Date post: | 04-Jan-2016 |
Category: |
Documents |
Upload: | jeffery-kevin-blake |
View: | 227 times |
Download: | 1 times |
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