generalized pairwise comparison on immuno- oncology clinical … oncology... · 2017. 11. 16. ·...
TRANSCRIPT
GeneralizedPairwiseComparisononImmuno-
Oncologyclinicaltrialdata:acasestudy
DrJulienPERON,PrDelphineMAUCORT-BOULCH,PrPascalROY,PrMarcBUYSENovember2017
DepartmentofBiosta>s>csHCL–LBBEUCBLDepartmentofMedicaloncologyHCL–LBBEUCBL
Casestudy
2
3
TheCA184-024trial
R
502metasta>cmelamoma
Placebo+dacarbazineIpilimumab+dacarbazine
252250
Robertetal.NEJM2011
4
OSresultsintheCA184-024trial
Pcb 252 160 89 64 44 37 26 7 0
Ipi 250 181 114 85 68 57 41 10 0
Outline
• Theprocedureofgeneralizedpairwisecomparisons
• Apa>ent-orientedmeasureoftreatmentbenefit
• Applica>ononimmuno-oncologytrials• Simula>onstudy• Illustra>ononanipilimumabtrial
5
Methods–Pairwisecomparisons
Let xi be the outcome of i thsubject in T (i = 1. … . n )
R
Control (C ) Treatment (T )
Let yj be the outcome of j thsubject in C (j = 1. … . m )
Yj Xi
favors T (favorable)
favors C (unfavorable)
pairwise comparison
Neutral or Uninformative6
BuyseM.statinmed2010
Methods–DefiniQonofthresholds
CouQnuousoutcome
7Buyse.statinmed2010
Pair Rating � > � Favorable
� < (� �) Unfavorable � � � ≤ � Neutral
or missing Uninformative
ConQnuousoutcome
Methods–Standardprocedureforpairwisescoring
innamed«netbenefit»
Anempiricaldistribu>onofcanbeobtainedbypermuta>on
8Buyse.statinmed2010
Δ =U = 1
m⋅n ijUj=1
m
∑i=1
n
∑
( )( )
otherwise 0
eunfavorabl is pair when the1
favorable is pair when the1
⎪⎪⎩
⎪⎪⎨
⎧
−
+
= Y j,X i
Y j,X i
U ij
Δ
Δ
9
SomenotaQons
10
�
Favorable Unfavorable Neutral
Favorable Uninforma>ve Uninforma>ve
Uninforma>ve Unfavorable Uninforma>ve
Uninforma>ve Uninforma>ve Uninforma>ve
Buyse M. Stat in med, 2010
ThestandardproceduretoincludeQme-to-event’outcome
11
0,5
1,0
SurvivalProbability
0,0
Time
Pa>enti:censoring
Treatmentgroup
Controlgroup
Pa>entj:event
ThestandardproceduretoincludeQme-to-eventoutcome
Gehan. Biometrika, 1965
BasedontheKaplan-Meieres>mateofthesurvivalfunc>on
𝕡[( 𝑥↓𝑖↑0 > 𝑦↓𝑗↑0 )�( 𝑥↓𝑖↑0 > 𝑥↓𝑖↑ )]= 𝑆 ↓𝑇𝑡𝑡 (𝑦↓𝑗 )/𝑆 ↓𝑇𝑡𝑡 ( 𝑥↓𝑖 ) = 0,5/0,8
Theextendedproceduretakingintoaccount‘non-informaQve’pairs
0,5
1,0
SurvivalProbability
0,0
Time
0,8
Péron J et al, SMMR 2016
Pa>enti:censoring
Pa>entj:event
Treatmentgroup
Controlgroup
13
𝕡[( 𝑥↓𝑖↑0 > 𝑦↓𝑗↑0 )�( 𝑥↓𝑖↑0 > 𝑥↓𝑖↑ ),( 𝑦↓𝑗↑0 > 𝑦↓𝑗↑ )]=−∑𝑡> 𝑦↓𝑗 ↑∞▒𝑆 ↓𝑇𝑡𝑡 (𝑡)/𝑆 ↓𝑇𝑡𝑡 (𝑥↓𝑖 )𝑆 ↓𝐶𝑡𝑟𝑙 (𝑦↓𝑗 ) ∙(𝑆 ↓𝐶𝑡𝑟𝑙 (𝑡↑+ )− 𝑆 ↓𝐶𝑡𝑟𝑙 (𝑡↑− ))
Efron, Berkeley Symp, 1967
0,5
1,0
0,0
Whenthees>ma>onofthesurvivalfunc>onisdiscon>nue:
SurvivalProbability
Time
Pa>enti:censoring
Treatmentgroup
Controlgroup
Pa>entj:censoring
Theextendedproceduretakingintoaccount‘non-informaQve’pairs
14
Theextendedproceduretakingintoaccount‘non-informaQve’pairs
benefitisthen:
• Reduc>onoftheBiasofinthepresenceofcensoredobserva>ons– Correc>onavailable
• Increasedpowerofthepermuta>ontestcomparedtostandardprocedure– Propor>onalhazardsandadministra>vecensoring<67%(BEfron,Stanford
Univ,1967)
– Latetreatmenteffect
15
Achievementsoftheextendedprocedure
(propor>onalhazards)
Péron J et al, SMMR 2016
Outline
• Theprocedureofgeneralizedpairwisecomparisons
• Apa>ent-orientedmeasureoftreatmentbenefit
• Applica>ononimmuno-oncologytrials• Simula>onstudy• Illustra>ononanipilimumabtrial
16
17
Probabilityforarandompa>entintheTreatmentgrouptohavea‘bederoutcome’thanarandompa>entintheControlgroup…
Δ=ℙ(𝑿>𝒀)−ℙ(𝑌>𝑋)
Thenetbenefit
Buyse M. Stat in med, 2010
Treatementgroup Controlgroup
18
Δ=ℙ(𝑋>𝑌)−ℙ(𝒀>𝑿)
Buyse M. Stat in med, 2010
Treatementgroup Controlgroup
…minustheoppositeprobability.
