Group sequential design using average hazard ratio under non-proportional hazards
Source:R/gs_design_ahr.R
gs_design_ahr.RdGroup sequential design using average hazard ratio under non-proportional hazards
Usage
gs_design_ahr(
enroll_rate = define_enroll_rate(duration = c(2, 2, 10), rate = c(3, 6, 9)),
fail_rate = define_fail_rate(duration = c(3, 100), fail_rate = log(2)/c(9, 18), hr =
c(0.9, 0.6), dropout_rate = 0.001),
alpha = 0.025,
beta = 0.1,
info_frac = NULL,
analysis_time = 36,
ratio = 1,
binding = FALSE,
upper = gs_b,
upar = gsDesign::gsDesign(k = 3, test.type = 1, n.I = c(0.25, 0.75, 1), sfu = sfLDOF,
sfupar = NULL)$upper$bound,
lower = gs_b,
lpar = c(qnorm(0.1), -Inf, -Inf),
h1_spending = TRUE,
test_upper = TRUE,
test_lower = TRUE,
info_scale = c("h0_h1_info", "h0_info", "h1_info"),
r = 18,
tol = 1e-06,
interval = c(0.01, 1000)
)Arguments
- enroll_rate
Enrollment rates.
- fail_rate
Failure and dropout rates.
- alpha
One-sided Type I error.
- beta
Type II error.
- info_frac
Targeted information fraction at each analysis.
- analysis_time
Minimum time of analysis.
- ratio
Experimental:Control randomization ratio (not yet implemented).
- binding
Indicator of whether futility bound is binding; default of
FALSEis recommended.- upper
Function to compute upper bound.
- upar
Parameters passed to
upper.- lower
Function to compute lower bound.
- lpar
Parameters passed to
lower.- h1_spending
Indicator that lower bound to be set by spending under alternate hypothesis (input
fail_rate) if spending is used for lower bound.- test_upper
Indicator of which analyses should include an upper (efficacy) bound; single value of
TRUE(default) indicates all analyses; otherwise, a logical vector of the same length asinfoshould indicate which analyses will have an efficacy bound.- test_lower
Indicator of which analyses should include an lower bound; single value of
TRUE(default) indicates all analyses; single valueFALSEindicated no lower bound; otherwise, a logical vector of the same length asinfoshould indicate which analyses will have a lower bound.- info_scale
Information scale for calculation. Options are:
"h0_h1_info"(default): variance under both null and alternative hypotheses is used."h0_info": variance under null hypothesis is used."h1_info": variance under alternative hypothesis is used.
- r
Integer value controlling grid for numerical integration as in Jennison and Turnbull (2000); default is 18, range is 1 to 80. Larger values provide larger number of grid points and greater accuracy. Normally,
rwill not be changed by the user.- tol
Tolerance parameter for boundary convergence (on Z-scale).
- interval
An interval that is presumed to include the time at which expected event count is equal to targeted event.
Examples
library(gsDesign)
#>
#> Attaching package: ‘gsDesign’
#> The following objects are masked from ‘package:gsDesign2’:
#>
#> as_gt, as_rtf
library(gsDesign2)
library(dplyr)
# Example 1 ----
# call with defaults
gs_design_ahr()
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 1
#>
#> $input$analysis_time
#> [1] 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 13.2
#> 2 All 2 26.4
#> 3 All 10 39.7
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 1 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.9 0.025 1.96 0.795 0.0250
#>
#> $analysis
#> # A tibble: 1 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 36 476. 292. 0.683 0.381 71.7 73.0 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# Example 2 ----
# Single analysis
gs_design_ahr(analysis_time = 40)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 1
#>
#> $input$analysis_time
#> [1] 40
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 11.9
#> 2 All 2 23.8
#> 3 All 10 35.6
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 1 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.9 0.025 1.96 0.791 0.0250
#>
#> $analysis
#> # A tibble: 1 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 40 428. 280. 0.678 0.389 68.8 69.9 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# Example 3 ----
# Multiple analysis_time
gs_design_ahr(analysis_time = c(12, 24, 36))
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3080415 0.7407917 1.0000000
#>
#> $input$analysis_time
#> [1] 12 24 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 14.0
#> 2 All 2 27.9
#> 3 All 10 41.9
