1. Equivalence Tests in Clinical Trials
Chunqin Deng, PhD
PPD Development
Research Triangle Park, NC 27560

2. Traditional Hypothesis Test
Test for Difference:
H0: T=R or H0: T-R=0
HA: TR HA: T-R0 or
H0: T/R=1
HA: T/R1

3. 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.

4. 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

5. 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.

6. Equivalence Test

7. 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

8. Bioequivalence & Bioavailability

9. Bioequivalence & Bioavailability
Clinical trials for drug development
Pre-
Clinical
Phase I
Phase II
Phase III
Phase IV
IND
NDA
After the experiment (brand name) drug is approved and is marketed, there is a patent protection for certain period

10. 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

11. 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
Codes of Federal Regulation (CFR) for Clinical Trials

12. Bioavailability

13. 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

14. 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)

15. Bioequivalence test Test for equivalence (indifference):
H0: T -R  L or T -R  U
HA: L < T -R < U
Two one-sided test procedure:
H01: T -R  L
HA1: T -R > L
and
H02: T -R  U
HA2: T -R < U

16. 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]

17. 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

18. A 2x2x2 Cross-over Design Randomization Washout Period I II
Sequence Trt A Trt B
Washout
Subjects
Sequence Trt B Trt A

19. 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

20. 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;

21. Bioequivalence test Ratio of Geometric Geometric 90% CI
Parameters Treatment N mean means for ratio
AUC(0-t) A (1.12, 1.27) B
AUC(0-inf) A (1.12, 1.27) B
Cmax A (0.98, 1.27) B

22. Confidence Interval vs P-value

23. Equivalence & Non-inferiority Test
When we talk about the bioequivalence/bioavailability, we mean the same product with the different formulations
or the same product under different conditions
or the same product used for the different populations
The moist (active chemical component) in the drug is the same
However, when we talk about the therapeutic equivalence test, we mean the two totally different product or regimen.

24. 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
When we talk about the bioequivalence/bioavailability, we mean the same product with the different formulations
or the same product under different conditions
or the same product used for the different populations
The moist (active chemical component) in the drug is the same
However, when we talk about the therapeutic equivalence test, we mean the two totally different product or regimen.
Equivalence approach:
Equivalence test
Non-inferiority test

25. 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.

26. 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
even though the therapeutic endpoints are not
superior (just equivalent with or no worse than the
active control)
Diversity

27. 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

28. 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

29. 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}

30. 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

31. 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

32. Equivalence of Two Products

33. Noninferiority of New Product

34. Equivalence Margin Clinically meaningful Pre-specified
Often chosen with reference to the effect of
the active control in historical placebo-controlled
trials
% retension (delta)
delta=0.5 -> 50% retention of control effect. If the active control has 3 years survival benefit, the test drug should retain at least 1.5 years survival benefit.
establish efficacy through testing a proportion retention of control effect
Margin could be expressed as mean, ratio...

35. Equivalence Margin Caveat: When this assumption does not hold,
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.

36. 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

37. 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

38. 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):
CPMP (2001) Switching between superiority and non-inferiority
British Journal of Clinical Pharmacology 52:219-
D’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-