Thenetbenefit
19
Δ=ℙ(𝑋>𝑌)−ℙ(𝑌>𝑋)
ℙ(𝒀=𝑿)
Buyse M. Stat in med, 2010
Treatementgroup Controlgroup
Thenetbenefit
20
Thenetsurvivalbenefit
ProporQonalhazards
TreatmentgroupControlgroup
Time(months)
Netsu
rvivalben
efit
Survivalprobability
Péron et al, JAMA oncology, 2016
21
Propor>onalHazards
Delayedtreatmenteffect
TreatmentgroupControlgroup
TreatmentgroupControlgroup
Time(months)
Netsu
rvivalben
efit
Survivalprobability
Time(months)
Netsu
rvivalben
efit
Survivalprobability
Péron et al, JAMA oncology, 2016
Thenetsurvivalbenefit
22
Oppositehazards
Péron et al, JAMA oncology, 2016
Propor>onalHazards
TreatmentgroupControlgroup
Time(months)
Netsu
rvivalben
efit
Survivalprobability
TreatmentgroupControlgroup
Time(months)
Netsu
rvivalben
efit
Survivalprobability
Thenetsurvivalbenefit
Outline
• Theprocedureofgeneralizedpairwisecomparisons
• Apa>ent-orientedmeasureoftreatmentbenefit
• Applica>ononimmuno-oncologytrials• Simula>onstudy• Illustra>ononanipilimumabtrial
23
SimulaQonstudy-Design
• ObjecQve:Toassessthepoweroftestsbasedongeneralizedpairwisecomparisonsfordelayedtreatmenteffect
• Simula>onofM=1000datasetswithN=200pa>ents– One>me-to-eventoutcome
25
Scenario1:Propor>onalhazards
Scenario2:Latetreatmenteffect
SimulaQonstudy-Design
Survival
Time(months)
Survival
Time(months)
0 10 20 30 40 50
0.0
0.5
1.0
Time (months)
Haza
rd ra
tio
• Administra>vecensoringpropor>on– Uniformdistribu>on– Between0%and20%
• Foreachsimulateddataset– Es>ma>onofthenetsurvivalbenefitofatleastτmonths[0to42
months](extendedprocedure)– Testofthenullhypothesis(Permuta>ontest,Log-Ranktest)
26
SimulaQonstudy-Design
27
ProporQonalHazards-POWER
28
Delayedtreatmenteffect-POWER
Whenalong-termsurvivalbenefitisexpected
(an>cancerimmunetherapy)
Thenetsurvivalbenefitis:
– Arguablymorerelevantthantradi>onalmethodsèfocusonlongtermsurvivaldifferences
– Morepowerfulthantradi>onalmethod
29
ConclusionsofthesimulaQonstudy
Outline
• Theprocedureofgeneralizedpairwisecomparisons
• Apa>ent-orientedmeasureoftreatmentbenefit
• Applica>ononimmuno-oncologytrials• Simula>onstudy• Illustra>ononanipilimumabtrial
30
31
ThenetsurvivalbenefitintheCA184-024trial
R
502metasta>cmelamoma
Placebo+dacarbazineIpilimumab+dacarbazine
252250
Robertetal.NEJM2011
32
OSresultsintheCA184-024trial
Pcb 252 160 89 64 44 37 26 7 0
Ipi 250 181 114 85 68 57 41 10 0
33
OSresultsintheCA184-024trial
34
OSresultsintheCA184-024trial
Δ(12)=11.5%(95%CI=3.5%-19.4%;P=0.0045)
Δ(0)=12.5%(95%CI=2.1%-23.0%;P=0.018)
LogrankP=0.0054
35
PFSresultsintheCA184-024trial
Pcb 252 52 20 13 2 1 0 0 0
Ipi 250 70 40 25 6 2 0 0 0
36
PFSresultsintheCA184-024trial
37
PFSresultsintheCA184-024trial
Δ(12)=7.6%(95%CI=1.5%-13.8%;P=0.015)
Δ(0)=9.3%(95%CI=-1.0%-19.6%;P=0.076)
LogrankP=0.022
ApackageR• AvailableonCRAN(“BuyseTest”)• Availableongithub(“hdps://github.com/bozenne/BuyseTest”)
38
SobwareimplementaQon
Thenetbenefit– Isequivalenttostandardnon-parametrictestsinsimplecases
– IsmeaningfulandpaQent-relevant– Canfocusonlong-termsurvivaldifferences– AllowsmulQcriteriaanalysis– Mayhavebederpowerthanthelogranktest(e.g.fordelayedtreatmenteffect)
– IsOKwhenhazardsarenotproporQonals– Isavailable
39
Conclusions
Thank you
40
41
References
Buyse M. Reformulating the hazard ratio to enhance communication with clinical investigators. Clin Trials 5: 641-2, 2008.
