Non-proportional Hazard in Cancer Immunotherapy
Aijing Zhang, Ph.D DISS, September 8th 2017
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OUTLINE
• The Presence of non-proportional hazard (NPH) in Cancer Immunotherapy (CIT)
• Motivation and Objectives of the Simulation Study
• Simulation Results and Discussions
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NPH Observed in CIT
Rittmeyer A et al, Lancert 2017 Jan 21; 389 (10066):255-265
Borghaei H et al. NEMJ 2015 October 22;373:1627-39
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Overall Survival Curves for NPH
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Time I I I I I I
I I I
Surv
ival P
robabili
ty
Proportional hazards: Target HR
Control arm CIT arm
Overall Survival Curves for NPH
Time I I I I I I
I I I
Surv
ival P
robabili
ty
Late separation
HR=1 Target HR
Observed: “average” HR
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Time I I I I I I
I I I
Surv
ival P
robabili
ty
Proportional hazards: Target HR
Control arm CIT arm
Overall Survival Curves for NPH
Time I I I I I I
I I I
Surv
ival P
robabili
ty
Observed: “average” HR
“Diluted” HR
“Cross-over” in
control arm
≈Target HR
Time I I I I I I
I I I
Surv
ival P
robabili
ty
Late separation
HR=1 Target HR
Observed: “average” HR
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Time I I I I I I
I I I
Surv
ival P
robabili
ty
Proportional hazards: Target HR
Control arm CIT arm
Overall Survival Curves for NPH
Time I I I I I I
I I I
Surv
ival P
robabili
ty
Observed: “average” HR
“Diluted” HR
“Cross-over” in
control arm
≈Target HR
Time I I I I I I
I I I
Surv
ival P
robabili
ty
Late separation
HR=1 Target HR
Observed: “average” HR
Time I I I I I I
I I I
Surv
ival P
robabili
ty
HR=1 ≈Target HR “Diluted” HR
Observed: “average” HR
Late separation “Cross-over” in
control arm
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Time I I I I I I
I I I
Surv
ival P
robabili
ty
Proportional hazards: Target HR
Control arm CIT arm
Motivation and Objectives
• In study design, study power/sample size is often calculated under PH assumption
• Use simulation to assess the impact on study power when OS is the primary endpoint with NPH coming from two sources: − Delayed treatment effect for the active treatment arm
− Dilution effect due to subsequent therapy in the control arm
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Patient-Level Survival Hazard due to Delayed Treatment and Dilution Effects
Survival Hazard
Progression
Dilution effect assumptions: • Probability that patients on control arm
would switch to new treatment after progression
• Hazard for control patients after switch
Control Arm
CIT Arm
Delayed treatment effect assumptions: • Hazard for patients on CIT arm
for the first x months
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Overall Survival Curve with Delayed Treatment and Dilution Effects
Time
I I I I I I
I I I
Overa
ll S
urv
ial
HR=1 ≈Target HR “Diluted” HR
Observed: “average” HR
Late separation
“Cross-over” in
control arm
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Control arm CIT arm
Simulation Settings: Trial Design Assumptions
• Median OS in control arm = 10 mon
• Target HR=0.65
• Sample size N =350 (two arms 1:1 randomized), analysis at 65% event patient ratio (i.e., 227 events)
• 90% power under PH assumption
• Type 1 error = 0.05, log-rank test, no interim analysis
• With the additional ramp-up accrual and dropout assumptions: accrual period is 25 months, analysis is done at 34 months
Simulation Settings: NPH Assumptions
• Delayed Treatment Effect − 1, 2 or 3 months
− before separation HR=1
• Dilution effect due to subsequent therapy − Timing of switch: mPFS in control arm
− 20, or 40% of the patients in control arm received subsequent therapy right after PD
− HR between study treatment and next line of therapy = 1 or 0.8
NPH Effect on Study Power – Simulation Results
Scenarios NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 90% - 0.654
Delayed Tx Effect
1 mon - - 82% -8% 0.682
2 mon - - 74% -16% 0.711
3 mon - - 62% -28% 0.743
Switch to subsequent
therapy
- 20% 1 77% -13% 0.704
- 40% 1 56% -34% 0.759
- 20% 0.8 84% -6% 0.677
- 40% 0.8 77% -13% 0.703
Combined
1 mon 20% 0.8 76% -14% 0.708
2 mon 20% 0.8 64% -26% 0.735
3 mon 20% 0.8 52% -38% 0.765
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results
Scenarios NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 90% - 0.654
Delayed Tx Effect
1 mon - - 82% -8% 0.682
2 mon - - 74% -16% 0.711
3 mon - - 62% -28% 0.743
Switch to subsequent
therapy
- 20% 1 77% -13% 0.704
- 40% 1 56% -34% 0.759
- 20% 0.8 84% -6% 0.677
- 40% 0.8 77% -13% 0.703
Combined
1 mon 20% 0.8 76% -14% 0.708
2 mon 20% 0.8 64% -26% 0.735
3 mon 20% 0.8 52% -38% 0.765
