# OS monitoring guideline retrospectively applied to Motivating Example 1
# with delta null = 1.3, delta alt = 0.80, gamma_FA = 0.025 and beta_PA = 0.10.
bounds(
events = c(60, 89, 110, 131, 178),
power_int = 0.9, # βPA
falsepos = 0.025, # γFA
hr_null = 1.3, # δnull
hr_alt = 0.8, # δalt
rand_ratio = 1,
hr_marg_benefit = NULL
)
#> $lhr_null
#> [1] 0.2623643
#>
#> $lhr_alt
#> [1] -0.2231436
#>
#> $lhr_pos
#> [1] 0.107751640 0.048544837 0.021238743 0.000795809 -0.031446759
#>
#> $summary
#> Deaths OS HR threshold for positivity One-sided false positive error rate
#> 1 60 1.114 0.275
#> 2 89 1.050 0.157
#> 3 110 1.021 0.103
#> 4 131 1.001 0.067
#> 5 178 0.969 0.025
#> Level of 2-sided CI needed to rule out delta null
#> 1 45
#> 2 69
#> 3 79
#> 4 87
#> 5 95
#> Probability of meeting positivity threshold under delta alt
#> 1 0.9
#> 2 0.9
#> 3 0.9
#> 4 0.9
#> 5 0.9
#> Posterior probability the true OS HR exceeds delta null given the data
#> 1 0.275
#> 2 0.157
#> 3 0.103
#> 4 0.067
#> 5 0.025
#> Predictive probability the OS HR estimate at Final Analysis does not exceed the positivity threshold
#> 1 25.394
#> 2 29.681
#> 3 32.744
#> 4 35.977
#> 5 NA# OS monitoring guideline applied to Motivating Example 2
# with delta null = 4/3, delta alt = 0.7, gamma_FA = 0.20, beta_PA = 0.1,
# randomization ratio 2 and 0.95 HR marginal benefit
bounds(
events = c(60, 89, 110, 131, 178),
power_int = 0.9, # βPA
falsepos = 0.025, # γFA
hr_null = 1.3, # δnull
hr_alt = 0.8, # δalt
rand_ratio = 2, # rand_ratio
hr_marg_benefit = 0.95
) # Marginal HR benefit
#> $lhr_null
#> [1] 0.2623643
#>
#> $lhr_alt
#> [1] -0.2231436
#>
#> $lhr_pos
#> [1] 0.12782380 0.06502550 0.03606302 0.01438001 -0.04926939
#>
#> $summary
#> Deaths OS HR threshold for positivity One-sided false positive error rate
#> 1 60 1.136 0.312
#> 2 89 1.067 0.190
#> 3 110 1.037 0.132
#> 4 131 1.014 0.090
#> 5 178 0.952 0.025
#> Level of 2-sided CI needed to rule out delta null
#> 1 38
#> 2 62
#> 3 74
#> 4 82
#> 5 95
#> Probability of meeting positivity threshold under delta alt
#> 1 0.900
#> 2 0.900
#> 3 0.900
#> 4 0.900
#> 5 0.863
#> Posterior probability the true OS HR exceeds delta null given the data
#> 1 0.301
#> 2 0.176
#> 3 0.118
#> 4 0.078
#> 5 0.019
#> Predictive probability the OS HR estimate at Final Analysis does not exceed the positivity threshold
#> 1 19.978
#> 2 22.290
#> 3 23.453
#> 4 23.921
#> 5 NA
#> Probability of meeting positivity threshold under incremental benefit
#> 1 0.743
#> 2 0.698
#> 3 0.667
#> 4 0.638
#> 5 0.505