2006, Tianjin, China sf.ppt - Faragalli 1 Statistical Hypotheses and Methods in Clinical Trials with Active Control Non-inferiority Design Yong-Cheng Wang Centocor, Inc., Johnson & Johnson Pharmaceutical Companies, PA, USA 2006 International Conference on Design of Experiments and Its Applications July 9-13, 2006, Tianjin, P. R. China Yong-Cheng Wang Centocor, Inc., Johnson & Johnson Pharmaceutical Companies, PA, USA 2006 International Conference on Design of Experiments and Its Applications July 9-13, 2006, Tianjin, P. R. China

2006, Tianjin, China sf.ppt - Faragalli 2 Outline ? Introduction – Notations & Definitions – Objectives of non-inferiority (NI) trials ? Non-inferiority Hypotheses – Fixed margin – Fraction retention ? Non-inferiority Analysis Methods – Fixed margin – Fraction retention – Two CI procedure – Bayesian ? Summary ? Introduction – Notations & Definitions – Objectives of non-inferiority (NI) trials ? Non-inferiority Hypotheses – Fixed margin – Fraction retention ? Non-inferiority Analysis Methods – Fixed margin – Fraction retention – Two CI procedure – Bayesian ? Summary

Yong-Cheng Wang Introduction Notations, Definitions, NI objectives

2006, Tianjin, China sf.ppt - Faragalli 4 Notations & Definitions ? Endpoint: time to event (e.g., survival, TTP) ? Hazard ratios: HR(T/C) and HR(P/C) ? Treatment effect:  1 = HR(T/C) -1 ? Control effect:  2 = HR(P/C) -1 ? Fraction retention of control effect:  = 1 – {  1 /  2 }, or ? Fraction loss of control effect:1 -  =  1 /  2, where, T, C and P are treatment, control and placebo, respectively, and are under the constancy assumption: C = C 1 (active control) = C 2 (historical control) ? Endpoint: time to event (e.g., survival, TTP) ? Hazard ratios: HR(T/C) and HR(P/C) ? Treatment effect:  1 = HR(T/C) -1 ? Control effect:  2 = HR(P/C) -1 ? Fraction retention of control effect:  = 1 – {  1 /  2 }, or ? Fraction loss of control effect:1 -  =  1 /  2, where, T, C and P are treatment, control and placebo, respectively, and are under the constancy assumption: C = C 1 (active control) = C 2 (historical control)

2006, Tianjin, China sf.ppt - Faragalli 5 Objectives of NI Trials To demonstrate new treatment effect by showing: ? Not worse than a given  _margin: Test Drug > Active Control -  _margin ? Retain a fraction of control effect: to test if new treatment preserves a fraction of control effect: Test Drug > %  Active Control To demonstrate new treatment effect by showing: ? Not worse than a given  _margin: Test Drug > Active Control -  _margin ? Retain a fraction of control effect: to test if new treatment preserves a fraction of control effect: Test Drug > %  Active Control

Yong-Cheng Wang NI Hypotheses Fraction retention / Fixed margin

2006, Tianjin, China sf.ppt - Faragalli 7 NI Hypotheses – Fraction Retention ? Fraction retention NI hypotheses: H 0 :  ≤  0 vs. H a :  >  0 or, if  2 = HR(P/C) - 1 > 0, H 0 :  1  (1-  0 )  2 vs. H a :  1 < (1 -  0 )  2 ? Fraction retention NI hypotheses: H 0 :  ≤  0 vs. H a :  >  0 or, if  2 = HR(P/C) - 1 > 0, H 0 :  1  (1-  0 )  2 vs. H a :  1 < (1 -  0 )  2

2006, Tianjin, China sf.ppt - Faragalli 8 Selection of Fraction Retention The selection of  depends on several factors: ? objective of active control trial – claim non-inferiority or equivalence – claim efficacy ? clinical judgment ? statistical judgment – distributional properties of the ratio of treatment effect vs. active control effect – mean effect size of active control – variability of active control effect The selection of  depends on several factors: ? objective of active control trial – claim non-inferiority or equivalence – claim efficacy ? clinical judgment ? statistical judgment – distributional properties of the ratio of treatment effect vs. active control effect – mean effect size of active control – variability of active control effect

2006, Tianjin, China sf.ppt - Faragalli 9 NI Hypotheses – Fixed Margin ? If fix control effect  2 = M 1 > 0, and define margin M =  0 * M 1, where  0 is a fixed level of fraction retention, then NI hypotheses become : H 0 :  1 /M 1   0 vs. H a :  1 /M 1 <  0, or H 0 : HR(T/C)  1+M vs. H a : HR(T/C) < 1+M ? If fix control effect  2 = M 1 > 0, and define margin M =  0 * M 1, where  0 is a fixed level of fraction retention, then NI hypotheses become : H 0 :  1 /M 1   0 vs. H a :  1 /M 1 <  0, or H 0 : HR(T/C)  1+M vs. H a : HR(T/C) < 1+M

2006, Tianjin, China sf.ppt - Faragalli 10 Selection of Fixed Margin ? Arbitrary margin: questionable ? Margin based on control effect ~ two CI method: Based on the lower limit (LL) of  % CI for HR(P/C), i.e. Margin =  0 *[LL of  % CI for HR(P/C) -1] e.g.,  0 = 0.5, LL of  % CI = 1.2, then margin = 0.1 If the 95% CI for HR(T/C) lies entirely beneath 1 + margin (NI cutoff), “non-inferiority” is concluded. ? Arbitrary margin: questionable ? Margin based on control effect ~ two CI method: Based on the lower limit (LL) of  % CI for HR(P/C), i.e. Margin =  0 *[LL of  % CI for HR(P/C) -1] e.g.,  0 = 0.5, LL of  % CI = 1.2, then margin = 0.1 If the 95% CI for HR(T/C) lies entirely beneath 1 + margin (NI cutoff), “non-inferiority” is concluded.

