Equivalence Tests in Clinical Trials

Chunqin Deng, PhD

PPD DevelopmentResearch Triangle Park, NC 27560

Traditional Hypothesis Test

Test for Difference:

H0: T=R or H0: T-R=0HA: TR HA: T-R0

or

H0: T/R=1

HA: T/R1

Issue with traditional hypothesis test

Inconsistent result between a significant statistical difference and a clinically meaningful difference

A clinically significant difference is a difference that is considered clinically meaningful and important to the investigators.

A statistically significant difference is referred to a difference that is unlikely to occur by chance alone.

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)

True False

Fail to reject No error Type II error

Reject Type I error Power

H0 (difference) True

(Inequivalent) False (Equivalent)

Fail to reject (Inequivalent)

No error

Type II error

Reject (Equivalent)

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

Clinical trials for drug development

Bioequivalence & Bioavailability

Phase I Phase II Phase IVPhase IIIPre-

Clinical

IND 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:

TherapeuticalEquivalence

Same amount of Drug at the

site of drug action

Same bioavailability

profile

Bioequivalence & Bioavailability

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 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.

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:

H01: T -R L HA1: T -R > L

and H02: T -R U

HA2: T -R < U

Two One-Side Test (TOST)

)(11

/2

)(v

LRT tns

XXt

)(12/2

)(v

RTU tns

XXt

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:

Equivalence Margin: 20 rule, 80/125 rule (0.8 – 1.25 for ratio)

Cross over design are usually used in bioequivalence studies A B B A

90% confidence interval is used.

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

A 2x2x2 Cross-over Design

Period I IIR

and

omization

Sequence 1 Trt A Trt B

Sequence 2 Trt B Trt A

Wash

out

Subjects

Cross-over Design

ijkmmkijiijkm tpbSy )(

y is the response (AUC, Cmax…)

S is the effect due to sequence

t is the effect due to treatment

p is the effect due to period

b is the effect due to subject nested within sequence

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% CIParameters 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------------------------------------------------------------------

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

Cost-effective

Easy to administer

Diversity

A new product or regimen may have better safety profile (less adverse events, less side effects)

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

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

Often chosen with reference to the effect of the active control in historical placebo-controlled trials

Margin could be expressed as mean, ratio...

Pre-specified

Equivalence Margin

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

Caveat: When this assumption does not hold, a non-effective treatment may be claimed to be effective.

Active Controlvs

Placebo

New treatmentvs

Active control

New treatment is equivalent or non-inferior to the active control, therefore is effective

Active control

is superior

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-inferiorityBritish 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-