Group Sequential Trials Using Bonferroni-Based Graphical Approaches

Obtains the test results for group sequential trials using graphical approaches based on weighted Bonferroni tests.

Usage

fseqbon(
  w,
  G,
  alpha = 0.025,
  kMax,
  typeAlphaSpending = NULL,
  parameterAlphaSpending = NULL,
  maxInformation = NULL,
  incidenceMatrix = NULL,
  k1,
  p,
  information,
  spendingTime = NULL,
  nthreads = 0
)

Arguments

w: The vector of initial weights for elementary hypotheses.
G: The initial transition matrix.
alpha: The significance level. Defaults to 0.025.
kMax: The maximum number of stages.
typeAlphaSpending: The vector of alpha spending functions for the hypotheses. Each element is 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. Defaults to "sfOF" if not provided.
parameterAlphaSpending: The vector of parameter values for the alpha spending functions for the hypotheses. Each element corresponds to the value of \(\rho\) for "sfKD" or \(\gamma\) for "sfHSD". Defaults to missing if not provided.
maxInformation: The vector of target maximum information for each hypothesis. Defaults to a vector of 1s if not provided.
incidenceMatrix: The kMax x m incidence matrix indicating whether the specific hypothesis will be tested at the given look. Here \(m\) is the number of hypotheses. If not provided, defaults to testing each hypothesis at all study looks.
k1: The number of study looks at the interim analysis.
p: The \(B k_1 \times m\) matrix of raw p-values for each hypothesis by study look. Here \(B\) is the number of replications for simulations. In other words, the number of rows must be a multiple of k1.
information: The \(B k_1 \times m\) matrix of observed information for each hypothesis by study look.
spendingTime: The \(B k_1 \times m\) matrix of spending time for alpha spending by study look. Each element must be between 0 and 1, and the spending time must be increasing by study look for each hypothesis. If not provided, it is the same as informationRates calculated from information and maxInformation.
nthreads: The number of threads to use in simulations (0 means the default RcppParallel behavior).

Value

A vector to indicate the first look the specific hypothesis is rejected (0 if the hypothesis is not rejected).

Details

The procedure allows the user to retest an unrejected hypothesis at earlier looks if its weight increased after rejection of other hypotheses. In this case, the procedure will return the first look at which the specific hypothesis is rejected. If the hypothesis is not rejected at any look, it will return 0.

References

Willi Maurer and Frank Bretz. Multiple testing in group sequential trials using graphical approaches. Statistics in Biopharmaceutical Research. 2013; 5:311-320.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


# Case study from Maurer & Bretz (2013)

fseqbon(
  w = c(0.5, 0.5, 0, 0),
  G = matrix(c(0, 0.5, 0.5, 0,  0.5, 0, 0, 0.5,
               0, 1, 0, 0,  1, 0, 0, 0),
             nrow=4, ncol=4, byrow=TRUE),
  alpha = 0.025,
  kMax = 3,
  typeAlphaSpending = rep("sfOF", 4),
  maxInformation = rep(1, 4),
  k1 = 2,
  p = matrix(c(0.0062, 0.017, 0.009, 0.13,
               0.0002, 0.0035, 0.002, 0.06),
             nrow=2, ncol=4, byrow=TRUE),
  information = matrix(c(rep(1/3, 4), rep(2/3, 4)),
                       nrow=2, ncol=4, byrow=TRUE),
  nthreads = 1)
#> [1] 2 2 2 0