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results
Scenarios NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 90% - 0.654
Delayed Tx Effect
1 mon - - 82% -8% 0.682
2 mon - - 74% -16% 0.711
3 mon - - 62% -28% 0.743
Switch to subsequent
therapy
- 20% 1 77% -13% 0.704
- 40% 1 56% -34% 0.759
- 20% 0.8 84% -6% 0.677
- 40% 0.8 77% -13% 0.703
Combined
1 mon 20% 0.8 76% -14% 0.708
2 mon 20% 0.8 64% -26% 0.735
3 mon 20% 0.8 52% -38% 0.765
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results
Scenarios NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 90% - 0.654
Delayed Tx Effect
1 mon - - 82% -8% 0.682
2 mon - - 74% -16% 0.711
3 mon - - 62% -28% 0.743
Switch to subsequent
therapy
- 20% 1 77% -13% 0.704
- 40% 1 56% -34% 0.759
- 20% 0.8 84% -6% 0.677
- 40% 0.8 77% -13% 0.703
Combined
1 mon 20% 0.8 76% -14% 0.708
2 mon 20% 0.8 64% -26% 0.735
3 mon 20% 0.8 52% -38% 0.765
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results
Scenarios NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 90% - 0.654
Delayed Tx Effect
1 mon - - 82% -8% 0.682
2 mon - - 74% -16% 0.711
3 mon - - 62% -28% 0.743
Switch to subsequent
therapy
- 20% 1 77% -13% 0.704
- 40% 1 56% -34% 0.759
- 20% 0.8 84% -6% 0.677
- 40% 0.8 77% -13% 0.703
Combined
1 mon 20% 0.8 76% -14% 0.708
2 mon 20% 0.8 64% -26% 0.735
3 mon 20% 0.8 52% -38% 0.765
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results (cont’d)
Scenarios Target HR Event
Number
NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control
Arm
Post-”Switch”
Hazard Ratio
PH
0.65 227 - - - 90% - 0.654
0.55 120 - - - 90% - 0.554
0.75 505 - - - 90% - 0.749
Delayed Tx Effect
0.65 227 3 mon - - 62% -28% 0.743
0.55 120 3 mon - - 63% -27% 0.653
0.75 505 3 mon - - 64% -26% 0.812
How would the target HR after separation affect the study power?
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power – Simulation Results (cont’d)
Scenarios mPFS NPH Effects
Power Δ Power Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH 5 mon - - - 90% - 0.654
Switch to subsequent
therapy
4 mon - 40% 0.8 76.2% -13.8% 0.698
5 mon - 40% 0.8 77.4% -12.6% 0.703
6 mon - 40% 0.8 77.3% -12.7% 0.702
How would the control mPFS (timing of switch) affect the study power?
Simulation runs: 10,000 PH: proportional hazard; Tx: treatment; HR: hazard ratio
NPH Effect on Study Power
• Delayed treatment effect − The power decreases as the curve separation occurs later; the relationship is not linear
− The power decreases more dramatically as the delay increases
− The power decrease is not affected much by the magnitude of the HR after separation
• Switch to subsequent therapy − The power decreases as the proportion of subsequent therapy use increases; the relationship
is not linear
− The power decreases more dramatically as more patients initiated subsequent therapy
− The power decreases less dramatically when the subsequent therapy is less efficacious
− The power decrease is not affected much by the initiation time of subsequent therapy
• Combined impact on power is not simple addition of individual effects
Length of Followup – Simulation Results NPH Effects
Analysis Timing (mon from FPI) Power Δ Power
Median HR Observed
Delayed Tx Effect
% ”Switch” in Control Arm
Post-”Switch” Hazard Ratio
PH - - - 34 90% -- 0.654
Delayed Tx Effect
2 mon - - 34 74% -16% 0.711
37 79% -11% 0.709
41 81% -9% 0.705
Combined
2 mon 20% 0.8 34 65% -25% 0.734
25% 37 67% -23% 0.742
30% 41 67% -23% 0.745
Length of Followup
• Analysis timing is determined when the pre-specified number of events are reached
• When there is delayed treatment effect, the power increases with longer follow up
• Increase FU time helps, however, with the cost of prolonged analysis timing
• In addition, when there is also dilution effect due to subsequent therapy, the length of FU need to be balanced considering NPH impact from both sources
NPH– Design Considerations
• When using the common practice of calculating the sample size and power under PH, assess the impact of potential NPH using simulation study considering difference types of NPH relevant to the study
• If there is evidence of strong NPH impact, points to be considered: • Assumption of treatment effect: using an “overall HR”, a weighted average of the
piecewise HR for sample size/power calculation
• Analyses: e.g. weighted log-rank test
• Endpoints: e.g. milestone OS
• Pre-specify the planned analyses method up front in the protocol and analysis plan and consult the HAs
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Acknowledgement
• Zhengrong Li
• Yijing Shen
• Yasuo Sugitani
• Ray Lin
• Dominik Heinzmann
• Almut Mecke
• Jing Yi
Doing now what patients need next
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