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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: H 0 : T = R or H 0 : T - R =0 H A : T R H A : T - R 0 or H 0 : T/R=1 H A : 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 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.

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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): H 0 : T - R L or T - R U H A : L < T - R < U H 0 : T / R L or T / R U H A : L < T / R < U L, U, L, U are pre-specified limits - Equivalence margin. H 0 assumes the difference, if H 0 is rejected, we accept the alternative hypothesis H a 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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Clinical trials for drug development Bioequivalence & Bioavailability Phase IPhase IIPhase IVPhase III Pre- Clinical INDNDA 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: Therapeutical Equivalence Same amount of Drug at the site of drug action Same bioavailability profile

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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.

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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): H 0 : T - R L or T - R U H A : L < T - R < U Two one-sided test procedure: H 01 : T - R L H A1 : T - R > L and H 02 : T - R U H A2 : T - R < 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: 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 H 01 : T / R L and H 02 : T / R U H A1 : T / R > L H A2 : T / R < U

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A 2x2x2 Cross-over Design Period I II Randomization Sequence 1 Trt A Trt B Sequence 2 Trt B Trt A Washout Subjects

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Cross-over Design 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

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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;

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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

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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 Cost-effective Easy to administer Diversity A new product or regimen may have better safety profile (less adverse events, less side effects)

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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) H 0 : T P with bigger being better; T and P could be rates or means H 0 : (T-P) 0 H 0 : (T/P) 1

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Hypothesis pertaining to equivalence To demonstrate the new product is equivalent to the comparator (within certain margin in both directions) H 0 : {T = (R - ) } versus H A : {(R - ) 0 H 0 : |T – R| >= versus H A : |T – R| < H 0 : {(T/R) = (R + )/R} versus H A : {(R- )/R ) < (T/R) < (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 H 0 : T (R - ) with > 0 and bigger response being better H 0 : (T - R) - H 0 : (T/R) (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 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

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

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

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