Active Control NonInferiority Trial The Hypothesis

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Active Control Non-Inferiority Trial The
Hypothesis

• George Y.H. Chi, Gang Chen, Kevin Liu
• Clinical Biostatistics
• Global Drug Development, JJ PRD
• Yong-Cheng Wang
• Food and Drug Administration
• November 1, 2004, BASS XI, Savannah, Georgia

2
Disclaimer

• This talk is based on research work that was
• initiated while Dr. Gang Chen and I were still
• at FDA. The views expressed here are those
• of the authors and do not represent those of
• the FDA in any way.

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Outline of Presentation

• Reasons for Active Control
• Purposes of Active Control Trials
• Fixed Margin Non-inferiority Hypothesis
• Fraction Retention Non-inferiority Hypothesis
• Critical Assumptions
• Summary

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Reasons for Active Control

• Ethics For trials involving mortality or
  serious morbidity outcome, it is unethical to use
  placebo when there are available active drugs on
  the market
• Assay sensitivity In trials involving
  psychotropic drugs, placebo often has large
  effect. An active control is sometime used to
  demonstrate that the trial has assay sensitivity.
• Comparative purpose To show how the
  experimental drug compares to another known
  active drug or a competitor

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Purposes of Active Trials

• The purpose of an active control trial could be
  to demonstrate that a new experimental treatment
  is either
• superior to the control
• equivalent to the control, or
• non-inferior to the control
• superior to a virtual placebo

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Scope of Our Discussion

• Focus on use of active control for ethical reason
• Placebo is not permitted in such trials
• The primary objective is to show that relative to
  either an efficacy or safety endpoint, the new
  experimental drug is either
• superior to the control
• equivalent to the control, or
• non-inferior to the control
• superior to a virtual placebo

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Some Notations

• Let T stand for an experimental drug
• Let C stand for an active control
• Let P stand for a placebo
• Relative to a given time to event endpoint, such
  as, mortality, let HR(T/C) stand for the hazard
  ratio of T relative to C and similarly for
  HR(P/C). Then,
• HR(T/C) 1 gt T C
• HR(T/C) gt 1 gt T lt C
• HR(T/C) lt 1 gt T gt C

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HR(T/C) Hazard Ratio of T Relative to CFigure 1

• T C
• T gt C
  T lt C
• 0.8 1
  1.05 HR(T/C)

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Active Control Superiority Trial

• In an active control trial, if we demonstrate
  that T gt C, then what can we claim?
• T is superior to the control, i.e., T gt C ?
• Not quite. We can only claim that T is effective
  in the sense that T is superior to a virtual
  placebo, that is, T gt P, if a placebo,
  P, were to be present.
• The reason being
• The control C may not be effective in the current
  trial, and hence we have
• T gt C P See Figure 2

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Active Control Superiority TrialFigure 2

• If HR(T/C) lt 1, then T is effective
• 0.8 1
  HR(T/C)

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Active Control Superiority Trial

• Therefore, in an active control superiority
  trial, if we demonstrate that T gt C, then we can
  claim that
• T is superior to C, i.e., T
  gt C ,
• only under the following assumption
• That the control C is effective in the current
  trial, i.e., if a placebo P were to be present,
  then the trial would also have demonstrated that
  C gt P
• For then, we have T gt C gt P See Figure 3.

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Active Control Superiority TrialFigure 3

• If HR(T/C) lt 1, then T is superior to
  C,
• provided C is effective.
  
• T gt C
• HR(T/C)
  HR(P/C)
• 0.8 1
  1.2 HR(T/C)

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Active Control Non-inferiority Trial

• To demonstrate that a new experimental drug T is
  superior to an active control, C, is usually
  difficult and requires a large sample size,
  unless T is really effective.
• Furthermore, even if we succeeded in showing
  T gt C, we can only claim that T is effective,
  because we cannot really prove the assumption
  that C is effective in this trial without the
  presence of a placebo, P.
• Even if C were effective, a regulatory authority
  may not be willing to grant a comparative claim.

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Active Control Non-inferiority Trial

• Therefore, it makes sense to show that the new
  experimental drug T is non-inferior to the
  control, C, i.e., no worse than the control, by a
  margin of ?.
• We shall denote this by
• T ?? C
• and it is depicted graphically in Figure
  4.