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 4 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000507 0.00000737 4.33 0.411 0.00000737
#> 2 1 lower 0.0111 0.100 -1.28 1.30 0.9
#> 3 2 upper 0.566 0.00965 2.34 0.734 0.00965
#> 4 3 upper 0.900 0.0251 2.01 0.795 0.0221
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 419. 95.0 0.811 0.210 23.4 23.8 0.309
#> 2 2 24 503. 228. 0.715 0.335 55.9 57.1 0.738
#> 3 3 36 503. 308. 0.683 0.381 75.8 77.1 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# Example 4 ----
# Specified information fraction
# \donttest{
gs_design_ahr(info_frac = c(.25, .75, 1), analysis_time = 36)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.25 0.75 1.00
#>
#> $input$analysis_time
#> [1] 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 14.2
#> 2 All 2 28.4
#> 3 All 10 42.5
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 4 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000282 0.00000737 4.33 0.376 0.00000737
#> 2 1 lower 0.0166 0.100 -1.28 1.34 0.9
#> 3 2 upper 0.585 0.00965 2.34 0.737 0.00965
#> 4 3 upper 0.900 0.0249 2.01 0.797 0.0221
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 10.7 371. 78.3 0.823 0.195 19.3 19.6 0.251
#> 2 2 24.4 510. 235. 0.714 0.337 57.4 58.7 0.747
#> 3 3 36 510. 313. 0.683 0.381 76.9 78.3 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# }
# Example 5 ----
# multiple analysis times & info_frac
# driven by times
gs_design_ahr(info_frac = c(.25, .75, 1), analysis_time = c(12, 25, 36))
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.25 0.75 1.00
#>
#> $input$analysis_time
#> [1] 12 25 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 14.0
#> 2 All 2 27.9
#> 3 All 10 41.9
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 4 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000507 0.00000737 4.33 0.411 0.00000737
#> 2 1 lower 0.0111 0.100 -1.28 1.30 0.9
#> 3 2 upper 0.600 0.00965 2.34 0.738 0.00965
#> 4 3 upper 0.900 0.0248 2.01 0.795 0.0221
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 419. 95.0 0.811 0.210 23.4 23.7 0.309
#> 2 2 25 503. 236. 0.711 0.341 57.8 59.1 0.763
#> 3 3 36 503. 308. 0.683 0.381 75.7 77.1 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# driven by info_frac
# \donttest{
gs_design_ahr(info_frac = c(1 / 3, .8, 1), analysis_time = c(12, 25, 36))
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3333333 0.8000000 1.0000000
#>
#> $input$analysis_time
#> [1] 12 25 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.332634 2.339816 2.011793
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -1.281552 -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 13.9
#> 2 All 2 27.8
#> 3 All 10 41.7
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 4 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000645 0.00000737 4.33 0.425 0.00000737
#> 2 1 lower 0.00928 0.100 -1.28 1.29 0.9
#> 3 2 upper 0.640 0.00965 2.34 0.742 0.00965
#> 4 3 upper 0.900 0.0244 2.01 0.795 0.0221
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12.5 439. 102. 0.806 0.216 25.2 25.6 0.334
#> 2 2 26.4 501. 246. 0.706 0.348 60.1 61.4 0.797
#> 3 3 36 501. 307. 0.683 0.381 75.4 76.8 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# }
# Example 6 ----
# 2-sided symmetric design with O'Brien-Fleming spending
# \donttest{
gs_design_ahr(
analysis_time = c(12, 24, 36),
binding = TRUE,
upper = gs_spending_bound,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
lower = gs_spending_bound,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
h1_spending = FALSE
)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3080415 0.7407917 1.0000000
#>
#> $input$analysis_time
#> [1] 12 24 36
#>
#> $input$upper
#> function (k = 1, par = list(sf = gsDesign::sfLDOF, total_spend = 0.025,
#> param = NULL, timing = NULL, max_info = NULL), hgm1 = NULL,
#> theta = 0.1, info = 1:3, efficacy = TRUE, test_bound = TRUE,
#> r = 18, tol = 1e-06)
#> {
#> if (length(test_bound) == 1 && k > 1) {
#> test_bound <- rep(test_bound, k)
#> }
#> if (!is.null(par$timing)) {
#> timing <- par$timing
#> }
#> else {
#> if (is.null(par$max_info)) {
#> timing <- info/max(info)
#> }
#> else {
#> timing <- info/par$max_info
#> }
#> }
#> spend <- par$sf(alpha = par$total_spend, t = timing, param = par$param)$spend
#> old_spend <- 0
#> for (i in 1:k) {
#> if (test_bound[i]) {
#> xx <- spend[i] - old_spend
#> old_spend <- spend[i]
#> spend[i] <- xx
#> }
#> else {
#> spend[i] <- 0
#> }
#> }
#> spend <- spend[k]
