2001) Switching between superiority and non-inferiority
British Journal of Clinical Pharmacology 52:219D’Agostino RB Sr et al (2003) Non-inferiority trials: design
concepts and issues – the encounters of academic consultants
in statistics. Statistics in Medicine 22(2) 169-