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Active Control Non-inferiority TrialFigure 4

• If HR(T/C) lt 1 ?, then T is non-inferior to C
  by a margin of ?.
• T ?? C
• 
  
  
• 
  ?
• 0.8 1
  1 ? HR(T/C)

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Active Control Non-inferiority Trial

• To design an active control non-inferiority
  trial, how does one specify the non-inferiority
  margin ??
• Can this ? be arbitrarily specified?
• If ? is arbitrarily set, then
• ? may be too tight and it requires a large
  sample size, or
• ? may be too liberal and as a consequence, a new
  experimental treatment may be shown to be
  non-inferior to the control, but in fact, it
  could be worse than placebo
• We need some reference

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Active Control Non-inferiority Trial

• If C P, then HR(P/C) 1, and if 1 lt HR(T/C) lt
  1 ?, then T is inferior to P, since HR(T/C)
  HR(T/P).
• 
  
  
  
  
  
• 
  
• 
  
  
  HR(T/C)
  

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Active Control Non-inferiority Trial

• If C gt P and 1 lt HR(P/C) lt 1 ?, then if HR(P/C)
  lt HR(T/C) lt 1 ?, then T is inferior to P.
• 
  
  
  
  
  
• 
  
• 
  
  
  HR(T/C)
  
• 
  
  
  HR(P/C)

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Active Control Non-inferiority Trial

• Thus, we cannot set ? such that HR(P/C)
  1 lt ?, i.e., we
• cannot allow HR(P/C) lt 1 ?.
• This implies that we must set
• 0 lt ? HR(P/C) - 1.
• This means that ? must be a fraction, ?, of the
  control
• effect, i.e.,
• ? ? HR(P/C) 1.

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Active Control Non-inferiority Trial

• We can interpret ? as the amount of loss of the
  control effect that we are willing to accept See
  Figure 5.
• Then
• HR(P/C) 1 ? HR(P/C) 1 - ?
  HR(P/C) 1
• (1 - ?)
  HR(P/C) 1
• d
  HR(P/C) 1
• is the amount of the control effect that
  we would like to retain, where d is the retention
  fraction.

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Active Control Non-inferiority TrialFigure 5

• 
  
  
  
  
  
• 
  
• 
  
  HR(T/C)
  

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Active Control Non-inferiority Trial

• Now from the previous equation, we can obtain the
  following expression
• d 1 - ? / HR(P/C)
  1
• i.e.,
• d HR(P/C) 1 ? /HR(P/C)
  -1.

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Active Control Non-inferiority Trial

• If we are interested in
  demonstrating that the new
• experimental treatment is not worse than the
  control C
• by an amount ?o, then we are interested in
  testing the
• following hypothesis
• Ho HR(T/C) 1 ?o vs.
  Ha HR(T/C) lt 1 ?o ,
• i.e.,
• Ho HR(T/C) -1 ? ?o vs. Ha
  HR(T/C) -1 ? lt ?o.

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Active Control Non-inferiority Trial

• Now if the true control effect, HR(P/C) 1, is
  known, or can
• be accurately estimated, and do lt HR(P/C) 1,
  then, this
• would be equivalent to testing the null
  hypothesis
• Ho d
  do vs. Ha d gt do ,
• where
• do HR(P/C) 1
  ?o/HR(P/C) -1,
• and
  ?
• d HR(P/C) 1 HR(T/C) 1
  /HR(P/C) -1,

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Active Control Non-inferiority Trial

• Now if the true control effect, HR(P/C) 1, is
  not known, or
• cannot be accurately estimated, then we can no
  longer be sure
• that a fixed margin ?o lt HR(P/C) -1.
• In this event, the fixed margin hypothesis may
  not be
• appropriate, if ?o gt HR(P/C) -1.
• Therefore, to avoid this problem, it seems
  natural to select a do
• such that 0 lt do lt 1, and test the following null
  hypothesis
• Ho ? (1 - do) HR(P/C) 1

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Active Control Non-inferiority Trial

• Now this hypothesis has two unknown parameters,
  and one
• can reformulate this hypothesis to the following
  hypothesis
• Ho d do vs.
  Ha d gt do ,
• where
• HR(P/C) 1 ?
  
• d
• HR(P/C) 1
  

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Active Control Non-inferiority Trial

• Note that
• if do 1, then this is the superiority trial.
• If 0 lt do lt 1, then this is the equivalence, or
  non-inferiority trial
• FDA had used do ½ for non-inferiority
  demonstration in Xeloda and in thrombolytic
  trials
• How should do be set?
• If do 0, then this is a superior to virtual
  placebo trial

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Active Control Non-inferiority Trial

• Summary
• Whether it is fixed margin or not, we need to
  have some information on HR(P/C) 1 as a
  reference
• If HR(P/C) 1 cannot be reliably estimated,
  then fixed margin approach may be problematic
• If the fraction retention approach is used, we
  need to satisfy some assumptions including
• HR(P/C) 1 gt 0
• There are relevant historical studies of the
  control compared to placebo, or other comparator
  such as standard of care for estimating the
  control effect
• How to set the level of retention fraction, do,
  needs to be investigated through some simulation
  work. In the end, it will be based on both
  clinical and statistical judgment

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• Thank You !