seqmbgx {MultiGroupSequential}

Maurer-Bretz sequential graphical approach

Description

seqmbgx() conducts group-sequential testing for multiple hypotheses based on Maurer-Bretz approach.

Usage

seqmbgx(
  xm = qnorm(matrix(rep(c(0.03, 0.04, 0.01), times = 4), ncol = 3, nrow = 4)),
  informationm = matrix(rep(c(0.4, 0.8, 1), each = 4), ncol = 3, nrow = 4),
  spending = rep("OBF", 4),
  param.spending = rep(1, 4),
  alpha = 0.025,
  sided = -1,
  W = c(0.5, 0.5, 0, 0),
  G = rbind(c(0, 0, 1, 0), c(0, 0, 0, 1), c(0, 1, 0, 0), c(1, 0, 0, 0)),
  tol = 1e-10,
  retrospective = 0
)

Arguments

xm

Numeric matrix of test statistics for each endpoint (in row) and each time point (in column).

informationm

Numeric matrix of information fractions for the statistics xm.

spending

Character vector for the type(s) of the spending function for each endpoint.

param.spending

parameter in the spending function

alpha

overall family-wise error rate

sided

Integer scalar indicating the side of the test:

• -1: Reject if test statistic is smaller than or equal to the critical value (one-sided)

• 1: Reject if test statistic is greater or equal to the critical value (one-sided)

• 0: Reject if the absolute value of the test statistic is greater than the critical value (two-sided)

W

Numeric vector of the weights of the graph.

G

Numeric transition matrix of the graph.

tol

Numeric scalar of tolerance level for computing the critical values.

retrospective

Integer scalar with the following potential values

• 0: (default) only compares the current test statistic with the updated critical value;

• 1: compares all the test statistics up to the current one with the updated critical values.

Even though retrospectively looking at the values is statistically valid in terms of control the type-1 error, not retrospectively looking at the past comparisons avoids the dilemma of retrospectively increasing the alpha level for the un-rejected hypothesis in the past.

Value

List with elements

• Hrej: rejected hypotheses

• rejected: the index set of rejected hypotheses

• decisionsm: rejection decision for each endpoint (row) at each timepoint (column)

• cumdecisionsm: cumulative rejection decision for each endpoint (row) at each timepoint (column)

Author(s)

Xiaodong Luo

Examples

seqmbgx(
  xm = qnorm(matrix(rep(c(0.03, 0.04, 0.01), times = 4), ncol = 3, nrow = 4)),
  informationm = matrix(rep(c(0.4, 0.8, 1), each = 4), ncol = 3, nrow = 4),
  spending = rep("OBF", 4),
  param.spending = rep(1, 4),
  alpha = 0.025,
  W = c(0.5, 0.5, 0, 0),
  G = rbind(c(0, 0, 1, 0), c(0, 0, 0, 1), c(0, 1, 0, 0), c(1, 0, 0, 0)),
  retrospective = 0
)