Therapeutic Equivalence & Active Control Clinical Trials

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

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

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

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

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

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

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

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).

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

Bayesian Design and Analysis of Active Control Clinical TrialsBiometrics 55:484-487, 1999

ayesiantatistics

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

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

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

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

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

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

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|y}>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 

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 & <k  |y}>0.95 • k=.5 represents 50% as effective as C • k=0 represents simply effective relative to P

Sample Size Planning for Therapeutic Equivalence Trial

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

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

Therapeutic Equivalence & Active Control Clinical Trials