Exact conditional power for a group sequential binomial design

Computes exact conditional probabilities of crossing future boundaries, given the cumulative experimental arm event count at an interim analysis.

Usage

gsCPBinomialExact(
  x,
  i = 1,
  x.i,
  theta = NULL,
  ve = NULL,
  ratio = x$ratio,
  binding = TRUE
)

Arguments

x

An exact binomial spending design returned by [toBinomialExact()].

i

Interim analysis at which conditioning occurs; must be less than `x$k`.

x.i

Cumulative experimental arm events observed at analysis `i`.

theta

Conditional probabilities that a future event occurs in the experimental arm. If `NULL`, the observed probability and the values in `x$theta` are used.

ve

Vaccine or prevention efficacy assumptions. These are converted to conditional event probabilities using `ratio`. Specify at most one of `theta` and `ve`.

ratio

Experimental-to-control randomization ratio. This defaults to the ratio retained by [toBinomialExact()]. It is required when `ve` is supplied and is also used to report efficacy corresponding to `theta`.

binding

Logical indicating whether future futility or harm boundaries stop the trial. With `FALSE`, conditional efficacy power ignores these future non-binding boundaries. This argument does not restrict the observed result at analysis `i`.

Value

An object of class `gsBinomialExactCP`. Components include future absolute event counts, assumed conditional event probabilities and efficacies, per-analysis efficacy and futility crossing probabilities, continuation probabilities, and total conditional power and futility.

Details

Conditional on the interim count, future experimental arm event increments are independent binomial random variables. Their distribution is propagated through the remaining integer boundaries. Thus the calculation is exact under the same conditional binomial assumptions used by [gsBinomialExact()].

The calculation conditions only on the statistic at analysis `i`, as [gsCP()] does. It is computed regardless of whether the observed count has crossed a current efficacy, futility, or harm boundary. This gives a hypothetical projection if follow-up were to continue; it does not reverse a stopping decision. The `binding` argument controls only whether futility or harm boundaries at future analyses are enforced. Thus, the default `binding = TRUE` includes future non-efficacy stopping, whereas `binding = FALSE` ignores it.

See also

[gsCP()], [toBinomialExact()], [VEtable()]

Examples

design <- gsSurv(
  k = 2, test.type = 4, timing = .5, ratio = 3,
  hr = .3, hr0 = .7
)
exact_design <- toBinomialExact(design)
gsCPBinomialExact(exact_design, i = 1, x.i = 20, ve = c(.5, .7))
#> $k
#> [1] 1
#> 
#> $analysis
#> [1] 2
#> 
#> $n.I
#> [1] 66
#> 
#> $i
#> [1] 1
#> 
#> $n.I.i
#> [1] 33
#> 
#> $x.i
#> [1] 20
#> 
#> $theta
#> [1] 0.6000000 0.4736842
#> 
#> $efficacy
#> [1] 0.5 0.7
#> 
#> $binding
#> [1] TRUE
#> 
#> $lower
#> $lower$bound
#> [1] 36
#> 
#> $lower$prob
#>            0.6000000 0.4736842
#> Analysis 2 0.1210987 0.6197621
#> 
#> 
#> $upper
#> $upper$bound
#> [1] 38
#> 
#> $upper$prob
#>            0.6000000 0.4736842
#> Analysis 2 0.7940754 0.2571398
#> 
#> 
#> $continuation
#>             0.6000000 0.4736842
#> Analysis 2 0.08482594 0.1230981
#> 
#> $conditional_power
#> [1] 0.1210987 0.6197621
#> 
#> $conditional_futility
#> [1] 0.7940754 0.2571398
#> 
#> attr(,"class")
#> [1] "gsBinomialExactCP"