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Exact repeated confidence intervals for vaccine or prevention efficacy

Source: R/ciBinomialExact.R
repeatedCIBinomialExact.Rd

Inverts exact binomial efficacy tests at each completed analysis to obtain repeated confidence intervals for vaccine or prevention efficacy.

Usage

repeatedCIBinomialExact(
  gsD,
  n.I = NULL,
  x = NULL,
  conf.level = 0.95,
  tol = 1e-08,
  maxiter = 100
)

Arguments

gsD

A gsSurv object with non-binding test.type 1, 4, 6, or 8.

n.I

Increasing integer total event counts at completed analyses. If NULL, planned integer event counts from toInteger(gsD) are used.

x

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

conf.level

Two-sided confidence level.

tol

Absolute tolerance for bisection on the conditional binomial event-probability scale.

maxiter

Maximum bisection iterations for each confidence limit.

Value

A data frame with one row per completed analysis containing the observed counts, efficacy estimate, repeated confidence limits, confidence level, and one-sided tail level.

Details

A two-sided interval with confidence level 1 - alpha uses the same spending function, spending times, and count-path ordering in both directions, with alpha / 2 in each tail. The lower efficacy limit inverts the usual lower event-count efficacy test. The upper efficacy limit inverts its mirror image after exchanging experimental- and control-arm event counts. This mirrored test is not the design's futility boundary.

Non-binding futility and harm are ignored in both directions. Coverage is generally conservative because the exact rejection regions are discrete. Spending time remains relative to the planned final event count.

This follows the repeated-confidence-interval construction of Jennison and Turnbull (1984), using exact Bernoulli ordering as in Coe and Tamhane (1993).

References

Jennison, C. and Turnbull, B. W. (1984). Repeated confidence intervals for group sequential clinical trials. Controlled Clinical Trials, 5, 33–45.

Coe, P. R. and Tamhane, A. C. (1993). Exact repeated confidence intervals for Bernoulli parameters in a group sequential clinical trial. Controlled Clinical Trials, 14, 19–29.

See also

ciBinomialExact, sequentialCIBinomialExact, repeatedPValueBinomialExact

Examples

design <- gsSurv(
  k = 3, test.type = 4, timing = c(.45, .7), ratio = 3,
  hr = .3, hr0 = .7
)
counts <- toBinomialExact(design)$n.I
# \donttest{
repeatedCIBinomialExact(design, counts, x = c(12, 23, 38))
#>   Analysis n.I  x  estimate  conf.low conf.high conf.level tail_alpha
#> 1        1  31 12 0.7894737 0.3792904 0.9345737       0.95      0.025
#> 2        2  48 23 0.6933333 0.3477728 0.8562642       0.95      0.025
#> 3        3  68 38 0.5777778 0.2902891 0.7471530       0.95      0.025
# }