1. Sample Size Determination Under Non-Proportional Hazards
Zhaowei Hua
Takeda Pharmaceuticals Inc.
Miao Yang
Oregon State University
Saran Vardhanabhuti
30JULY2018

2. Routine Event Size Determination
Assume proportional hazards
Log-rank test is the most powerful test under proportional hazards
Power depends on the event size D
Peto and Peto, JRSS-A, 1972; 135(2):
Lakatos, Biometrics, 1988; 44:
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3. Empirical Power under Proportional Hazards
331 events, 90% power, HR=0.7 More patients with shorter study duration = fewer patients with longer study duration
Number of Patients
Number of Events
Number of Patients
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4. Real Examples: Non-proportional Hazards
Delayed separation, crossing curve, and diminishing effect could lead to power loss
Long-term survivors prolong study duration if not accommodated in design
Ferris, et al. N Engl J Med 2016;375:
Delayed separation
at ~4 months
Long-term
survivors
CheckMate 141
IPASS: Cross Curve
Sunitinib: RCC
Diminishing
Motzer, et al. J Clin Oncol 27:
Mok, et al. N Engl J Med 2009;361:947-57
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5. Sample Size: Non-Proportional Hazards
Under NPH, we can no longer use the equation:
No HR θ
Logrank test: may not be most powerful
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6. Sample Size: Non-Proportional Hazards
Delayed effect: HR = 1 in the first 5 months, HR = 0.7 after 5 months
Diminishing effect: hazard ratios increasing from 0.5 to 1 by 0.1 for every 1.2 months
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7. Power Analysis: Delayed Separation
Heatmap for a delayed effect model with hazard ratio 1 in the first 5 months and 0.7 after 5 months
Number of Events (D)
Number of Patients
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8. Power Analysis: Diminishing Effect
Heatmap for a diminishing effect model with hazard ratio increasing from 0.5 to 1 by 0.1 for every 1.2 months
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9. Power Analysis: Diminishing Effect
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10. Power Analysis: Diminishing Effect
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11. Power Analysis: Non-Proportional Hazards
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12. Delay Effect, Search (N, D)
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13. Diminishing Effect, Search (N, D)
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14. Searching Results
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15. Summary Design: non-proportional hazards
Sample size determination needs to consider an “optimal” combination of number of patients and number of events
Simulation can be used to find cost-effective combination of number of patients and number of events
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16. Thanks!
Q&A
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