Analysing Survival Endpoints in Randomized Clinical Trials using Generalized Pairwise Comparisons

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1 Analysing Survival Endpoints in Randomized Clinical Trials using Generalized Pairwise Comparisons Dr Julien PERON October 2016 Department of Biostatistics HCL LBBE UCBL Department of Medical oncology HCL LBBE UCBL

2 Outline The standard procedure of generalized pairwise comparisons An extension for right-censored data A patient-oriented measure of treatment benefit Benefit-risk balance NCIC PA.3 trial => erlotinib in pancreatic cancer 2

3 Outline The standard procedure of generalized pairwise comparisons NCIC PA.3 trial => erlotinib in pancreatic cancer 3

4 Methods Pairwise comparisons R Treatment (T ) Let x i be the outcome of i th subject in T (i = 1.. n ) Control (C ) Let y j be the outcome of j th subject in C (j = 1.. m ) X i pairwise comparison Y j favors T (favorable) favors C (unfavorable) Neutral or Uninformative Buyse M. stat in med

5 Methods Definition of thresholds Coutinuous outcome Pair x i y j > x i y j < ( ) x i y j x i or y j missing Rating Favorable Unfavorable Neutral Uninformative Buyse. stat in med

6 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 Buyse. stat in med

7 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 Buyse. stat in med

8 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 Buyse. stat in med

9 Methods Standard procedure for pairwise scoring U ij 1when the pair 1when the pair 0 otherwise X i,y j, X i Y j is favorable is unfavorable U 1 m n n m i 1 j 1 U ij Δ in named «net chance of a better outcome» Buyse. stat in med

10 Some notations x i 0 and y j 0 : time-to-event x i and y j : time-to-observation Event indicator : Survival function: δ i = 1 if x i = x i 0 0 if x i < x i 0 ε j = 1 if y j = y j 0 0 if y j < y j 0 in group T in group C S Ttt t = P x i 0 t and S Ctrl t = P y j 0 t 10

11 The standard procedure to include time-toevent outcome (δ i, ε j ) x i y j τ x i y j τ x i y j < τ (1, 1) Favorable Unfavorable Neutral (0, 1) Favorable Uninformative Uninformative (1, 0) Uninformative Unfavorable Uninformative (0, 0) Uninformative Uninformative Uninformative Buyse M. Stat in med,

12 Survival Probability The standard procedure to include time-to-event outcome 1,0 Patient i : censoring 0,5 Treatment group Control group Patient j : event 0,0 Time Gehan. Biometrika,

13 Outline An extension for right-censored data NCIC PA.3 trial => erlotinib in pancreatic cancer 13

14 Survival Probability The extended procedure taking into account non-informative pairs Based on the Kaplan-Meier estimate of the survival function p ( x i 0 > y j 0 ) x i 0 > x i = S Ttt y j = 0,5 S Ttt (x i ) 0,8 1,0 0,8 Patient i : censoring 0,5 Treatment group Control group Patient j : event 0,0 Time Péron J et al, SMMR 2016

15 Survival Probability The extended procedure taking into account non-informative pairs When the estimation of the survival function is discontinue : 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 1,0 Patient i : censoring 0,5 Treatment group Control group Patient j : censoring 0,0 Time Efron, Berkeley Symp,

16 The extended procedure taking into account non-informative pairs For pairs that can not be decidely classified because of censoring, we compute: P x i 0 > y j 0 + τ, et P y j 0 > x i 0 + τ, et P x i 0 y j 0 < τ The pairwise score is: s ij = P x i 0 > y j 0 + τ P y j 0 > x i 0 + τ The net chance of a better outcome is then: = 1 m n n m i=1 j=1 The pairwise weight the analysis of an outcome of lower priority is: ω ij = P x i 0 y j 0 < τ s ij 16

17 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

18 Simulation study - Design Survival time: exponential distributions Scenario 1 : Proportional hazards Scenario 2 : Late treatment effect Scenario 3 : early treatment effect HR HR HR 18

