# Equivalence Tests in Clinical Trials

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

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

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.

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

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 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

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

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

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)
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 Randomization Washout Period I II
Sequence Trt A Trt B Washout Subjects Sequence Trt B Trt A

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

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 (1.12, 1.27) B AUC(0-inf) A (1.12, 1.27) B Cmax A (0.98, 1.27) B

Confidence Interval vs P-value

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.

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

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

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.

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): 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-

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