gs_prob.RdGroup sequential boundary crossing probabilities
gs_prob(theta, upper = gs_b, lower = gs_b, upar, lpar, info, r = 18)
| theta | natural parameter for group sequentia design representing expected drift at time of each analysis |
|---|---|
| upper | function to compute upper bound |
| lower | function to compare lower bound |
| upar | parameter to pass to upper |
| lpar | parameter to pass to lower |
| info | statistical information at each analysis |
| r | Integer, at least 2; default of 18 recommended by Jennison and Turnbull |
A `tibble` with a row for each finite bound and analysis containing the following variables: Analysis analysis number Bound Upper (efficacy) or Lower (futility) Z Z-value at bound Probability probability that this is the first bound crossed under the given input theta approximate natural parameter value required to cross the bound
Approximation for theta is based on Wald test and assumes the observed information is equal to the expected.
# Asymmetric 2-sided design gs_prob(theta = 0, upar = rep(2.2, 3), lpar = rep(0, 3), upper=gs_b, lower=gs_b, info = 1:3)#> # A tibble: 6 x 6 #> Analysis Bound Z Probability theta info #> <int> <chr> <dbl> <dbl> <dbl> <int> #> 1 1 Upper 2.2 0.0139 0 1 #> 2 2 Upper 2.2 0.0236 0 2 #> 3 3 Upper 2.2 0.0305 0 3 #> 4 1 Lower 0 0.5 0 1 #> 5 2 Lower 0 0.625 0 2 #> 6 3 Lower 0 0.687 0 3# One-sided design x <- gs_prob(theta = 0, upar = rep(2.2, 3), lpar = rep(-Inf, 3), upper=gs_b, lower=gs_b, info = 1:3) # Without filtering, this shows unneeded lower bound x#> # A tibble: 6 x 6 #> Analysis Bound Z Probability theta info #> <int> <chr> <dbl> <dbl> <dbl> <int> #> 1 1 Upper 2.2 0.0139 0 1 #> 2 2 Upper 2.2 0.0237 0 2 #> 3 3 Upper 2.2 0.0311 0 3 #> 4 1 Lower -Inf 0 0 1 #> 5 2 Lower -Inf 0 0 2 #> 6 3 Lower -Inf 0 0 3#> # A tibble: 3 x 6 #> Analysis Bound Z Probability theta info #> <int> <chr> <dbl> <dbl> <dbl> <int> #> 1 1 Upper 2.2 0.0139 0 1 #> 2 2 Upper 2.2 0.0237 0 2 #> 3 3 Upper 2.2 0.0311 0 3