Buyse M. Generalized pairwise comparisons for prioritized outcomes in the two-sample problem. Statist Med 29: 3245-57, 2010.
Péron J, Buyse M, Ozenne B, Roche L, Roy P. An extension of generalized pairwise
comparisons for prioritized outcomes in the presence of censoring. Statist Meth Med Res DOI: 10.1177/0962280216658320, 2017.
Péron J, Roy P, Ding K, Parulekar W, Roche L, Buyse M. Benejit-risk assessment of adding erlotinib to gemcitabine for the treatment of advanced pancreatic
cancer. Brit J Cancer 112: 971-976, 2015.
Péron J, Roy P, Ozenne B, Roche L, Buyse M. The net chance of a longer survival as a patient-oriented measure of benejit in randomized clinical trials. JAMA Oncology DOI: 10.1001/jamaoncol.2015. 6359, 2016.
Methods – Definition of priority
First priority outcome
Second priority outcome
Pair rating
Favorable NA Favorable Unfavorable NA Unfavorable
Neutral/Uninf Favorable Favorable Neutral/Uninf Unfavorable Unfavorable Neutral/Uninf Neutral/Uninf Neutral/Uninf
42 Buyse. stat in med 2010
Methods – Definition of priority
First priority outcome
Second priority outcome
Pair rating
Favorable NA Favorable Unfavorable NA Unfavorable
Neutral/Uninf Favorable Favorable Neutral/Uninf Unfavorable Unfavorable Neutral/Uninf Neutral/Uninf Neutral/Uninf
43 Buyse. stat in med 2010
Methods – Definition of priority
First priority outcome
Second priority outcome
Pair rating
Favorable NA Favorable Unfavorable NA Unfavorable
Neutral/Uninf Favorable Favorable Neutral/Uninf Unfavorable Unfavorable Neutral/Uninf Neutral/Uninf Neutral/Uninf
44 Buyse. stat in med 2010
Simulation study - Design
• Objective: To compare the standard and the extended procedures of generalized pairwise comparison
• Simulation of M = 1000 datasets of with N = 200 patients – One time-to-event outcome
– Threshold 𝜏 = 0 months
HR HR HR
46
• Survival time: exponential distributions
Scenario 1 : Proportional hazards
Scenario 2 : Late treatment effect
Scenario 3 : early treatment effect
Simulation study - Design
47
• Several treatment effect sizes
– Hazard ratio {0,5;0,7;1}
• Administrative censoring proportion – Uniform distribution – Between 0% and 70%
Simulation study - Design
48
• For each simulated dataset – Estimation of the net chance of a better outcome (standard and extended
procedure) – Test of the null hypothesis (Permutation test, Log-Rank test)
• Endpoints – Bias – Power – Type 1 error
Simulation study - Design
HR = 0,5
HR = 0,7
49
Scenario 1 – Proportional hazards
Péron, et al. SMMR 2016
HR = 0,5
HR = 0,7
50
Scenario 1 – Proportional hazards
Péron, et al. SMMR 2016
51
An explanation for this bias? 1,0
Sur
viva
l Pro
babi
lity
0,0
Time
C𝐞𝐧𝐬𝐨𝐫𝐢𝐧𝐠 𝒚↓𝒋 E𝐯𝐞𝐧𝐭 𝒙↓𝒊
Standard procedure: U𝐧𝐢𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐯𝐞 →𝑝↓𝑖𝑗 =0
U𝐧𝐢𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐯𝐞 𝐚𝐥𝐬𝐨→𝑝↓𝑖𝑗 =0
Treatment group
Control group
52
A correction for this bias
HR=0,5
Mean bias
Censoring rate
Péron, et al. SMMR 2016
HR = 0,5
HR = 0,7
53
Scenario 1 – Proportional hazards
Censoring rate
Péron, et al. SMMR 2016
54
Scenario 2 et 3 – Non Proportional hazards
Censoring rate Censoring rate
Pow
er
Early treatment effect Late treatment effect
Type 1 error rate ≈ 5%
Péron, et al. SMMR 2016