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# 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