Yong-Cheng Wang NI Analysis Methods

2006, Tianjin, China sf.ppt - Faragalli 12 NI Statistical Tests ? Linearization method (Mark Rothmann) ? Ratio test (Yong-Cheng Wang) ? Two 90% (or 95%) CI procedure (CBER/FDA/US) ? CI for the ratio (Hasselblad & Kong) ? Bayesian (Richard Simon) ? Linearization method (Mark Rothmann) ? Ratio test (Yong-Cheng Wang) ? Two 90% (or 95%) CI procedure (CBER/FDA/US) ? CI for the ratio (Hasselblad & Kong) ? Bayesian (Richard Simon)

2006, Tianjin, China sf.ppt - Faragalli 13 NI Tests – Linearization Method (Rothmann) ? NI hypotheses: Assuming HR(P/C) > 1 H 0 (1) : logHR(T/C)  (1-  0 )logHR(P/C) vs. H a (1) : logHR(T/C) < (1-  0 )logHR(P/C) Test statistic for H 0 (1) vs. H a (1) : ? NI hypotheses: Assuming HR(P/C) > 1 H 0 (1) : logHR(T/C)  (1-  0 )logHR(P/C) vs. H a (1) : logHR(T/C) < (1-  0 )logHR(P/C) Test statistic for H 0 (1) vs. H a (1) :

2006, Tianjin, China sf.ppt - Faragalli 14 NI Tests – Ratio Test (Wang) ? Estimate of  : where and are estimates of hazard ratios. ? Estimate of  : where and are estimates of hazard ratios.

2006, Tianjin, China sf.ppt - Faragalli 15 NI Tests – Ratio Test (Wang) ? NI hypothesis: H 0 :    0 vs. H a :  >  0 ? Test statistic: Concern: Is Z* normal? ? NI hypothesis: H 0 :    0 vs. H a :  >  0 ? Test statistic: Concern: Is Z* normal?

2006, Tianjin, China sf.ppt - Faragalli 16 NI Tests – Ratio Test (Wang) Asymptotic Normality of Z *

2006, Tianjin, China sf.ppt - Faragalli 17 NI Tests – Ratio Test (Wang) Asymptotic Normality of Z *

2006, Tianjin, China sf.ppt - Faragalli 18 NI Tests – Ratio Test (Wang) ? Interim statistic: ? Z k * is approximately normally distributed, and ? Interim statistic: ? Z k * is approximately normally distributed, and

2006, Tianjin, China sf.ppt - Faragalli 19 NI Tests – Ratio Test (Wang) Normality of Z * (Xeloda trials, simulation runs=100,000) Number of Events p68.2%80.9%88.9%93.8%96.6%98.2%99.1% where p = proportion of simulation runs passed Shapiro-Wilk test.

2006, Tianjin, China sf.ppt - Faragalli 20 NI Tests – Two 95% CI Method (FDA/US) Two 95% CI method: ? Define the non-inferiority cutoff (1+margin) as  + 0.5*  LL of 95% CI for HR(P/C) - 1) ? If the 95% CI for HR(T/C) lies entirely beneath this cutoff, non-inferiority is concluded. Two 95% CI method: ? Define the non-inferiority cutoff (1+margin) as  + 0.5*  LL of 95% CI for HR(P/C) - 1) ? If the 95% CI for HR(T/C) lies entirely beneath this cutoff, non-inferiority is concluded.

2006, Tianjin, China sf.ppt - Faragalli 21 NI Tests – CI of Ratio Method (H & K) ? A “95%” confidence interval is calculated using a normal distribution with standard error

2006, Tianjin, China sf.ppt - Faragalli 22 NI Tests – Bayesian Method (Simon) The posterior density for  1 =logHR(T/C) is normal with mean (  1 +  2 ) and variance (  1 +  2 ).  1 : log HR(T/C)  2 : logHR(C/P)  1 : var(log HR(T/C))  2 : var(logHR(C/P)) The posterior prob (T is superior to C): P( <0)=1-  [(  1 +  2 )/sqrt(  1 +  2 )] The prob (1-k)100% of the effect of C to P is not lost with T is Pr( -k  <0,  <0). The posterior density for  1 =logHR(T/C) is normal with mean (  1 +  2 ) and variance (  1 +  2 ).  1 : log HR(T/C)  2 : logHR(C/P)  1 : var(log HR(T/C))  2 : var(logHR(C/P)) The posterior prob (T is superior to C): P( <0)=1-  [(  1 +  2 )/sqrt(  1 +  2 )] The prob (1-k)100% of the effect of C to P is not lost with T is Pr( -k  <0,  <0).

Yong-Cheng Wang Summary

2006, Tianjin, China sf.ppt - Faragalli 24 Summary of Active Control NI Trials ? If control effect is small, active control trial should be a “superiority” trial, not a “non-inferiority” trial. ? Appropriate assessment of the control effect based on historical data may be difficult when – few trials, especially only one trial – changing the population – changing the standard care ? Selection of the fraction retention should be based on both clinical and statistical judgments. ? Interpretation of results needs to be with caution. ? If control effect is small, active control trial should be a “superiority” trial, not a “non-inferiority” trial. ? Appropriate assessment of the control effect based on historical data may be difficult when – few trials, especially only one trial – changing the population – changing the standard care ? Selection of the fraction retention should be based on both clinical and statistical judgments. ? Interpretation of results needs to be with caution.

Yong-Cheng Wang END Thanks