19 Simulation study - Design Several treatment effect sizes Hazard ratio 0,5; 0,7; 1 Administrative censoring proportion Uniform distribution Between 0% and 70% 19

20 Simulation study - Design 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 20

21 Scenario 1 Proportionnal hazards HR = 0,5 HR = 0,7 Péron, et al. SMMR

22 Scenario 1 Proportionnal hazards HR = 0,5 HR = 0,7 Péron, et al. SMMR

23 Survival Probability 1,0 An explanation for this bias? Treatment group Control group Censoring y j Event x i 0,0 Time Standard procedure: Uninformative p ij = 0 Extended procedure: P x i 0 >yj 0 +τ = 1 S C x i τ S C (y j ) P y j 0 >x i 0 +τ = S C x i +τ S C (y j ) Uninformative also p ij = 0 23

24 A correction for this bias f m : Proportion of informative pairs for the trial m(m = 1,, M) corr m = m f m : corrected net chance of a better outcome HR=0,5 Mean bias Censoring rate Bias = E Péron, et al. SMMR

25 Scenario 1 Proportional hazards HR = 0,5 HR = 0,7 Censoring rate Péron, et al. SMMR

26 Power Scenario 2 et 3 Non Proportional hazards Early treatment effect Late treatment effect Censoring rate Censoring rate Type 1 error rate 5% Péron, et al. SMMR

27 Conclusions of the simulation study Bias in the estimation of Δ Less important Correction available when only one endpoint Power of the permutation test extended procedure > standard procedure Exponential distribution Proportional hazards and administrative censoring < 67% (B Efron, Stanford Univ, 1967) Late treatment effect 27

28 Outline A patient-oriented measure of treatment benefit NCIC PA.3 trial => erlotinib in pancreatic cancer 28

29 The net chance of a better outcome Probability for a random patient in the Treatment group to have a better outcome than a random patient in the Control group Treatement group Control group Δ = P X > Y ) Buyse M. Stat in med,

30 The net chance of a better outcome minus the opposite probability. Treatement group Control group Δ = P X > Y P(Y > X) Buyse M. Stat in med,

31 The net chance of a better outcome Treatement group P(Y = X) Control group Buyse M. Stat in med,

32 Survival probability Net chance of a longer survival The net chance of a longer survival Proportional hazards Treatment group Control group Time (months) Péron et al, JAMA oncology,

33 Survival probability Net chance of a longer survival Survival probability Net chance of a longer survival The net chance of a longer survival Treatment group Control group Proportional Hazards Time (months) Treatment group Control group Delayed treatment effect Time (months) Péron et al, JAMA oncology,

34 Survival probability Net chance of a longer survival Survival probability Net chance of a longer survival The net chance of a longer survival Treatment group Control group Proportional Hazards Time (months) Treatment group Control group Opposite hazards Time (months) Péron et al, JAMA oncology,

35 Simulation study - Design Objective: To assess the power of tests based on generalized pairwise comparisons for delayed treatment effect Simulation of M = 1000 datasets of with N = 200 patients One time-to-event outcome

36 Scenario 1 : Proportional hazards Simulation study - Design Scenario 2 : Late treatment effect Survival Survival Time (months) Time (months) 36

37 Simulation study - Design Administrative censoring proportion Uniform distribution Between 0% and 40% For each simulated dataset Estimation of the net chance of a better outcome (extended procedure) with threshold τ 0 to 20 months Test of the null hypothesis (Permutation test, Log-Rank test) 37

38 Delayed treatment effect - POWER 38

39 Proportional Hazards - POWER 39

40 Conclusions When a long-term survival benefit is expected (anticancer immune therapy) The net chance of a longer survival is: Arguably more relevant than traditional methods More powerful than traditional method 40

41 Outline Benefit-risk balance NCIC PA.3 trial => erlotinib in pancreatic cancer 41

42 The benefit-risk balance in the PA.3 trial 569 advanced pancreatic cancer R Gemcitabine + erlotinib Gemcitabine + placebo Moore et al. JCO

