Impact of long term survival and delayed clinical effect on statistical power and study duration

PHMPHCRMNPHMNPHCRM
Cure rate0.10 vs. 0.180.10 vs. 0.17
Delayed clinical effect (month)33
Sample size680680680680
Number of events512512512512
Hazard ratio (pre- and post- separation)0.750.751/0.751/0.75
Type I error0.050.050.050.05
Power0.900.900.700.70
Accrual duration (month)34343434
Study duration (month)48554754

A study designed to detect a hazard ratio of 0.75 with two-sided type I error rate of 5% and power of 90% requires 512 events under exponential assumption. The study would take 48 months with accrual rate of 20 patients per month for 34 months. When a cured fraction of patients exists in both arms, the study duration is extended to 55 months. A delayed separation in overall survival effect would lead to a loss in power. The presence of both long term survival and delayed clinical effect would lead to an underpowered and lengthy study.