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Conditional power computation with non-constant effect size for (non-)crossing an upper/lower boundary at future analyses given Z value at analysis i

Source: R/gs_cp.R
gs_cp.Rd

Conditional power computation with non-constant effect size for (non-)crossing an upper/lower boundary at future analyses given 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 \(i\).

Value

A list of conditional powers:

  • prob_alpha is a numeric vector of (\(\alpha_{i,i+1}, ..., \alpha_{i,j-1}, \alpha_{i,j}\)), where

    • for \(j = i+1\), \(\alpha_{i,j} = P(\{Z_j \geq b_j\} \mid Z_i = z_i)\);

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

  • prob_alpha_plus is a numeric vector of (\(\alpha^+_{i,i+1}, ..., \alpha^+_{i,j-1}, \alpha^+_{i,j}\)), where

    • for \(j = i+1\), \(\alpha^+_{i,j} = P(\{Z_j \geq b_j\} \mid Z_i = z_i)\);

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

  • prob_beta is a numeric vector of (\(\beta_{i,i+1}, ..., \beta_{i,j-1}, \beta_{i,j}\)), where

    • for \(j = i+1\), \(\beta_{i,j} = P(\{Z_j \leq a_j\} \mid Z_i = z_i)\);

    • for \(j > i+1\), \(\beta_{i,j} = P(\{Z_j \leq a_j\} \& \{\cap_{m=i+1}^{j-1} a_m \leq Z_m < b_m\} \mid Z_i = z_i)\).

Examples

library(gsDesign2)
library(gsDesign)
#> 
#> Attaching package: ‘gsDesign’
#> The following objects are masked from ‘package:gsDesign2’:
#> 
#>     as_gt, as_rtf
library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union

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))

# Example 1: futility is tested at all analyses
# original design ----
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))
#> $prob_alpha
#> [1] 1.264453e-09 1.010150e-03 1.242573e-02
#> 
#> $prob_alpha_plus
#> [1] 1.264453e-09 1.432083e-03 1.186581e-01
#> 
#> $prob_beta
#> [1] 0.971766584 0.027223265 0.004116917
#> 

# 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))
#> $prob_alpha
#> [1] 8.260564e-09 8.860056e-03 3.790670e-02
#> 
#> $prob_alpha_plus
#> [1] 8.260564e-09 1.477123e-02 5.011579e-01
#> 
#> $prob_beta
#> [1] 0.944398183 0.046741752 0.001632655
#> 

# Example 2: futility is only tested at IA1
# original design ----
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),
                   test_upper = c(FALSE, TRUE, TRUE, TRUE),
                   lower = gs_spending_bound,
                   lpar = list(sf = sfLDOF, total_spend = 0.1),
                   test_lower = c(TRUE, FALSE, FALSE, FALSE),
                   h1_spending = 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))
#> $prob_alpha
#> [1] 1.282562e-09 1.144666e-03 1.033265e-01
#> 
#> $prob_alpha_plus
#> [1] 1.282562e-09 1.144666e-03 1.033422e-01
#> 
#> $prob_beta
#> [1] 0.0000000 0.9988553 0.8955453
#> 

# 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))
#> $prob_alpha
#> [1] 7.790501e-09 1.168612e-02 4.566769e-01
#> 
#> $prob_alpha_plus
#> [1] 7.790501e-09 1.168612e-02 4.562043e-01
#> 
#> $prob_beta
#> [1] 0.0000000 0.9883139 0.5318764
#>