Equivalence Tests in Clinical Trials

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

2. 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 Traditional Hypothesis Test

3. Inconsistent result between a significant statistical difference and a clinically meaningful difference Issue with traditional hypothesis test • 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. When our purpose is to test for the indifference (equivalence), the traditional approach is not appropriate Issue with traditional hypothesis test • 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. 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, Uare pre-specified limits - Equivalence margin. • H0 assumes the difference, if H0 is rejected, we accept the alternative hypothesis Ha and claim equivalence. Equivalence Test

6. Equivalence Test

7. Equivalence test in the analysis of bioavailability (or PK/PD) • Bioequivalence Application of Equivalence Test • Equivalence test in therapeutic efficacy comparison • Equivalence or Non-inferiority test • In Active Control Trials

8. Bioequivalence & Bioavailability

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

10. 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 Bioequivalence & Bioavailability Assumption: Same amount of Drug at the site of drug action Same bioavailability profile Therapeutical Equivalence

11. Bioavailabilitymeans 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 & Bioavailability • Bioequivalencemeans 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

12. Bioavailability

13. Bioequivalence: Test for equivalence In terms of bioavailability endpoints • Two products are bioequivalent Two products are therapeutically equivalent • Generic Copies = Brand Name Drug Bioequivalence & Bioavailability

14. 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) Examples of BE/BA Clinical Trial

15. Test for equivalence (indifference): • H0: T -R  L or T -R  U • HA: L < T -R < U Bioequivalence test • 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. 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 Bioequivalence test • 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. Period • I II Randomization Sequence 1 Trt A Trt B Washout A 2x2x2 Cross-over Design Subjects Sequence 2 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. 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; Cross-over Design

21. 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 ------------------------------------------------------------------ Bioequivalence test

22. Confidence Interval vs P-value

23. Equivalence & Non-inferiority Test

24. When comparing two different drugs (or regimens), direct comparison of the therapeutic endpoints (efficacy endpoints) need to be performed. Therapeutic Equivalence Test • Traditional approach: • Test for Difference: Superiority test. • Usually comparing with placebo • Equivalence approach: • Equivalence test • Non-inferiority test

25. Superiority Test • To demonstrate superiority (or difference) by rejecting • the null hypothesis of no difference. Therapeutic Equivalence Test • 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. Placebo-controlled trial is unethical when there are existing drugs on the market – Active control trial Why equivalence and non-inferiority? • A new product or regimen may have better safety profile (less adverse events, less side effects) • Cost-effective • Easy to administer • Diversity

27. Placebo Control Trial • Placebo as control arm • To demonstrate the superiority of the new product Placebo Control vs Active Control Trials • 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. 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 superiority

29. 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 equivalence

30. 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 Hypothesis pertaining to non-inferiority

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. Clinically meaningful Equivalence Margin • 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...

35. Assumption: the effect of the active control in the current trial is similar to its effect in the historical trials. Equivalence Margin 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. 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. Switch between superiority and noninferiority Interpreting a noninferiority trial as a superiority trial Interpreting a superiority trial as a noninferiority trial

37. Equivalence tests are driven by the needs in clinical trials, and are now gaining the popularity in clinical trials and other areas Summaries • Equivalence tests have major applications in bioequivalence / bioavailability studies and active control trials

38. 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 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- References