The changing landscape of interim analyses for efficacy / futility

1. The changing landscape of interim analyses for efficacy / futility Marc Buyse, ScD IDDI, Louvain-la-Neuve, Belgium marc.buyse@iddi.com Massachusetts Biotechnology Council Cambridge, Mass June 2, 2009

2. Reasons for Interim Analyses Early stopping for safety extreme efficacy futility Adaptation of design based on observed data to play the winner / drop the loser maintain power make any adaptation, for whatever reason and whether or not data-derived, whilst controlling for 

3. Methods for Interim Analyses Multi-stage designs / seamless transition designs Group-sequential designs Stochastic curtailment Sample size adjustments Adaptive (« flexible ») designs

4. Early Stopping • Helsinki Declaration: “Physician should cease any investigation if the hazards are found to outweigh the potential benefits.”(« Primum non nocere ») • Trials with serious, irreversible endpoints should be stopped if one treatment is “proven” to be superior, and such potential stopping should be formally pre-specified in the trial design.

5. The Cost of Delay « Blockbusters » reach sales > 500 M$ a year (> 1 M$ a day)

6. Fixed Sample Size Trials… 1 – the sample size is calculated to detect a given difference at given significance and power2 – the required number of patients is accrued3 – patient outcomes are analyzed at the end of the trial, after observation of the pre-specified number of events

7. …vs(Group) Sequential Trials… 1 – the sample size iscalculated to detect a givendifferenceatgivensignificance and power2 – patients are accrueduntil a pre-plannedinterimanalysisof patient outcomestakes place3a – the trial isterminatedearly, or3b – the trial continues unchanged4 – patient outcomes are analyzed at the end of the trial, after observation of the pre-specifiednumber of events

8. …vs Adaptive Trials 1 – the sample size iscalculated to detect a givendifferenceatgivensignificance and power2 – patients are accrueduntil a pre-plannedinterimanalysisof patient outcomestakes place3a – the trial isterminatedearly, or3b – the trial continues unchanged, or3c – the trial continues withadaptations4 – patient outcomes are analyzed at the end of the trial, after observation of the pre-specified or modifiednumber of events

9. PHASE III PHASE II Randomized phase II trial with continuation as phase III trial Simultaneous screening of several treatment groups with continuation as phase III trial : Arm 1 Arm 2 Arm 3 Early stopping ofone or more arms Comparison of the arms

10. PHASE III PHASE III INTERIM Phase III trial with interim analysis Phase III trial with interim look at data: Arm 1 Arm 2 Arm 3 Interim comparison ofthe arms Comparison of the arms

11. Seamless transition designs(e.g. for dose selection) Designs can be operationally or inferentially seamless:

12. GroupSequential Trials • If several analyses are carried out, the Type I error is inflated if each analysis is carried out at the target level of significance. • So, the interim analyses must use an adjusted level of significance so as to preserve the overall type I error.

13. Inflation of  with multiple analyses With 5 analyses performed at level 0.05, the overall level is 0.15

14. Adjusting  for multiple analyses The 5 analyses must be performed at level 0.0159 in order to preserve an overall level of 0.05

15. Group sequential designs • Test H0: Δ = 0 vs. HA: Δ ≠ 0 • m pts. accrued to each arm between analyses • Use standardized test statistic Zk, k=1,...,K

16. Group-Sequential Designs – Type I Error • Probability of wrongly stopping/rejecting H0at analysis k PH0(|Z1|<c1, ..., |Zk-1|<ck-1, | Zk |≥ck) = πk • “Type I error spent at stage k” • P(Type I error) = ∑πk • Choose ck’s so that ∑πkα

17. Group-Sequential Designs – Type II Error • Probability of Type II error is 1-PHA( U {|Z1|<c1, ..., |Zk-1|<ck-1, | Zk |≥ck} ) • Depends on K, α, β, ck’s. • Given the values, the required sample size can be computed • it can be expressed as R x (fixed sample size)

18. Pocock Boundaries • Reject H0 if | Zk| > cP(K,α) • cP(K,α) chosen so that P(Type I error) = α • All analyses are carried out at the same adjusted significance level • The probability of early rejection is high but the power at the final analysis may be compromised

19. Pocock Boundaries • p-values for Zk (two-sided)per interim analysis (K=5)

20. O’Brien-Fleming Boundaries • Reject H0 if | Zk | > cOBF(K,α)√(K / k) • fork=K we get | ZK | > cOBF(K,α) • cOBF(K,α) chosen so that P(Type I error) = α • Early analyses are carried out at extreme adjusted significance levels • The probability of early rejection is low but the power at the final analysis is almost unaffected

21. O’Brien-Fleming Boundaries • p-values for Zk (two-sided)per interim analysis (K=5)

22. Wang & Tsiatis Boundaries • Wang & Tsiatis (1987): Reject H0if | Zk | > cWT(K,α,θ)(K / k)θ - ½ • θ = 0.5 gives Pocock’s test; θ = 0, O’Brien-Fleming • implemented in some software (e.g. EaSt) • Can accomodate any intermediate choice between Pocock and O’Brien-Fleming

