getDesignRiskRatioFM {lrstat}R Documentation

Group Sequential Design for Two-Sample Risk Ratio Based on the Farrington-Manning Score Test

Description

Obtains the power given sample size or obtains the sample size given power for a group sequential design for two-sample risk ratio based on the Farrington-Manning score test

Usage

getDesignRiskRatioFM(
  beta = NA_real_,
  n = NA_real_,
  riskRatioH0 = 1,
  pi1 = NA_real_,
  pi2 = NA_real_,
  nullVariance = TRUE,
  allocationRatioPlanned = 1,
  rounding = TRUE,
  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_
)

Arguments

beta

The type II error.

n

The total sample size.

riskRatioH0

The risk ratio under the null hypothesis. Defaults to 1.

pi1

The assumed probability for the active treatment group.

pi2

The assumed probability for the control group.

nullVariance

Whether to use the variance under the null or the empirical variance under the alternative.

allocationRatioPlanned

Allocation ratio for the active treatment versus control. Defaults to 1 for equal randomization.

rounding

Whether to round up sample size. Defaults to 1 for sample size rounding.

kMax

The maximum number of stages.

informationRates

The information rates. 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.

Details

Consider a group sequential design for two-sample risk ratio. The parameter of interest is

\rho = \pi_1 / \pi_2

where \pi_1 is the response probability for the active treatment group and \pi_2 is the response probability for the control group. Let \rho_0 denote the risk ratio under the null hypothesis. The Farrington-Manning score test statistic is constructed as

Z = \frac{\hat{\pi}_1 - \rho_0 \hat{\pi}_2}{ \sqrt{Var(\hat{\pi}_1 - \rho_0 \hat{\pi}_2)}}

The variance can be derived from the binomial distributions as follows:

Var(\hat{\pi}_1 - \rho_0 \hat{\pi}_2) = \frac{1}{n} \{ \frac{\pi_1(1-\pi_1)}{r} + \frac{\rho_0^2\pi_2(1-\pi_2)}{1-r} \}

where n is the total number of subjects and r is the randomization probability for the active treatment group. When nullVariance = TRUE, the variance is computed under the null hypothesis. In this case, the values of \pi_1 and \pi_2 in the variance formula are replaced with their restricted maximum likelihood counterparts, subject to the constraint

\pi_1 / \pi_2 = \rho_0

Value

An S3 class designRiskRatioFM object with three components:

Author(s)

Kaifeng Lu, kaifenglu@gmail.com

Examples


(design1 <- getDesignRiskRatioFM(
  beta = 0.2, riskRatioH0 = 1.3, pi1 = 0.125, pi2 = 0.125,
  alpha = 0.05))


[Package lrstat version 0.2.15 Index]