gs_cp: Conditional power computation with non-constant effect size...

In gsDesign2: Group Sequential Design with Non-Constant Effect

Conditional power computation with non-constant effect size for non-/crossing an upper boundary at analysis j given observed Z value at analysis i

Description

Conditional power computation with non-constant effect size for non-/crossing an upper boundary at analysis j given observed Z value at analysis i

Usage

gs_cp(x = NULL, theta = NULL, i = 1, zi = NULL)

Arguments

x	An object of type gsDesign2.
theta	Optional numeric vector with length j-i+1, which specifies the natural parameter for treatment effect of interim analysis i through analysis j. The default is NULL.
i	Index of current analysis, with default of 1.
zi	Numeric scalar z-value observed at analysis i.

Details

We assume Z_i, i = 1, ..., K are the z-statistics at an interim analysis i, respectively. We assume further Z_i, i = 1, ..., K follows multivariate normal distribution

E(Z_i) = \theta_i\sqrt{I_i}

Cov(Z_i, Z_j) = I_i/I_j

. See https://merck.github.io/gsDesign2/articles/story-npe-background.html for assumption details.

The returned value is list of

P(\{Z_j \geq b_j\} \& \{\cap_{m=i+1}^{j-1} a_m \leq Z_m < b_m\} \mid Z_i = z_i).

P(\{Z_j \geq b_j\} \& \{\cap_{m=i+1}^{j-1} Z_m < b_m\} \mid Z_i = z_i).

P(\{Z_j \leq b_j\} \& \{\cap_{m=i+1}^{j-1} a_m \leq Z_m < b_m\} \mid Z_i = z_i).

Value

A list with the following elements:

prob_alpha

A numeric vector of (\alpha_{i,i+1}, \ldots, \alpha_{i,j-1}, \alpha_{i,j}), where \alpha_{i,j} = P(\{Z_j \geq b_j\} \& \{\cap_{m=i+1}^{j-1} a_m \leq Z_m < b_m\} \mid Z_i = z_i).

prob_alpha_plus

A numeric vector of (\alpha^+_{i,i+1}, \ldots, \alpha^+_{i,j-1}, \alpha^+_{i,j}), where \alpha^+_{i,j} = P(\{Z_j \geq b_j\} \& \{\cap_{m=i+1}^{j-1} Z_m < b_m\} \mid Z_i = z_i).

prob_beta

A numeric vector of (\beta_{i,i+1}, \ldots, \beta_{i,j-1}, \beta_{i,j}), where \beta_{i,j} = P(\{Z_j \leq b_j\} \& \{\cap_{m=i+1}^{j-1} a_m \leq Z_m < b_m\} \mid Z_i = z_i).

Examples

library(gsDesign2)
library(gsDesign)
library(dplyr)
library(mvtnorm)
# Example 1
# original design ----
enroll_rate <- define_enroll_rate(duration = c(2, 2, 2, 18),
                                  rate = c(1, 2, 3, 4))
fail_rate <- define_fail_rate(duration = c(3, Inf),
                              fail_rate = log(2) / 10,
                              dropout_rate = 0.001,
                              hr = c(1, 0.7))
x <- gs_design_ahr(enroll_rate = enroll_rate, fail_rate = fail_rate,
                   alpha = 0.025, beta = 0.1, ratio = 1,
                   info_frac = c(0.4, 0.6, 0.8, 1), analysis_time = 30,
                   binding = FALSE,
                   upper = gs_spending_bound,
                   upar = list(sf = sfLDOF, total_spend = 0.025, param = NULL),
                   lower = gs_spending_bound,
                   lpar = list(sf = sfLDOF, total_spend = 0.1),
                   h1_spending = TRUE,
                   test_lower = TRUE,
                   info_scale = "h0_h1_info") |> to_integer()

# calculate conditional power
# case 1: currently at IA1, compute conditional power at IA2, IA3 and FA, 
# with default theta = NULL
gs_cp(x = x, i = 1, 
zi = -gsDesign::hrn2z(hr = 0.8, n = 150+180, ratio = 1))

# case 2: currently at IA1, compute conditional power at IA2, IA3 and FA, 
# with user-input theta
gs_cp(x = x, 
  theta = c(0.15, 0.2, 0.25, 0.3), 
  i = 1, 
  zi = -gsDesign::hrn2z(hr = 0.8, n = 150+180, ratio = 1))

gsDesign2 documentation built on July 1, 2026, 1:08 a.m.