Therapeutic Equivalence

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

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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

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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).

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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
• Using the upper 95 confidence limit as the
  estimate of effectiveness is not statistically
  sensible

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Bayesian Design and Analysis of Active Control
Clinical TrialsBiometrics 55484-487, 1999
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ayesiantatistics
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? log of hazard ratio of C to P? log of
hazard ratio of E to P ? - ? log of HR of C
to E
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Prior Distributions

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

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Prior Distributions

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

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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/ ?
• ylt0 means E looked better than C

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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

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Probability that E is Effective and at least 50
as Effective as C
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Type I Error

• Posterior distribution of ? is N(y? , ?2?2)
• Conclude E is effective relative to P if
• If EP, predictive distribution of y is
• N(-? , ?2?2)
• If EP, predictive probability of concluding E is
  effective is ?

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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?lt0ygt0.95
• 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 ?

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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?lt0 ?ltk ? ygt0.95
• k.5 represents 50 as effective as C
• k0 represents simply effective relative to P

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Sample Size Planning for Therapeutic Equivalence
Trial
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Tamoxifen Alternative Therapeutic Equivalence
Trial. Invasive disease
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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 its effectiveness varies
  among trials

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Conclusions

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