An Adaptive Design for Survival Studies with Subgroup Selection based on Predictive Biomarkers RSS / MRC HTMR Workshop on Stratified Medicine Thomas Hamborg t.hamborg@warwick.ac.uk Warwick Medical School The University of Warwick Funded by AstraZeneca 30 June 2010
Introduction Adaptive Design Framework Survival Studies Discussion Outline Introduction 1 Adaptive Design Framework 2 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion Outline Introduction 1 Adaptive Design Framework 2 Survival Studies 3 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion Outline Introduction 1 Adaptive Design Framework 2 Survival Studies 3 Discussion 4 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion Outline Introduction 1 Adaptive Design Framework 2 Survival Studies 3 Discussion 4 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion Problem Definition Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim Thomas Hamborg 1
Introduction Adaptive Design Framework Survival Studies Discussion Problem Definition Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim Method Seamless phase IIb/III clinical trial design Thomas Hamborg 1
Introduction Adaptive Design Framework Survival Studies Discussion Problem Definition Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim Method Seamless phase IIb/III clinical trial design Thomas Hamborg 1
Introduction Adaptive Design Framework Survival Studies Discussion Illustration: KRAS Biomarker Panitumumab Metastatic colorectal cancer Monoclonal antibody directed at EGFR Subgroups KRAS mutant & wild-type [Amado et al., 2008] Figure: Outcome for KRAS mutant tumour patients - Amado et al (2008) JCO, 26 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion Illustration: KRAS Biomarker Panitumumab Metastatic colorectal cancer Monoclonal antibody directed at EGFR Subgroups KRAS mutant & wild-type [Amado et al., 2008] Figure: Outcome for KRAS wild-type tumour patients - Amado et al (2008) JCO, 26 Thomas Hamborg 2
Introduction Adaptive Design Framework Survival Studies Discussion General Design Framework Test Statistics Efficient score Z = ∂ℓ ( 0 ) ∂θ : cumulative measure of advantage of experimental treatment E over control C (Observed) Fisher’s information V = − ∂ 2 ℓ ( 0 ) ∂θ 2 : amount of information on treatment difference contained in Z θ = Z V - Measure of treatment difference Z V ∼ N ( 0 , 1 ) Under H 0 : (Score test) √ Here: +ve patients: Z + , 1 , -ve patients: Z − , 1 , all patients: Z B , 1 Final analysis Z S V correspondingly Thomas Hamborg 3
Introduction Adaptive Design Framework Survival Studies Discussion General Design Framework Test Statistics Efficient score Z = ∂ℓ ( 0 ) ∂θ : cumulative measure of advantage of experimental treatment E over control C (Observed) Fisher’s information V = − ∂ 2 ℓ ( 0 ) ∂θ 2 : amount of information on treatment difference contained in Z θ = Z V - Measure of treatment difference Z V ∼ N ( 0 , 1 ) Under H 0 : (Score test) √ Here: +ve patients: Z + , 1 , -ve patients: Z − , 1 , all patients: Z B , 1 Final analysis Z S V correspondingly Thomas Hamborg 3
Introduction Adaptive Design Framework Survival Studies Discussion Design Illustration + v e V1 - ve Interim select +ve no sel. V1 + v e - ve + v e V2 Pr(Z>=c & sel. +ve) Pr(Z>=c & no sel.) Thomas Hamborg 4
Introduction Adaptive Design Framework Survival Studies Discussion Design Illustration + v e V1 - ve Interim select +ve no sel. V1 + v e - ve + v e V2 Pr(Z>=c & sel. +ve) Pr(Z>=c & no sel.) Thomas Hamborg 4
Introduction Adaptive Design Framework Survival Studies Discussion Design Illustration Cochran’s Q test + v e V1 - ve m � (ˆ θ i − ˆ θ ) 2 ω i Q = Interim i = 1 select +ve no sel. In terms of Z and V: V1 + v e - ve + v e V2 Z + , 1 V − , 1 − Z − , 1 V + , 1 Q = �� � V + , 1 + V − , 1 V + , 1 V − , 1 Pr(Z>=c & sel. +ve) Pr(Z>=c & no sel.) Subgroup selection if: Q ∼ N ( 0 , 1 ) ≥ k Thomas Hamborg 4
