1. Therapeutic Equivalence & Active Control Clinical Trials Richard Simon, D.Sc. Chief, Biometric Research Branch National Cancer Institute

2. Objectives Determine whether a new treatment is therapeutically equivalent to an established effective treatment Determine whether a new treatment is effective relative to no treatment

3. Problems With Therapeutic Equivalence Trials It is impossible to demonstrate therapeutic equivalence –At best, one can establish that results are only consistent with differences in efficacy within specified limits

4. Problems With Therapeutic Equivalence Trials When your only tool is a hammer, everything looks like a nail –Failure to reject the null hypothesis may be the result of inadequate sample size, not demonstration of equivalence

5. Problems With Therapeutic Equivalence Trials Large sample sizes are needed to establish that differences in efficacy are within narrow limits

6. Problems With Therapeutic Equivalence Trials The limits within which difference in efficacy should be bounded should depend on –The degree of effectiveness of the active control –The precision with which the effectiveness of the active control is estimated

7. Problems With Therapeutic Equivalence Trials Therapeutic equivalence trials are not feasible or interpretable unless there is strong quantifiable evidence for the effectiveness of the active control

8. Problems With Therapeutic Equivalence Trials Demonstrating that E (experimental rx) is at least 80% as effective as C (active control) is interpretable only in the context of knowledge of how effective C is with regard to P (previous standard or no rx).

9. Problems With Therapeutic Equivalence Trials In evaluating whether 80% effectiveness relative to C represents effectiveness relative to P, one must account for the uncertainty in effectiveness of C relative to P

10. Bayesian Design and Analysis of Active Control Clinical Trials Biometrics 55:484-487, 1999

11. ayesian tatistics

12.  = log of hazard ratio of C to P  = log of hazard ratio of E to P  -  = log of HR of C to E

13. Prior Distributions Prior distribution for  is N( , 2 ) –Determined from random-effects meta-analysis of relevant randomized trials of C versus P

14. Prior Distributions Prior distribution for  is N(0,  ) –Reflecting no quantitative randomized evidence for effectiveness of E

15. Results of Therapeutic Equivalence Trial Observed maximum likelihood estimate of log of hazard ratio of E to C is y with standard error  “z value” is y/  y<0 means E looked better than C

16. Posterior Distributions Given Data From Equivalence Trial Posterior distribution of  is same as prior distribution Posterior distribution of  is N(y+ , 2 +  2 ) Correlation of  and  is /  2 +  2

17. Probability that E is Effective and at least 50% as Effective as C

18. Planning Sample Size for Therapeutic Equivalence Trial If E and C are equivalent, we want high probability (e.g. 0.80) of concluding that E is effective relative to P –Pr{  0.95 –0.95 is probability of effectiveness The calculation is made assuming  = , and using the predictive distribution of y with regard to the prior distribution of 

19. Planning Sample Size for Therapeutic Equivalence Trial A more stringent requirement is if E and C are equivalent, we want high probability (e.g. 0.80) of concluding that E is effective relative to P and at least 100k% as effective as C –Pr{  0.95 –k=.5 represents 50% as effective as C –k=0 represents simply effective relative to P

20. Sample Size Planning for Therapeutic Equivalence Trial

21. Conclusions Therapeutic equivalence trials cannot be meaningfully interpreted without quantitative consideration of the evidence that the control C is effective: –The strength of evidence that C is effective –The degree to which it is effective –The degree to which it’s effectiveness varies among trials

22. Conclusions Therapeutic equivalence trials are not practical or appropriate in situations where strong quantitative evidence for the effectiveness of C is not available