Confidence Interval After Trial Termination

Obtains the p-value, median unbiased point estimate, and confidence interval after the end of a group sequential trial.

Usage

getCI(
  L = NA_integer_,
  zL = NA_real_,
  IMax = NA_real_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  spendingTime = NA_real_
)

Arguments

L: The termination look.
zL: The z-test statistic at the termination look.
IMax: The maximum information of the trial.
informationRates: The information rates up to look L.
efficacyStopping: Indicators of whether efficacy stopping is allowed at each stage up to look L. Defaults to true if left unspecified.
criticalValues: The upper boundaries on the z-test statistic scale for efficacy stopping up to look L.
alpha: The significance level. Defaults to 0.025.
typeAlphaSpending: The type of alpha spending for the 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 for the alpha spending. Corresponds to \(\Delta\) for "WT", \(\rho\) for "sfKD", and \(\gamma\) for "sfHSD".
spendingTime: The error spending time up to look L. Defaults to missing, in which case, it is the same as informationRates.

Value

A data frame with the following components:

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.

Details

If typeAlphaSpending is "OF", "P", "WT", or "none", then informationRates, efficacyStopping, and spendingTime must be of full length kMax, and informationRates and spendingTime must end with 1.

References

Anastasios A. Tsiatis, Gary L. Rosner and Cyrus R. Mehta. Exact confidence intervals following a group sequential test. Biometrics 1984;40:797-803.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


# group sequential design with 90% power to detect delta = 6
delta <- 6
sigma <- 17
n <- 282
(des1 <- getDesign(IMax = n/(4*sigma^2), theta = delta, kMax = 3,
                   alpha = 0.05, typeAlphaSpending = "sfHSD",
                   parameterAlphaSpending = -4))
#>                                                                          
#> Group-sequential design with 3 stages                                    
#> theta: 6, maximum information: 0.24                                      
#> Overall power: 0.9029, overall alpha (1-sided): 0.05                     
#> Drift parameter: 2.963, inflation factor: 1.014                          
#> Expected information under H1: 0.19, expected information under H0: 0.24 
#> Alpha spending: HSD(gamma = -4), beta spending: None                     
#>                                                                          
#>                           Stage 1 Stage 2 Stage 3
#> Information rate          0.333   0.667   1.000  
#> Efficacy boundary (Z)     2.794   2.289   1.680  
#> Cumulative rejection      0.1395  0.5588  0.9029 
#> Cumulative alpha spent    0.0026  0.0125  0.0500 
#> Efficacy boundary (theta) 9.797   5.676   3.401  
#> Efficacy boundary (p)     0.0026  0.0110  0.0465 
#> Information               0.08    0.16    0.24   

# crossed the boundary at the second look
L <- 2
n1 <- n*2/3
delta1 <- 7
sigma1 <- 20
zL <- delta1/sqrt(4/n1*sigma1^2)

# confidence interval
getCI(L = L, zL = zL, IMax = n/(4*sigma1^2),
      informationRates = c(1/3, 2/3), alpha = 0.05,
      typeAlphaSpending = "sfHSD", parameterAlphaSpending = -4)
#>        pvalue thetahat cilevel    lower    upper
#> 1 0.009815172 6.931527     0.9 2.069564 11.75432