getADRCI: Repeated Confidence Interval After Adaptation

Description

Obtains the repeated p-value, conservative point estimate, and repeated confidence interval for an adaptive group sequential trial.

Usage

getADRCI(
  L = NA_integer_,
  zL = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  Lc = NA_integer_,
  zLc = NA_real_,
  INew = NA_real_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Value

A data frame with the following variables:

pvalue: Repeated p-value for rejecting the null hypothesis.
thetahat: Point estimate of the parameter.
cilevel: Confidence interval level.
lower: Lower bound of repeated confidence interval.
upper: Upper bound of repeated confidence interval.

Arguments

L: The interim adaptation look of the primary trial.
zL: The z-test statistic at the interim adaptation look of the primary trial.
IMax: The maximum information of the primary trial.
kMax: The maximum number of stages of the primary trial.
informationRates: The information rates of the primary trial.
efficacyStopping: Indicators of whether efficacy stopping is allowed at each stage of the primary trial. Defaults to true if left unspecified.
criticalValues: The upper boundaries on the z-test statistic scale for efficacy stopping for the primary trial.
alpha: The significance level of the primary trial. Defaults to 0.025.
typeAlphaSpending: The type of alpha spending for the primary trial. 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, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpending: The parameter value of alpha spending for the primary trial. Corresponds to \(\Delta\) for "WT", \(\rho\) for "sfKD", and \(\gamma\) for "sfHSD".
spendingTime: The error spending time of the primary trial. Defaults to missing, in which case, it is the same as informationRates.
MullerSchafer: Whether to use the Muller and Schafer (2001) method for trial adaptation.
Lc: The look of interest in the integrated trial.
zLc: The z-test statistic at the look of the integrated trial.
INew: The maximum information of the secondary trial.
informationRatesNew: The spacing of looks of the secondary trial.
efficacyStoppingNew: The indicators of whether efficacy stopping is allowed at each look of the secondary trial up to look L2. Defaults to true if left unspecified.
typeAlphaSpendingNew: The type of alpha spending for the secondary trial. 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, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpendingNew: The parameter value of alpha spending for the secondary trial. Corresponds to \(\Delta\) for "WT", \(\rho\) for "sfKD", and \(\gamma\) for "sfHSD".
spendingTimeNew: The error spending time of the secondary trial. up to look L2. Defaults to missing, in which case, it is the same as informationRatesNew.

Author

Kaifeng Lu, kaifenglu@gmail.com

Details

If typeAlphaSpendingNew is "OF", "P", "WT", or "none", then informationRatesNew, efficacyStoppingNew, and spendingTimeNew must be of full length kNew, and informationRatesNew and spendingTimeNew must end with 1.

References

Cyrus R. Mehta, Peter Bauer, Martin Posch and Werner Brannath. Repeated confidence intervals for adaptive group sequential trials. Stat Med. 2007;26:5422–5433.

Examples

Run this code

# two-arm randomized clinical trial with a normally distributed endpoint
# 90% power to detect mean difference of 15 with a standard deviation of 50
# Design the Stage I Trial with 3 looks and Lan-DeMets O'Brien-Fleming type
# spending function
delta <- 15
sigma <- 50

(des1 <- getDesignMeanDiff(
  beta = 0.1, meanDiff = delta, stDev = sigma,
  kMax = 3, alpha = 0.025, typeAlphaSpending = "sfOF"
))

s1 <- des1$byStageResults$informationRates
b1 <- des1$byStageResults$efficacyBounds
n <- des1$overallResults$numberOfSubjects

# Monitoring the Stage I Trial
L <- 1
nL <- des1$byStageResults$numberOfSubjects[L]
deltahat <- 8
sigmahat <- 55
sedeltahat <- sigmahat * sqrt( 4 / nL)
zL <- deltahat / sedeltahat

# Making an Adaptive Change: Stage I to Stage II
# revised clinically meaningful difference downward to 10 power the study
# retain the standard deviation at the design stage
# Muller & Schafer (2001) method to design the secondary trial
# with 2 looks and Lan-DeMets Pocock type spending function
# re-estimate sample size to reach 90% conditional power
deltaNew <- 10

(des2 <- adaptDesign(
  betaNew = 0.1, L = L, zL = zL, theta = deltaNew,
  IMax = n / (4 * sigma^2), kMax = 3, informationRates = s1,
  alpha = 0.025, typeAlphaSpending = "sfOF",
  MullerSchafer = TRUE, kNew = 2, typeAlphaSpendingNew = "sfP"
))

INew <- des2$secondaryTrial$maxInformation
(nNew <- ceiling(INew * 4 * sigma^2))
(nTotal <- nL + nNew)

# Monitoring the Integrated Trial
s2 <- des2$secondaryTrial$informationRates

Lc <- 2
deltahatc <- 9.5
sigmahatc <- 52.759
L2 <- Lc - L
nL2 <-  nNew * s2[L2]
nc <- nL + nL2
sedeltahatc <- sigmahatc * sqrt(4 / nc)
zLc <- deltahatc / sedeltahatc
zL2 <- (zLc * sqrt(nc) - zL * sqrt(nL)) / sqrt(nL2)

getADRCI(
  L = L, zL = zL, IMax = n / (4 * sigmahatc^2), kMax = 3,
  informationRates = s1, alpha = 0.025, typeAlphaSpending = "sfOF",
  MullerSchafer = TRUE, Lc = Lc, zLc = zLc,
  INew = nNew / (4 * sigmahatc^2), informationRatesNew = s2,
  typeAlphaSpendingNew = "sfP")

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