getNeventsFromHazardRatio: Required Number of Events Given Hazard Ratio

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Required Number of Events Given Hazard Ratio

Description

Obtains the required number of events given the hazard ratios under the null and alternative hypotheses for a group sequential design.

Usage

getNeventsFromHazardRatio(
  beta = 0.2,
  kMax = 1L,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityHR = NULL,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = NA_real_,
  spendingTime = NA_real_,
  hazardRatioH0 = 1,
  hazardRatio = NA_real_,
  allocationRatioPlanned = 1,
  rounding = TRUE
)

Arguments

beta	Type II error. Defaults to 0.2.
kMax	The maximum number of stages.
informationRates	The information rates in terms of number of events. Fixed prior to the trial. Defaults to (1:kMax) / kMax if left unspecified.
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage. Defaults to TRUE if left unspecified.
futilityStopping	Indicators of whether futility stopping is allowed at each stage. Defaults to TRUE if left unspecified.
criticalValues	Upper boundaries on the z-test statistic scale for stopping for efficacy.
alpha	The significance level. Defaults to 0.025.
typeAlphaSpending	The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpending	The parameter value for the alpha spending. Corresponds to \Delta for "WT", \rho for "sfKD", and \gamma for "sfHSD".
userAlphaSpending	The user defined alpha spending. Cumulative alpha spent up to each stage.
futilityBounds	Lower boundaries on the z-test statistic scale for stopping for futility at stages 1, ..., kMax-1. Defaults to rep(-8, kMax-1) if left unspecified. The futility bounds are non-binding for the calculation of critical values.
futilityCP	A vector of length kMax - 1 for the futility bounds on the conditional power scale.
futilityHR	A vector of length kMax - 1 for the futility bounds on the hazard ratio scale.
typeBetaSpending	The type of beta spending. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early futility stopping. Defaults to "none".
parameterBetaSpending	The parameter value for the beta spending. Corresponds to \rho for "sfKD", and \gamma for "sfHSD".
userBetaSpending	The user defined beta spending. Cumulative beta spent up to each stage.
spendingTime	A vector of length kMax for the error spending time at each analysis. Defaults to missing, in which case, it is the same as informationRates.
hazardRatioH0	Hazard ratio under the null hypothesis for the active treatment versus control. Defaults to 1 for superiority test.
hazardRatio	Hazard ratio under the alternative hypothesis for the active treatment versus control.
allocationRatioPlanned	Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.
rounding	Whether to round up the number of events. Defaults to 1 for rounding.

Value

The required number of events.

Author(s)

Kaifeng Lu, [e-mail]

Examples

getNeventsFromHazardRatio(
  beta = 0.2, kMax = 2,
  informationRates = c(0.5,1),
  alpha = 0.025, typeAlphaSpending = "sfOF",
  typeBetaSpending = "sfP",
  hazardRatio = 0.673)

lrstat documentation built on May 13, 2026, 9:06 a.m.