Predictive probability of success using surrogate endpoints Ga¨elleSaint-Hilary1 Valentine Barboux2, Matthieu Pannaux2, Mauro Gasparini1, V´eroniqueRobert2, Gianluca Mastrantonio1 1Politecnico Di Torino (Italy) 2Institut de Recherches Internationales Servier (France) [email protected] PSI Conference, 06 June 2018 Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 1/23 Introduction (1/2) The Predictive Probability of Success (PPoS) of a future clinical trial is a key quantitative tool for decision-making in drug development Spiegelhalter et al., 1986 ; O'Hagan et al., 2005 ; Gasparini et al., 2013 Derived from prior knowledge and available evidence Typically, available evidence = accumulated data on the clinical endpoint of interest in previous clinical trials However, a surrogate endpoint could be used as primary endpoint in early development, and no or limited data are collected on the clinical endpoint of interest ) General methodology to predict the success of a future trial from surrogate endpoints Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 2/23 Introduction (2/2) Terminology used in this presentation Surrogate endpoint: marker used in early phase as a measure of the treatment effect Final endpoint: clinical endpoint of interest (accepted for confirmatory phase from a regulatory perspective) \A correlate does not a surrogate make" Fleming and DeMets, 1996 A relationship between endpoints estimated from a single trial is insufficient to support predictions across trials It focuses on the patient level association, while we are interested in the relationship between treatment effects on the endpoints at the trial level ) Meta-analytic approaches have been proposed to overcome Daniels and Hughes, 1997 ; Buyse et al., 2000 ; Gail et al., 2000 ; Baker and Kramer, 2003 ; Burzykowski this issue et al., 2005 ; Buyse et al., 2016 ; Alonso et al., 2017 Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 3/23 Proposed approach Drug development of interest External data Data on the External CTs with surrogate endpoints both surrogate and in past trials final endpoints Joint distribution between If available, data on Informative prior for the surrogate and final the final endpoint final endpoint parameter endpoint parameters in past trials (\surrogate prior") Prior-data conflict? Next trial design Posterior distribution of the with final endpoint final endpoint parameter Predictive distribution Success of the final endpoint criteria estimate in the next trial CT = Clinical Trial PPoS = Predictive Probability of Success PPoS of the next trial Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 4/23 Motivating example Fictive but realistic case-study in Multiple Sclerosis Drug development of interest External data Data on the Phase II trial (completed) External CTs with surrogate endpoints Experimental arm vs Control arm both surrogate and in past trials N/arm = 100 final endpoints Primary (surrogate): Relapse rate at 1 year If available, data on InformativeSecondary prior (final): for the 19 clinical trials the final endpoint finalDisability endpoint progression parameter at 2 (5 multi-arm) in past trials years(\surrogate prior") with both endpoints evaluated Phase III trial (planned) Next trial design PosteriorExperimental distribution arm vs Control of the arm Pozzi et al., 2016 with final endpoint final endpointN/arm parameter = 337 Primary (final): Bujkiewicz et al., 2016 Disability progression at 2 Sormani et al., 2010 years Predictive distribution Success of the final endpoint criteria estimateSuccess: in p-value the next< trial2.5 % (one-sided) Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 5/23 Without considering the surrogate endpoint... (1/2) PPoS based on the final endpoint only (reminders) Drug development of interest External data Data on the External CTs with surrogate endpoints both surrogate and in past trials final endpoints Joint distribution between If available, data on Informative prior for the surrogate and final the final endpoint final endpoint parameter endpoint parameters in past trials (\surrogate prior") Prior-data conflict? Next trial design Posterior distribution of the with final endpoint final endpoint parameter Predictive distribution Success of the final endpoint criteria estimate in the next trial CT = Clinical Trial PPoS = Predictive Probability of Success PPoS of the next trial Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 6/23 Without considering the surrogate endpoint... (2/2) PPoS based on the final endpoint only (reminders) V 2 Disability progression at 2 years Vague prior πθ (·): θ ∼ N(θ0; σ0) V 2 Results of the Phase II trial Posterior gθ (·): θ ∼ N(θp; σp) at the time of the main analysis Predictive hV (·): θ^ ∼ N θ ; σ2 + σ2 θ^ f p p f ^ f θ (σ) V ^ 2 R V PPoS = P θf < zασf = u<z σ2 h^ (u)du N/arm 10 α f θf log(RR) (SE) -0.386 (0.646) The prediction variance depends on: • The precision of the evidence on the final endpoint • The precision planned in the future trial on the final endpoint RR=Relative Risk