23. Wang & Tsiatis Boundaries • p-values for Zk (two-sided)per interim analysis (K=5) with  = .2

24. Haybittle & Peto Boundaries • Haybittle & Peto (1976): Reject H0 if | Zk | > 3 for k = 1,...,K-1 Reject H0 if | Zk | > cHP(K,α) for k = K • | Zk | > 3corresponds to using p < 0.0026 • Early analyses are carried out at extreme, yet reasonable adjusted significance levels • Intuitive and easily implemented if correction to final significance level is ignored (pragmatic approach)

25. Haybittle & Peto Boundaries • p-values for Zk (two-sided)per interim analysis (K=5)

26. Boundaries compared • p-values for Zk (two-sided)per interim analysis (K=5)

27. Boundaries compared • Zk per interim analysis (K=5)

28. Potential savings / costs in using group sequential designs Expected sample sizes for different designs (K=5): - outcomes normally distributed with  = 2-  = 0.05-  = 0.1 for A - B = 1

29. Error-Spending Approach • Removing the requirement of a fixed number of equally- spaced analyses • Lan & DeMets (1983): two-sided tests “spending” Type I error. • Maximum information design: • Error spending function → • Defines boundaries • Accept H0 if Imaxattained without rejecting the null

30. Error-Spending Approach • f(t)=min(2-2Φ(z1-α/2),α) yields ≈ O’B-F boundaries • f(t)=min(α ln (1+(e -1)t,α) yields ≈ Pocock boundaries • f(t)=min(αtθ,α): • θ=1 or 3 corresponds to Pocock and O’B-F, respectively

31. How Many Interim Analyses? • One or two interim analyses give most benefit in terms of a reduction of the expected sample size • Not much gain from going beyond 5 analyses

32. When to Conduct Interim Analyses? • With error-spending, full flexibility as to number and timing of analyses • First analysis should not be “too early” (often at  50% of information time) • Equally-spaced analyses advisable • In principle, strategy/timing should not be chosen based on the observed results

33. Who conducts interim analyses? • Independent Data Monitoring Committee • Experts from different disciplines (clinicians, statisticians, ethicists, patient advocates, …) • Reviews trial conduct, safety and efficacy data • Recommends • Stopping the trial • Continuing the trial unchanged • Amending the trial

34. Sample Size Re-Estimation • Assume normally distributed endpoints • Sample size depends on σ2 • If misspecified, nIcan be too small • Idea: internal pilot study • estimate σ2 based on early observed data • compute new sample size, nA • if necessary, accrue extra patients above nI

35. Early Stopping for Futility • Stopping to reject H0ofno treatment difference • Avoids exposing further patients to the inferiortreatment • Appropriate if no further checks are needed on, e.g.,treatment safety or long-term effects. • Stopping to acceptH0 ofno treatment difference • Stopping “for futility” or “abandoning a lost cause” • Saves time and effort when a study is unlikely to leadto a positive conclusion.

36. Two-Sided Test

37. Stochastic Curtailment Idea: • Terminate the trial for efficacy if there is high probability of rejecting the null, given the current data and assuming the null is true among future patients • Conversely, terminate the trial for futility if there is low probability of rejecting the null, given the current data and assuming the alternative is true among future patients

38. Conditional Power • At the interim analysis k, define pk(Δ) = PHA(Test will reject H0 | current data) • A high value of pk(0) suggests T will reject H0 • terminate the trial & reject H0ifpk(0) > ξ • terminate the trial & accept H0if 1-pk(Δ) > ξ’ (1-sided) • probabilities of error, type I  α/ ξ, type II  β / ξ’ Note: ξ and ξ’ 0.8

39. Conditional Power • Unconditional power for α=0.05 and β=0.1 at Δ=0.2 • Conditional power for a mid-trial analysis with an estimate of Δof 0.1 • probability of rejecting the null at the end of the trial has been reduced from 0.9 to 0.1

40. Conditional Power B(t) = Z(t)t1/2 = t

41. Conditional Power Slope = assumed treatment effect in future patients

42. Conditional Power Crosshatched area = conditional power

43. Predictive Power • Problem with the conditional power approach: it is computed assuming Δ not supported by the current data. • A solution: average across the values of Δ • “Predictive power” • π(Δ | data)is the posterior density • Termination against H0ifPk > ξetc. • What prior ?

44. Futility guidelines

45. Overruling futility boundaries

46. Adaptive Designs • Based on combining p-values from different analyses • Allow for flexible designs • sample size re-calculation • any changes to the design (including endpoint, test, etc!)

47. Adaptive Designs • Lehmacher and Wassmer (1999): At stage k, combine one-sided p-values p1,... ,pk L = k-1/2∑Φ-1(1-pk) • Use any group sequential design for L • Slight power loss as compared to a group-sequential plan • Flexibility as to design modifications: OK for control of type I error, BUT…

48. Potential concerns with adaptive designs • Major changes between cohorts make clinical interpretation difficult • If eligibility / endpoint changed, what is adequate label? • Temporal trends • Operational bias • Less efficient than group sequential for sample size adjustments • Modest gains (in general), high risks