eugm 2011 | jehl | group sequential designs with 2 time to event endpoints

Group sequential designs with two time-to-event endpoints

Valentine Jehl, Novartis Pharma AG, Switzerland Paris, 14-Oct-2011

3 | Group sequential designs with two time-to-event endpoints| Jehl V| 14-Oct-2011 | Business Use Only

Motivations

  In oncology, time-to-event type variables are the most commonly used endpoints for phase III trials  Ex. Progression free survival, Overall survival

 Objective of the phase III = proof of efficacy as soon as possible  Condideration of group sequential design with interim looks  Consideration of surrogate endpoints, if applicable

 Multiple tests performed  Multiplicity has to be taken into account

Definition

 Primary endpoint • should be the clinical measures that best characterize the

efficacy of the treatment, and used to judge the overall success of the study.

• should be clinically meaningful, and, ideally, fully characterize the treatment effect

 Secondary endpoint • may provide additional characterization of the treatment effect. •  if positive might be mentionned in the label


Handling multiplicity

 How to deal with more than one endpoints in a group sequential design (GSD)? • Hierachical procedure • Different spending functions • Simultaneous testing


 Stagewise hierarchical testing • Two-arm, two-stage design to demonstrate superiority • One primary endpoint P, one secondary endpoint S

-  Example from the respiratory therapeutic area: •  Primary endpoint P: change in area under curve of the forced expiratory volume

from 1 second of exhalation (FEV1) after 12 weeks of treatment •  Secondary endpoint S: trough FEV1

• Overall significance level α = 0.025 • One interim analysis (IA) after n1 = n/2 patients per group • Trial success = primary endpoint is significant:

-  Trial stops at interim when P is significant at interim, otherwise continues to final analysis

Hierarchical testing for primary and secondary endpoints in GSD - the “easier” case of non time-to-event endpoints


Hierarchical testing for primary and secondary endpoints in GSD - the “easier” case of non time-to-event endpoints

 Stagewise hierarchical testing: •  HS is tested only if HP is rejected

 Primary hypothesis tested with O’Brien-Fleming boundaries •  Nominal rejection level for HP : α1 = 0.0026 , α2 = 0.0240 if α = 0.025

 Secondary hypothesis is tested only once; at what level? • At level α ? ..... or at same level as primary? ... or something else?


 Naive idea: Since S is tested only once and only when P was significant, S can be tested at full level α

This is not true!

 Naive strategy leads to type I error rate inflation •  (Hung, Wang and O‘Neill (2007))

Inflation of type I error rate for HS


 Maximum type I error for conditional testing HS at level α is

• For n1/n = 0.5 and α = 0.025, maximum type I error is 0.041.

Significance level for HS must be adjusted to keep a given significance level αS for the secondary variable

 For conditional testing HS at levels α*1 = α*2 = 0.0147 > α/2, the maximum type I error attained is αS = 0.025 • α*1 = α*2 are the „Pocock“-boundaries

( )2 1 1 11 , ; /z z n nα α− −− Φ

Actually, it can be shown that …


  Consequences for the stagewise hierarchical testing problem:

•  If FWER control is desired, a group-sequential approach must be used for both HP and HS (each at level α)

•  The two approaches do not have to be the same. •  Regarding design, it does not matter if the trial is stopped at

IA when both HP and HS are rejected or if just HP is rejected

Stagewise hierarchical testing


  Is there a “best” choice of spending function for HS given a spending function for HP?

  Not real “best“ choice however : •  If correlation between P and S is 1 (i.e. expected values are the same),

using the same spending function for P and S is always better.

•  In realistic scenarios, study powered for primary endpoint with 80-90%, some correlation between primary and secondary Pocock is a good choice for S.

Stagewise hierarchical testing


  S tested only if and at the point in time when P is significant.

  Testing S at full level α does not keep the FWER.

  For FWER control, set up a group-sequential-approach each for P and S.

  Spending functions don‘t have to be the same.

  If study stops when P is significant: Usually advantageous to plan for more aggressive stopping rules for S than for P (e.g. OBF for P, Pocock for S).

  More than one interim: approach is equally valid

Do the same principles apply to time-to-events analysis ?

Summary: stagewise hierarchical testing


An important example for oncology:

 Primary endpoint: disease related time-to-event endpoint •  ex: progression-free survival (PFS) could also be Time to progression (TTP) •  correlated with OS but exact correlation unknown.

 Overall survival (OS) as the ‘key secondary’ endpoint, for which a control of the type I error rate is also required.

 Hierarchical testing procedure for OS consistent with seeking inclusion of OS results in the drug label

Two endpoints: PFS and OS


 Depending on context: • OS primary endpoint and PFS secondary endpoint • Both co-primary endpoints.

 Event-driven interim looks: two cases 1. Either OS (or PFS) drives interim looks

e.g. interim after n1 of a total n OS events, PFS just „carried along“ → requires estimation of PFS information fractions

2. Event-driven trials for PFS and OS

Two endpoints: PFS and OS


 Example : OS only driver for the trial • A total number of OS is fixed, # of PFS events is „left open“ •  IA after 50% of planned OS events • At design stage, rough estimate of # PFS events at interim and at

final (knowing that these are not precise) • At interim, a certain α spend for PFS based on #(interim PFS

events)/#(planned finalPFS events) • At the final, critical value u2 recalculated based on # PFS events

actually observed at the final analysis and at interim such as 1-PH0(t1<u1,t2<u2)=α.