SE=Standard Error Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 7/23 Joint distribution between surrogate and final endpoint parameters Meta-analytic approach using external CTs (1/2) Drug development of interest External data Data on the External CTs with surrogate endpoints both surrogate and in past trials final endpoints Joint distribution between If available, data on Informative prior for the surrogate and final the final endpoint final endpoint parameter endpoint parameters in past trials (\surrogate prior") Prior-data conflict? Next trial design Posterior distribution of the with final endpoint final endpoint parameter Predictive distribution Success of the final endpoint criteria estimate in the next trial CT = Clinical Trial PPoS = Predictive Probability of Success PPoS of the next trial Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 8/23 Joint distribution between surrogate and final endpoint parameters Meta-analytic approach using external CTs (2/2) 2 Conditional distribution: θi j γi ; a; b; τ ∼ N(a + bγi ; τ ) ^ 2 2 θi a + bγi σi + τ ρi σi δi Joint distribution: γi ; a; b; τ ∼ N ; 2 The variance of the joint dist. γ^i γi ρi σi δi δi between endpoints depends on: • The variance of the joint post. dis- tribution fa;b,τ (·): small if the amount of data in the meta- analysis is large • The dependence between the end- points: τ is small if the surrogate is `good' Regression parameters Posterior means and 95% credible intervals (CrI) Parameter Mean [95% CrI] Intercept a 0.08 [-0.10,0.24] Pozzi et al., 2016 Slope b 0.76 [ 0.47,1.02] Error τ 0.15 [ 0.05,0.29] Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 9/23 Informative prior for the final endpoint parameter (1/3) \Surrogate prior" Drug development of interest External data Data on the External CTs with surrogate endpoints both surrogate and in past trials final endpoints Joint distribution between If available, data on Informative prior for the surrogate and final the final endpoint final endpoint parameter endpoint parameters in past trials (\surrogate prior") Prior-data conflict? Next trial design Posterior distribution of the with final endpoint final endpoint parameter Predictive distribution Success of the final endpoint criteria estimate in the next trial CT = Clinical Trial PPoS = Predictive Probability of Success PPoS of the next trial Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 10/23 Informative prior for the final endpoint parameter (2/3) \Surrogate prior" 2 Relapse rate at 1 year Surrogate endpoint: Vague prior: γ ∼ N(γ0; δ0) 2 Results of the Phase II trial Posterior: γ ∼ N(γp; δp) (main analysis) Final endpoint: 2 2 2 γ^ (δ) Conditional distribution fθja;b,τ (:): θ j a; b; τ ∼ N(a + bγp; τ + b δp) S R N/arm 100 Unconditional distribution πθ (·): fθja;b,τ (:)fa;b,τ (x; y; z)d(x; y; z) log(RR) (SE) -0.693 (0.397) The variance of the unconditional distribution depends on: • The variance of the joint post. distribution fa;b,τ (·) • The dependence between the endpoints • The precision of the evidence on the 2 surrogate: δp is small if the amount of data on the surrogate is large RR=Relative Risk SE=Standard Error Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 11/23 Informative prior for the final endpoint parameter (3/3) \Surrogate prior" Final endpoint \Surrogate prior": We call this distribution S R πθ (·) = fθja;b,τ (:)fa;b,τ (x; y; z)d(x; y; z) the \surrogate prior" (Distribution derived from data on the surrogate endpoint, to be used as a prior for the final endpoint) Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 12/23 Without considering the data on the final endpoint... (1/2) PPoS based on the surrogate endpoint only Drug development of interest External data Data on the External CTs with surrogate endpoints both surrogate and in past trials final endpoints Joint distribution between If available, data on Informative prior for the surrogate and final the final endpoint final endpoint parameter endpoint parameters in past trials (\surrogate prior") Prior-data conflict? Next trial design Posterior distribution of the with final endpoint final endpoint parameter Predictive distribution Success of the final endpoint criteria estimate in the next trial CT = Clinical Trial PPoS = Predictive Probability of Success PPoS of the next trial Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 13/23 Without considering the data on the final endpoint... (2/2) PPoS based on the surrogate endpoint only S R Surrogate prior πθ (·) = fθja;b,τ (:)fa;b,τ (x; y; z)d(x; y; z) Posterior = prior (no data) S R S Predictive h^ (·) = f^ (·)πθ (t)dt θf θf jθ=t S R S PPoS = 2 h^ (u)du u<zασf θf The prediction variance depends on: • The variance of the joint post. distribution fa;b,τ (·) • The dependence between the endpoints • The precision of the evidence on the surrogate • The precision planned in the future trial 2 on the final endpoint: σf is small if the planned # of patients / events is large Ga¨elleSaint-Hilary Decision-Making - PPoS using surrogates 14/23 Considering the whole evidence..