Equivalence Tests in Clinical Trials

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Equivalence Tests in Clinical Trials
Chunqin Deng, PhD PPD Development Research
Triangle Park, NC 27560
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Traditional Hypothesis Test

• Test for Difference
• H0 ?T?R or H0 ?T-?R0
• HA ?T??R HA ?T-?R?0
• or
• H0 T/R1
• HA T/R?1

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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.

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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

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Equivalence Test
Test for Equivalence (indifference) H0 ?T -?R
? ?L or ?T -?R ? ?U HA ?L lt ?T -?R lt ?U
H0 ?T /?R ? ?L or ?T / ?R ? ?U
HA ?L lt ?T / ?R lt ?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.
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Equivalence Test
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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

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Bioequivalence Bioavailability
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Bioequivalence Bioavailability
Clinical trials for drug development
Phase I
Phase II
Phase IV
Phase III
Pre- Clinical
IND
NDA
After the experiment (brand name) drug is
approved and is marketed, there is a patent
protection for certain period
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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
Same amount of Drug at the site of drug action
Same bioavailability profile
Therapeutical Equivalence
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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

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Bioavailability

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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

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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)

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Bioequivalence test
Test for equivalence (indifference) H0 ?T -?R ?
?L or ?T -?R ? ?U HA ?L lt ?T -?R lt ?U

Two one-sided test procedure H01 ?T -?R ? ?L
HA1 ?T -?R gt ?L and H02 ?T -?R ? ?U HA2 ?T
-?R lt ?U
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Two One-Side Test (TOST)


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
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Bioequivalence test
In practice

• Log-normal distribution is assumed for
  bioavailability endpoints
• H01 ?T /?R ? ?L and
  H02 ?T / ?R ? ?U
• HA1 ?T / ?R gt ?L
  HA2 ?T / ?R lt ?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

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A 2x2x2 Cross-over Design

Period
I II
Randomization

Sequence 1 Trt A Trt B
Washout
Subjects
Sequence 2 Trt B Trt A
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Cross-over Design

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
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Cross-over Design

proc mixed alpha0.1 class treat sequence
period subject model lCmax treat sequence
period random sequence(subject) lsmeans
treat/pdiff cl alpha 0.1 run
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Bioequivalence test

Ratio of
Geometric Geometric 90 CI Parameters
Treatment N mean means for
ratio --------------------------------------------
---------------------- AUC(0-t) A 13
37693.44 1.19 (1.12, 1.27)
B 13 44904.33 AUC(0-inf) A
13 37952.40 1.19 (1.12, 1.27)
B 13 45340.64 Cmax
A 13 8944.31 1.11
(0.98, 1.27) B 13
9959.24 ------------------------------------------
------------------------
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Confidence Interval vs P-value

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Equivalence Non-inferiority Test

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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

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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.

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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

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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/non-
• inferiority of the new product

• Combination of Placebo and Active Control Trial
• Both Placebo and Active drug as control arms

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Hypothesis pertaining to superiority

• To demonstrate the superiority of the new
  product (usually comparing to the placebo)
• H0 TltP versus HA TgtP with bigger being
  better T and P
• could be rates or means
• H0 (T-P)lt0 versus HA (T-P)gt0
• H0 (T/P)lt1 versus HA (T/P)gt1

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Hypothesis pertaining to equivalence

• To demonstrate the new product is equivalent to
  the
• comparator (within certain margin in both
  directions)
• H0 T lt (R - ?) or T gt (R - ?) versus
• HA (R - ?) lt T lt (R ?) with ? gt 0
• H0 T R gt ? versus HA T R lt ?
• H0 (T/R) lt (R - ?)/R or (T/R) gt (R ?)/R
  versus
• HA (R- ? )/R ) lt (T/R) lt (R ? )/R

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Hypothesis pertaining to non-inferiority

• To demonstrate the new product is not worse than
  the comparator by certain margin
• H0 T lt (R - ?) versus HA T gt (R - ?) with ?
  gt 0
• and bigger response being better
• H0 (T - R) lt - ? versus HA (T - R) gt - ?
• H0 (T/R) lt (R - ?)/R versus HA (T/R) gt (R- ?
  )/R

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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
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Equivalence of Two Products


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Noninferiority of New Product


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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...

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Equivalence Margin

Assumption the effect of the active control in
the current trial is similar to its effect in
the historical trials.

New treatment is equivalent or non-inferior to
the active control, therefore is effective
Active Control vs Placebo
New treatment vs Active control
Active control
is superior
Caveat When this assumption does not hold, a
non-effective treatment may be claimed to be
effective.
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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
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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

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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 52219- DAgostino 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-