bounds {monitOS}

Bounds

Description

OS 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.

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).

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)

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
)
# 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
)