43 The benefit-risk balance in the PA.3 trial 43

44 The benefit-risk balance in the PA.3 trial Worst grade related AE Erlotinib group (n=282) Placebo group (n=280) Grade 1 48 (17%) 69 (24.6%) Grade (41.8%) 89 (31.8%) Grade 3 72 (25.5%) 47 (16.8%) Grade 4 11 (3.9%) 6 (2.1%) Grade 5 4 (1.4%) 3 (1.1%) 44

45 The benefit-risk balance in the PA.3 trial Worst grade related AE Erlotinib group (n=282) Placebo group (n=280) Grade 1 48 (17%) 69 (24.6%) Grade (41.8%) 89 (31.8%) 29,4% 18,9% Grade 3 72 (25.5%) 47 (16.8%) Grade 4 11 (3.9%) 6 (2.1%) Grade 5 4 (1.4%) 3 (1.1%) 45

46 Benefit-risk balance Extended procedure Priority Erlotinib > Placebo Placebo > Erlotinib [erlotinib] 1 : OS (Threshold = 2 months) 40.3 % 34.5 % 5.8 % 2 : Worst related AE grade 6.8 % 12.4 % -5.6 % Global 47.1 % 46.9 % 0.2 % (P=.96) Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

47 Benefit-risk balance Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

48 Software implementation A package R corresponding to the standard procedure and to the extended procedure Available on CRAN ( BuyseTest ) Available on github ( ) 48

49 Conclusions The net chance of a better outcome Is flexible Is meaningful Allows multicriteria analysis Can focus on long-term survival differences Is OK when hazards are not proportionals Is available 49

50 Thank you 50

51 Scénario 1 Mean squared error HR=0,5 Mean squared error Mean squared error = E 2 51

52 Methods Pairwise comparisons R Treatment (T ) Let x i be the outcome of i th subject in T (i = 1.. n ) Control (C ) Let y j be the outcome of j th subject in C (j = 1.. m ) X i pairwise comparison Y j favors T (favorable) favors C (unfavorable) Neutral or Uninformative 52 Buyse M. stat in med 2010

53 Methods Definition of thresholds Coutinuous outcome Pair x i y j > x i y j < ( ) x i y j x i or y j missing Rating Favorable Unfavorable Neutral Uninformative Buyse. stat in med

54 Methods Definition of thresholds Coutinuous outcome Pair x i y j > x i y j < ( ) x i y j x i or y j missing Rating Favorable Unfavorable Neutral Uninformative Buyse. stat in med

55 Methods Definition of priority First priority outcome Second priority outcome Pair rating Favorable NA Favorable Unfavorable NA Unfavorable Uninformative Favorable Favorable Uninformative Unfavorable Unfavorable Uninformative Uninformative Uninformative Buyse. stat in med

56 Methods Definition of priority First priority outcome Second priority outcome Pair rating Favorable NA Favorable Unfavorable NA Unfavorable Uninformative Favorable Favorable Uninformative Unfavorable Unfavorable Uninformative Uninformative Uninformative Buyse. stat in med

57 Methods Definition of priority First priority outcome Second priority outcome Pair rating Favorable NA Favorable Unfavorable NA Unfavorable Uninformative Favorable Favorable Uninformative Unfavorable Unfavorable Uninformative Uninformative Uninformative Buyse. stat in med

58 Méthodes Standard procedure for pairwise scoring 1when the pair U ij 1when the pair 0 otherwise X i,y j, X i Y j is favorable is unfavorable U 1 m n n m i 1 j 1 U ij Δ in named «chance of a better outcome» Buyse. stat in med

59 Survival Probability The extended procedure taking into account non-informative pairs Based on the Kaplan-Meier estimate of the survival function 1,0 0,8 p ( x i 0 > y j 0 ) x i 0 > x i = Patient i : censoring t>y j t y j ε j =1 S T t ds C t S T x i S C y j 0,5 Treatment group Control group Patient j : censoring 0,0 Time Péron J et al, SMMR 2016

