Generalized Pairwise Comparison on Immuno- Oncology clinical … Oncology... · 2017. 11. 16. ·...

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


14


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




16

17

Probabilityforarandompa>entintheTreatmentgrouptohavea‘bederoutcome’thanarandompa>entintheControlgroup…

Δ=ℙ(𝑿>𝒀)−ℙ(𝑌>𝑋)

Thenetbenefit


Treatementgroup Controlgroup

18

Δ=ℙ(𝑋>𝑌)−ℙ(𝒀>𝑿)



…minustheoppositeprobability.

Thenetbenefit

19

Δ=ℙ(𝑋>𝑌)−ℙ(𝑌>𝑋)

ℙ(𝒀=𝑿)



Thenetbenefit

20

Thenetsurvivalbenefit

ProporQonalhazards

TreatmentgroupControlgroup

Time(months)

Netsu

rvivalben

efit

Survivalprobability

Péron et al, JAMA oncology, 2016

21

Propor>onalHazards

Delayedtreatmenteffect



Time(months)

Netsu

rvivalben

efit

Survivalprobability

Time(months)

Netsu

rvivalben

efit

Survivalprobability



22

Oppositehazards


Propor>onalHazards


Time(months)

Netsu

rvivalben

efit

Survivalprobability


Time(months)

Netsu

rvivalben

efit

Survivalprobability


Outline




23

SimulaQonstudy-Design

•  ObjecQve:Toassessthepoweroftestsbasedongeneralizedpairwisecomparisonsfordelayedtreatmenteffect

•  Simula>onofM=1000datasetswithN=200pa>ents–  One>me-to-eventoutcome

25

Scenario1:Propor>onalhazards

Scenario2:Latetreatmenteffect


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


27

ProporQonalHazards-POWER

28

Delayedtreatmenteffect-POWER

Whenalong-termsurvivalbenefitisexpected

(an>cancerimmunetherapy)

Thenetsurvivalbenefitis:

–  Arguablymorerelevantthantradi>onalmethodsèfocusonlongtermsurvivaldifferences

–  Morepowerfulthantradi>onalmethod

29

ConclusionsofthesimulaQonstudy

Outline




30

31

ThenetsurvivalbenefitintheCA184-024trial

R

502metasta>cmelamoma

Placebo+dacarbazineIpilimumab+dacarbazine

252250

Robertetal.NEJM2011

32


Pcb 252 160 89 64 44 37 26 7 0

Ipi 250 181 114 85 68 57 41 10 0

33


34


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


37


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




Pair rating







Pair rating




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


47

•  Several treatment effect sizes

–  Hazard ratio {0,5;0,7;1}

•  Administrative censoring proportion –  Uniform distribution –  Between 0% and 70%


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


HR = 0,5

HR = 0,7

49

Scenario 1 – Proportional hazards

Péron, et al. SMMR 2016

HR = 0,5

HR = 0,7

50



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


HR = 0,5

HR = 0,7

53


Censoring rate


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%


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