• Could reveal that the fraction spend at interim was inappropriate •  u2 ↓ if more events than anticipated are observed at interim !

PFS and OS: OS event-driven trials


PFS: one final analysis only OS: i) interim OS analysis at the time of the final PFS analysis ii) final OS analysis after additional follow-up

Final # deaths not expected to be observed at this time point

Required # deaths for final OS analysis observed after additional follow-up

Trials driven by both event types - simple case


Trials driven by both event types - simple case


Example: Study RAD001C2324 (RADIANT-3)

 Phase III study of RAD001 & BSC vs. BSC & Placebo in patients with advanced pancreatic neuroendocrine tumor (pNET)

 Primary endpoint: PFS •  targeted number of PFS events = 282, •  total number of patients to be randomized = 392 (1:1 randomization)

 OS as key secondary endpoint, • a total of 250 deaths would allow for at least 80% power to demonstrate

a 30% risk reduction

 Originally IA planned for PFS, but canceled (amendment) due to fast recruitment (expected time between IA and final analysis 4 months only) ⇒ one final PFS analysis only, IA for OS at final PFS analysis, ⇒ Final OS analysis planned with 250 OS events


First interim at s1 (Final analysis)

Final analysis at s2 (Final OS analysis)

Information fraction (%) 47.2 100 Number of events 118 250 Patients accrued 392 392

Boundaries Efficacy ( reject H0) Z-scale 3.0679 1.9661 p-scale 0.001078 0.024644

Cumulative Stopping probability (%)2 Under H0 for activity2 0.10% 2.39% Under Ha for activity2 12.57% 80.09%

2 results obtained by simulations. Probabilities are reported as if OS was tested alone, regardless of the testing strategy with . The true probabilities should take into account the probability of at each look.

At OS interim analysis, information fraction will be computed as the ratio of the number of events actually observed relative to the number targeted for the final analysis. The critical value for the final analysis will be calculated using the exact number of observed events at the final cut-off date, and considering the α-levels spent at interim analysis (analyses), in order to achieve a cumulative type I error smaller than 2.5% for one-sided test.

Example: RADIANT-3 (cont‘ed) Statistical considerations in statistical analysis plan

estimated

101 OS observed (40.4% of targeted) => boundary z=3.33846, p=0.000421


PFS: interim and final analysis OS: i) 2 interim OS analyses at interim/final PFS analysis ii) final OS analysis after additional follow-up

s1 s2* s3

Analysis determined before study start: •  IA 1 after s1 PFS events •  IA 2 after s2* PFS events •  IA 3 after s3 OS events

Trials driven by both event types - more complex case


 PFS as primary and OS as key secondary



 Calculation of critical values / α spent: •  Interim 1: Critical value cOS,1 such that PH0 (tOS,1> cOS,1) = αOS,1, αOS,1 from selected α-spending approach for the observed OS info fraction (#OS events in stage 1)/(total # OS events planned)

•  Interim 2: Critical value cOS,2 such that PH0 (tOS,1≤ cOS,1, tOS,2> cOS,2) = αOS,2 -αOS,1, αOS,2 from selected α-spending approach for the observed OS info fraction (OS events in stage 2)/s3, using αOS,1 „already spent“ and observed information fraction (OS events in stage 1)/(OS events in stage 1 and 2)

• Final analysis: Critical value cOS,3 such that PH0 (tOS,1≤ cOS,1, tOS,2 ≤ cOS,2, tOS,3> cOS,3) = α-αOS,2

 Easy to do with EAST



 Adequate handling of multiplicity in group-sequential time-to-event trials has many aspects: •  Importance of endpoints: (co-)primary, secondary? A mix of all? • Study conduct:

-  stop as soon as primary endpoint is significant? -  Event-driven by just one endpoint?

 General strategy: • Set up an appropriate GS-approach per endpoint. • Select an appropriate multiplicity-adjustment method • Merge the two. •  Investigate operation-characteristics.

Summary


Thank you


For providing this material • Ekkehard Glimm • Norbert Hollaender

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prob

(rej

S)

gamma

ρ = 0.2 ρ = 0.5 ρ = 0.8

OBF Pocock

δP=4, δS=3

δP=3, δS=2

Power comparisons: OBF type spending function for HP, different spending functions for HS

... but we still know the correlation between stage 1 and 2   To each of the hypotheses Hj, j = 1,…,h, a significance level αj is

assigned such that •  and define group sequential testing strategies with spending functions ai(y)

separately for each of the hypotheses at level αj .

1

hjj

α α=

=∑

t 0 1 2 3

H1 H2 Hh

α1 α2 αh

Bonferroni on endpoints, then GS. Note: First calculating the GS boundaries for α, then „bonferronizing“ them does not keep the multiple type I error rate in general.

Several primary endpoints: correlation unknown

eugm 2011 | jehl | group sequential designs with 2 time to event endpoints

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