Exact binomial repeated p-values for a group sequential design

Computes repeated p-values for the exact binomial design implied by a [gsSurv()] object. The p-value at analysis `j` is the smallest local one-sided alpha level for which the observed experimental-arm event count crosses the exact lower efficacy bound at that analysis. Non-binding futility bounds are ignored for the Type I error calculation.

Usage

repeatedPValueBinomialExact(
  gsD,
  n.I = NULL,
  x = NULL,
  interval = c(1e-20, 0.9999),
  tol = 1e-08,
  maxiter = 100,
  check = FALSE
)

Arguments

gsD

A `gsSurv` object with `test.type` 1 or 4.

n.I

Increasing integer total event counts at completed analyses. If `NULL`, the planned exact binomial event counts from `toBinomialExact(gsD)` are used. This must have at most 1 value greater than or equal to planned final events (`gsD$maxn.IPlan` if available, otherwise `max(gsD$n.I)`).

x

Integer experimental-arm event counts at the analyses in `n.I`.

interval

Search interval for the p-values. As in [sequentialPValue()], values outside this interval are truncated to the nearest endpoint.

tol

Relative tolerance for the monotone bisection search on the alpha scale.

maxiter

Maximum number of bisection iterations for each analysis.

check

Logical. If `TRUE`, checks the monotonicity of the alpha-indexed integer efficacy bounds on a coarse grid and warns if it is violated.

Value

A data frame with one row per completed analysis containing:

`Analysis`

Analysis index.

`n.I`

Total events at analysis.

`x`

Observed experimental-arm events.

`repeated_p_value`

Repeated p-value for the analysis.

`bound_at_repeated_p_value`

Integer efficacy bound at the repeated p-value.

See also

[sequentialPValueBinomialExact()], [sequentialPValue()], [toBinomialExact()], [gsBinomialExact()]

Examples

x <- gsSurv(
  k = 3, test.type = 4, alpha = 0.025, beta = 0.1, timing = c(0.45, 0.7),
  sfu = sfHSD, sfupar = -4, sfl = sfLDOF, sflpar = 0,
  lambdaC = 0.001, hr = 0.3, hr0 = 0.7, eta = 5e-04,
  gamma = 10, R = 16, T = 24, minfup = 8, ratio = 3
)
counts <- toBinomialExact(x)$n.I
repeatedPValueBinomialExact(gsD = x, n.I = counts, x = c(12, 23, 38))
#>   Analysis n.I  x repeated_p_value bound_at_repeated_p_value
#> 1        1  31 12      0.008683036                        12
#> 2        2  48 23      0.013085131                        23
#> 3        3  69 38      0.019672838                        38