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 / y/ ss(E vs C)/ss(C vs P)

Prob( <0) Pr{ <0 & <0.5 }

-2 0 1 .92 .80-2 -1 1 .98 .94-2 1 1 .76 .49

-2 0 4 .96 .82-2 0 1/4 .81 .71

-3 0 1 .98 .91-3 1 1 .92 .67

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

Prob of effectiveness / k ss(E vs C) /ss(C vs P)

95% -3 0 1.295% -3 0.5 4.895% -2 0 9.6

90% -3 0 0.790% -3 0.5 2.690% -2 0 2.8

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