Bounds
bounds.RdOS monitoring guidelines as proposed in manuscript "Monitoring Overall Survival in Pivotal Trials in Indolent Cancers". Calculate thresholds for positivity that can be used at an analysis to judge whether emerging evidence about the effect of treatment on OS is concerning or not. The threshold for positivity at any given analysis is the value below which the observed hazard ratio must be in order to provide sufficient reassurance that the effect on OS does not reach the selected unacceptable level of detriment (the margin hr_null). Terminology follows the manuscript "Monitoring Overall Survival in Pivotal Trials in Indolent Cancers", publication submitted
Usage
bounds(
events,
power_int = 0.9,
falsepos = 0.025,
hr_null = 1.3,
hr_alt = 0.9,
rand_ratio = 1,
hr_marg_benefit = NULL
)Arguments
- events
Vector. Target number of deaths at each analysis
- power_int
Scalar. Marginal power required at the Primary Analysis when true hazard ratio (HR) is hr_alt.
- falsepos
Scalar. Marginal one-sided false positive error rate we are prepared to tolerate at the Final Analysis. Determines the positivity threshold at Final Analysis
- hr_null
Scalar. The unacceptably large detrimental effect of treatment on OS we want to rule out (on HR scale)
- hr_alt
Scalar. Plausible clinically relevant beneficial effect of treatment on OS (on HR scale)
- rand_ratio
Integer. If patients are randomized k:1 between experimental intervention and control, rand_ratio should be inputted as k. Example: if patients are randomized 1:1 between experimental and control, k=1. If patients are randomized 2:1 between experimental and control, k=2.
- hr_marg_benefit
Scalar. We may be uncertain about what a plausible beneficial effect of treatment on OS is. User can enter a second plausible OS benefit (on HR scale) and function will evaluate the probability we meet the positivity threshold at each analysis under this HR. This second OS benefit will usually be closer to 1 than hr_alt.
Value
List that contains:
lhr_null: Scalar, unacceptable OS log-HR,lhr_alt: Scalar, plausible clinically relevant log-HR,lhr_pos: Scalar, positivity thresholds for log-HR estimates,summary: Dataframe, which contains:OS HR threshold for positivity,One sided false positive error rate,Level of 2 sided CI needed to rule out hr_null,Probability of meeting positivity threshold under hr_alt,Positivity_Thres_Posterior: Pr(true OS HR >= minimum unacceptable OS HR | current data),Positivity_Thres_PredProb: Pr(OS HR estimate at Final Analysis <= Final Analysis positivity threshold | current data)
Details
Monitoring guidelines assume that the hazard ratio (HR) can adequately summarize the size of the benefits and harms of the experimental intervention vs control on overall survival (OS). Furthermore, guidelines assume that an OS HR < 1 is consistent with a beneficial effect of the intervention on OS (and smaller OS HRs <1 indicate increased efficacy).
Examples
# Example 01: 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, # beta_PA
falsepos = 0.025, # gamma_FA
hr_null = 1.3, # delta_null
hr_alt = 0.8, # delta_alt
rand_ratio = 1, # rand_ratio
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
#>
# Example 02: OS monitoring guideline applied to Motivating Example 2
# with delta null = 4/3, delta alt = 0.7, gamma_FA = 0.20 and beta_PA = 0.1.
bounds(
events = c(60, 89, 110, 131, 178),
power_int = 0.9, # beta_PA
falsepos = 0.025, # gamma_FA
hr_null = 1.3, # delta_null
hr_alt = 0.8, # delta_alt
rand_ratio = 1, # rand_ratio
hr_marg_benefit = 0.95
)
#> $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
#> Probability of meeting positivity threshold under incremental benefit
#> 1 0.731
#> 2 0.681
#> 3 0.648
#> 4 0.617
#> 5 0.553
#>