Design   δ =1.5 δ =1.6 δ =1.7
κ Test *n2 α 1 - β n2 α 1 - β n2 α 1 - β
0.5 Z(τ) 262 0.052 0.795 152 0.051 0.804 108 0.049 0.817
  S(τ) 285 0.051 0.799 149 0.05 0.802 100 0.051 0.804
  L(τ) 262 0.053 0.795 152 0.051 0.804 108 0.049 0.818
1 Z(τ) 305 0.053 0.793 170 0.05 0.807 118 0.049 0.813
  S(τ) 344 0.052 0.799 168 0.05 0.802 111 0.052 0.806
  L(τ) 305 0.053 0.793 170 0.05 0.807 118 0.049 0.813
2 Z(τ) 367 0.054 0.795 191 0.053 0.803 130 0.05 0.811
  S(τ) 445 0.049 0.801 195 0.051 0.8 124 0.051 0.802
  L(τ) 367 0.054 0.794 191 0.053 0.802 130 0.05 0.81
Design   δ =1.8 δ =1.9 δ =2.0
κ Test n2 α 1 - β n2 α 1 - β n2 α 1 - β
0.5 Z(τ) 84 0.049 0.823 70 0.047 0.833 60 0.046 0.84
  S(τ) 75 0.05 0.806 61 0.051 0.813 51 0.051 0.815
  L(τ) 84 0.049 0.823 70 0.048 0.834 60 0.047 0.842
1 Z(τ) 92 0.048 0.823 75 0.046 0.828 65 0.046 0.838
  S(τ) 82 0.051 0.807 66 0.05 0.812 55 0.051 0.814
  L(τ) 92 0.049 0.823 75 0.047 0.828 65 0.047 0.839
2 Z(τ) 99 0.048 0.817 81 0.047 0.825 69 0.047 0.833
  S(τ) 90 0.051 0.805 71 0.051 0.806 59 0.051 0.812
  L(τ) 99 0.048 0.815 81 0.048 0.824 69 0.048 0.832
Table 1: Sample size and simulated empirical type I error (α) and power (1-β) based on 100,000 simulation runs for the Weibull distribution for fixed sample Z(τ) test, log-rank test L(τ) and S(τ) test with a nominal type I error of 0.05 and power 80% (one-sided test).