60 Survival Probability The extended procedure taking into account non-informative pairs When the estimation of the survival function is discontinue : 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 1,0 Patient i : censoring 0,5 Treatment group Control group Patient j : censoring 0,0 Time Efron, Berkeley Symp,

61 Extension prenant en compte les temps jusqu à censure (δ i, ε j ) x i y j > τ x i y j < τ x i y j < τ (1, 1) (0, 1) 1 S T y j + τ + S T y j τ S T (x i ) 1 S T y j + τ S T x i (1, 0) 1 S C x i + τ + S C x i τ S C (y j ) -1 S C x i + τ S C y j (0, 0) 1 S C x i τ + S C x i + τ S C y j t>x i τ t y j ε j =1 t>x i +τ t y j ε j =1 S T t + τ S T x i S C y j S T t τ S T x i S C y j ds C ds C t t t>y j t y j ε j =1 S T t + τ + S T t τ S T x i S C y j ds C t 1 t>y j t y j ε j =1 S C t>x i +τ t y j ε j =1 S C S T t + τ S T x i S C y j ds C t S T t τ S T x i S C y j x i + τ y j ds C t Valeurs du score attribué à chaque paire en fonction d un seuil τ représentant la différence minimale cliniquement significative 61

62 Sensitivity analysis proportion of pairs (%) Priority Threshold Erlotinib > Placebo > erlotinib Placebo Erlotinib 1 : OS 6 months : PFS 6 months : Worst related AE grade 3 grades : OS 3 months : PFS 3 months : Worst related AE grade 2 grades : OS 0 months : PFS 0 months : Worst related AE grade 1 grade Overall (P=.82) 62

63 Survival Probability Hypothesis of the correction 1,0 Treatment group Control group Censoring y j Event x i 0,0 Temps 63

64 With the standard procedure proportion of pairs (%) Priority Erlotinib > Placebo Placebo > Erlotinib erlotinib 1 : OS (Threshold = 2 months) : Worst related AE grade Overall (P=.51) Main analysis of the benefit-risk balance of the erlotinib and gemcitabine combination Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

65 Sensitivity analysis Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

66 Benefit-risk balance Standard procedure Priority Erlotinib > Placebo Placebo > Erlotinib [erlotinib] 1 : OS (Threshold = 2 months) 37.0 % 32.3 % 4.7 % 2 : Worst related AE grade 7.5 % 15.7 % -8.3 % Global 44.5 % 48.1 % -3.6% (P=.51) Extended procedure Priority Erlotinib > Placebo Placebo > Erlotinib [erlotinib] 1 : OS (Threshold = 2 months) 40.3 % 34.5 % 5.8 % 2 : Worst related AE grade 6.8 % 12.4 % -5.6 % Global 47.1 % 46.9 % 0.2 % (P=.96) Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

67 Benefit-risk balance Standard procedure Extended procedure Péron J. Roy P. Ding K. Parulekar WR. Roche L and Buyse M. BJC

68 Benefit-risk balance PRODIGE 4 trial Priority FOLFIRINOX > Gemcitabine > [FOLFIRINOX] Gemcitabine FOLFIRINOX 1 : OS (Threshold = 2 months) 43.0% 21.7% 21.3% 2 : Worst related AE grade 8.2% 15.4% -7.2% Global 51.2% 37.1% 14.0% (P=0.029) 68

69 Benefit-risk balance PRODIGE 4 trial Priority FOLFIRINOX > Gemcitabine > [FOLFIRINOX] Gemcitabine FOLFIRINOX 1 : OS (Threshold = 2 months) 43.0% 21.7% 21.3% 2 : Worst related AE grade 8.2% 15.4% -7.2% Global 51.2% 37.1% 14.0% (P=0.029) NCIC PA-3 trial Priority Erlotinib > Placebo Placebo > Erlotinib [erlotinib] 1 : OS (Threshold = 2 months) 37.0 % 32.3 % 4.7 % 2 : Worst related AE grade 7.5 % 15.7 % -8.3 % Global 44.5 % 48.1 % -3.6% (P=.51) 69

70 NCIC PA-3 trial 70