getADCI: Confidence Interval After Adaptation

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

Confidence Interval After Adaptation

Description

Obtains the p-value, median unbiased point estimate, and confidence interval after the end of an adaptive trial.

Usage

getADCI(
  L = NA_integer_,
  zL = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.25,
  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_
)

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 termination look of the integrated trial.
zLc	The z-test statistic at the termination look of the integrated trial.
INew	The maximum information of the secondary trial.
informationRatesNew	The spacing of looks of the secondary trial up to look L2.
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.

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.

Value

A data frame with the following variables:

• pvalue: p-value for rejecting the null hypothesis.

• thetahat: Median unbiased point estimate of the parameter.

• cilevel: Confidence interval level.

• lower: Lower bound of confidence interval.

• upper: Upper bound of confidence interval.

Author(s)

Kaifeng Lu, [e-mail]

References

Ping Gao, Lingyun Liu and Cyrus Mehta. Exact inference for adaptive group sequential designs. Stat Med. 2013;32(23):3991-4005.

See Also

adaptDesign

Examples

# 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)

getADCI(
  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")

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