Introduction Adaptive Design Framework Survival Studies Discussion Design Illustration Cochran’s Q test + v e V1 - ve m � (ˆ θ i − ˆ θ ) 2 ω i Q = Interim i = 1 select +ve no sel. In terms of Z and V: V1 + v e - ve + v e V2 Z + , 1 V − , 1 − Z − , 1 V + , 1 Q = �� � V + , 1 + V − , 1 V + , 1 V − , 1 Pr(Z>=c & sel. +ve) Pr(Z>=c & no sel.) Subgroup selection if: Q ∼ N ( 0 , 1 ) ≥ k Thomas Hamborg 4
Introduction Adaptive Design Framework Survival Studies Discussion Interim Analysis in Detail Futility Stopping Criterion Cond. power (CP) approach Z + , 1 CP stopping unlikely if early in study ⇒ stop if: CP θ R ( V ) ≤ 1 − β CP continue +ve Z i , 1 ≤ 0, i ∈ { + , B } or no for respective interim decision selection Z -,1 Upper Selection Limit Criterion futility stop Undesireable to select if drug has certain effect in -ve patients Do not select +ve patients if: ˆ θ − , 1 ≥ τθ R , 0 < τ ≤ λ Natural choice τ = 1 Thomas Hamborg 5
Introduction Adaptive Design Framework Survival Studies Discussion Interim Analysis in Detail Futility Stopping Criterion Cond. power (CP) approach Z + , 1 CP stopping unlikely if early in study ⇒ stop if: CP θ R ( V ) ≤ 1 − β CP continue +ve no Z i , 1 ≤ 0, i ∈ { + , B } or selection for respective interim decision Z -,1 Upper Selection Limit Criterion futility stop Undesireable to select if drug has continue -ve certain effect in -ve patients Do not select +ve patients if: ˆ θ − , 1 ≥ τθ R , 0 < τ ≤ λ Natural choice τ = 1 Thomas Hamborg 5
Introduction Adaptive Design Framework Survival Studies Discussion Power Requirements Power Requirement I Study-wise type-I error rate + v e Pr ( Z S ≥ c | θ + = θ − = 0 ) = α V1 - ve Interim Power Requirement II select +ve Pr ( Z S ≥ c ∩ no sel. | θ + = θ − = θ R ) = no sel. 1 − β B = Power B V1 + v e θ R reference improvement - ve + v e V2 Pr(Z>=c) = type-I error rate Thomas Hamborg 6
Introduction Adaptive Design Framework Survival Studies Discussion Power Requirements Power Requirement I Study-wise type-I error rate + v e Pr ( Z S ≥ c | θ + = θ − = 0 ) = α V1 - ve Interim Power Requirement II select +ve Pr ( Z S ≥ c ∩ no sel. | θ + = θ − = θ R ) = no sel. 1 − β B = Power B V1 + v e θ R reference improvement - ve + v e V2 Power Requirement III Pr ( Z S ≥ c ∩ sel +ve | θ + = λθ R , θ − = 0 ) = Pr(Z>=c & no sel.)=Power B 1 − β + = Power + λ ≥ 1 ⇒ demand larger effect for selection Thomas Hamborg 6
Introduction Adaptive Design Framework Survival Studies Discussion Power Requirements Power Requirement I Study-wise type-I error rate + v e Pr ( Z S ≥ c | θ + = θ − = 0 ) = α V1 - ve Interim Power Requirement II select +ve Pr ( Z S ≥ c ∩ no sel. | θ + = θ − = θ R ) = no sel. 1 − β B = Power B V1 θ R reference improvement + v e - ve + v e V2 Power Requirement III Pr ( Z S ≥ c ∩ sel +ve | θ + = λθ R , θ − = 0 ) = Pr(Z>=c & sel. +ve)=Power + 1 − β + = Power + λ ≥ 1 ⇒ demand larger effect for selection Thomas Hamborg 6
Introduction Adaptive Design Framework Survival Studies Discussion Calculation of Design Variables Score function properties: Approximately Z ∼ N ( θ V , V ) 1 Independent increment structure 2 Numerical root finding procedure For each Power Requirement: u + u − i i Z Z ` c − ( z · ) − θ j ( V S − V · , 1 ) ´ff X Pr ( Z S ≥ c ) = 1 − Φ √ V S − V · , 1 f ( z + ) f ( z − ) dz + dz − , i l + l − i i “ ” 1 z − θ V where f ( z ) = V φ √ √ V Thomas Hamborg 7
Introduction Adaptive Design Framework Survival Studies Discussion Design Framework for Survival Outcome Superiority Trial Outcome: time to unfavourable event S E ( t ) , S C ( t ) survival probabilities H 0 : θ = 0 vs H 1 : θ > 0 Proportional Hazard Model Assumption: h E ( t ) = ψ h C ( t ) , t > 0 Parameterisation: θ = − log ( h E ( t ) / h C ( t )) Thomas Hamborg 8
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