getNeventsFromHazardRatio {lrstat}

Get the 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 = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NA_real_,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = NA_real_,
  spendingTime = NA_real_,
  hazardRatioH0 = 1,
  hazardRatio = NA_real_,
  allocationRatioPlanned = 1,
  rounding = 1L
)

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(-6, kMax-1) if left unspecified. The futility bounds are non-binding for the calculation of critical values.

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. Defaults to 0.5.

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)