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Active Control Non-Inferiority Trial – The Hypothesis

Active Control Non-Inferiority Trial – The Hypothesis. George Y.H. Chi, Gang Chen, Kevin Liu Clinical Biostatistics Global Drug Development, J&J PRD Yong-Cheng Wang Food and Drug Administration November 1, 2004, BASS XI, Savannah, Georgia. Disclaimer.

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Active Control Non-Inferiority Trial – The Hypothesis

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  1. Active Control Non-Inferiority Trial – The Hypothesis George Y.H. Chi, Gang Chen, Kevin Liu Clinical Biostatistics Global Drug Development, J&J 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.

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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 => T ~ C HR(T/C) > 1 => T < C HR(T/C) < 1 => T > C

  8. HR(T/C): Hazard Ratio of T Relative to CFigure 1 T = C T > C T < C 0.8 1 1.05 HR(T/C)

  9. Active Control Superiority Trial In an active control trial, if we demonstrate that T > C, then what can we claim? T is superior to the control, i.e., T > 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 > ‘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 > C ≥ ‘P’ [See Figure 2]

  10. Active Control Superiority TrialFigure 2 If HR(T/C) < 1, then T is effective 0.8 1 HR(T/C)

  11. Active Control Superiority Trial Therefore, in an active control superiority trial, if we demonstrate that T > C, then we can claim that T is superior toC, i.e., T > 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 > P For then, we have T > C > P [See Figure 3].

  12. Active Control Superiority TrialFigure 3 If HR(T/C) < 1, then T is superior to C, provided C is effective. T > C HR(T/C) HR(P/C) 0.8 1 1.2 HR(T/C)

  13. 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 > 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.

  14. 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.

  15. Active Control Non-inferiority TrialFigure 4 If HR(T/C) < 1 + , then T is non-inferior to Cby a margin of . T  C  0.8 1 1+ HR(T/C)

  16. 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

  17. Active Control Non-inferiority Trial If C = P, then HR(P/C) = 1, and if 1 <HR(T/C)<1 + , then T isinferior to P, since HR(T/C) = HR(T/P). HR(T/C) 0.8 1 1+HR(T/C) 

  18. Active Control Non-inferiority Trial If C > P and 1 < HR(P/C) < 1 + , then if HR(P/C)< HR(T/C) <1 + , then T isinferior to P. HR(T/C) HR(P/C) 0.8 1 1+HR(T/C) 

  19. Active Control Non-inferiority Trial Thus, we cannot set  such that HR(P/C) – 1 < , i.e., we cannot allow HR(P/C) < 1 + . This implies that we must set 0 <  ≤ HR(P/C) - 1. This means that  must be a fraction, , of the control effect, i.e.,  = [HR(P/C) – 1].

  20. 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, whered is the retention fraction.

  21. Active Control Non-inferiority TrialFigure 5 HR(T/C) HR(P/C) 0.8 1 1+HR(T/C)  d [HR(P/C) -1]

  22. 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].

  23. 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 + ovs. Ha: HR(T/C) < 1 + o , i.e., Ho: HR(T/C) -1 = ≥ ovs. Ha: HR(T/C) -1=  <o.

  24. Active Control Non-inferiority Trial Now if the true control effect, [HR(P/C) – 1], is known, or can be accurately estimated, and do < [HR(P/C) – 1], then, this would be equivalent to testing the null hypothesis: Ho: d≤ do vs. Ha: d >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],

  25. 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 < [HR(P/C) -1]. In this event, the fixed margin hypothesis may not be appropriate, if o > [HR(P/C) -1]. Therefore, to avoid this problem, it seems natural to select a do such that 0 < do < 1, and test the following null hypothesis: Ho:  ≥ (1 - do) [HR(P/C) – 1]

  26. 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 >do , where [HR(P/C) – 1] –  d = [HR(P/C) – 1]

  27. Active Control Non-inferiority Trial Note that if do = 1, then this is the superiority trial. If 0 < do < 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

  28. 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] > 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

  29. Thank You !

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