#> if (!efficacy) {
#> if (spend <= 0) {
#> return(-Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> a <- qnorm(spend) + sqrt(info[k]) * theta[k]
#> if (k == 1) {
#> return(a)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> adelta <- 1
#> j <- 0
#> while (abs(adelta) > tol) {
#> hg <- hupdate(theta = theta[k], info = info[k], a = -Inf,
#> b = a, thetam1 = theta[k - 1], im1 = info[k -
#> 1], gm1 = hgm1, r = r)
#> i <- length(hg$h)
#> pik <- sum(hg$h)
#> adelta <- spend - pik
#> dplo <- hg$h[i]/hg$w[i]
#> if (adelta > dplo) {
#> adelta <- 1
#> }
#> else if (adelta < -dplo) {
#> adelta <- -1
#> }
#> else {
#> adelta <- adelta/dplo
#> }
#> a <- a + adelta
#> if (a > extreme_high) {
#> a <- extreme_high
#> }
#> else if (a < extreme_low) {
#> a <- extreme_low
#> }
#> if (abs(adelta) < tol) {
#> return(a)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> else {
#> if (spend <= 0) {
#> return(Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> b <- qnorm(spend, lower.tail = FALSE)
#> if (k == 1) {
#> return(b)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> bdelta <- 1
#> j <- 1
#> while (abs(bdelta) > tol) {
#> hg <- hupdate(theta = 0, info = info[k], a = b, b = Inf,
#> thetam1 = 0, im1 = info[k - 1], gm1 = hgm1, r = r)
#> pik <- sum(hg$h)
#> bdelta <- spend - pik
#> dpikdb <- hg$h[1]/hg$w[1]
#> if (bdelta > dpikdb) {
#> bdelta <- 1
#> }
#> else if (bdelta < -dpikdb) {
#> bdelta <- -1
#> }
#> else {
#> bdelta <- bdelta/dpikdb
#> }
#> b <- b - bdelta
#> if (b > extreme_high) {
#> b <- extreme_high
#> }
#> else if (b < extreme_low) {
#> b <- extreme_low
#> }
#> if (abs(bdelta) < tol) {
#> return(b)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> }
#> <bytecode: 0x557dd1cabf28>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> $input$upar$sf
#> function (alpha, t, param = NULL)
#> {
#> checkScalar(alpha, "numeric", c(0, Inf), c(FALSE, FALSE))
#> checkVector(t, "numeric", c(0, Inf), c(TRUE, FALSE))
#> if (is.null(param) || param < 0.005 || param > 20)
#> param <- 1
#> checkScalar(param, "numeric", c(0.005, 20), c(TRUE, TRUE))
#> t[t > 1] <- 1
#> if (param == 1) {
#> rho <- 1
#> txt <- "Lan-DeMets O'Brien-Fleming approximation"
#> parname <- "none"
#> }
#> else {
#> rho <- param
#> txt <- "Generalized Lan-DeMets O'Brien-Fleming"
#> parname <- "rho"
#> }
#> z <- -qnorm(alpha/2)
#> x <- list(name = txt, param = param, parname = parname, sf = sfLDOF,
#> spend = 2 * (1 - pnorm(z/t^(rho/2))), bound = NULL, prob = NULL)
#> class(x) <- "spendfn"
#> x
#> }
#> <bytecode: 0x557dd108f3d8>
#> <environment: namespace:gsDesign>
#>
#> $input$upar$total_spend
#> [1] 0.025
#>
#> $input$upar$param
#> NULL
#>
#> $input$upar$timing
#> NULL
#>
#>
#> $input$lower
#> function (k = 1, par = list(sf = gsDesign::sfLDOF, total_spend = 0.025,
#> param = NULL, timing = NULL, max_info = NULL), hgm1 = NULL,
#> theta = 0.1, info = 1:3, efficacy = TRUE, test_bound = TRUE,
#> r = 18, tol = 1e-06)
#> {
#> if (length(test_bound) == 1 && k > 1) {
#> test_bound <- rep(test_bound, k)
#> }
#> if (!is.null(par$timing)) {
#> timing <- par$timing
#> }
#> else {
#> if (is.null(par$max_info)) {
#> timing <- info/max(info)
#> }
#> else {
#> timing <- info/par$max_info
#> }
#> }
#> spend <- par$sf(alpha = par$total_spend, t = timing, param = par$param)$spend
#> old_spend <- 0
#> for (i in 1:k) {
#> if (test_bound[i]) {
#> xx <- spend[i] - old_spend
#> old_spend <- spend[i]
#> spend[i] <- xx
#> }
#> else {
#> spend[i] <- 0
#> }
#> }
#> spend <- spend[k]
#> if (!efficacy) {
#> if (spend <= 0) {
#> return(-Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> a <- qnorm(spend) + sqrt(info[k]) * theta[k]
#> if (k == 1) {
#> return(a)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> adelta <- 1
#> j <- 0
#> while (abs(adelta) > tol) {
#> hg <- hupdate(theta = theta[k], info = info[k], a = -Inf,
#> b = a, thetam1 = theta[k - 1], im1 = info[k -
#> 1], gm1 = hgm1, r = r)
#> i <- length(hg$h)
#> pik <- sum(hg$h)
#> adelta <- spend - pik
#> dplo <- hg$h[i]/hg$w[i]
#> if (adelta > dplo) {
#> adelta <- 1
#> }
#> else if (adelta < -dplo) {
#> adelta <- -1
#> }
#> else {
#> adelta <- adelta/dplo
#> }
#> a <- a + adelta
#> if (a > extreme_high) {
#> a <- extreme_high
#> }
#> else if (a < extreme_low) {
#> a <- extreme_low
#> }
#> if (abs(adelta) < tol) {
#> return(a)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> else {
#> if (spend <= 0) {
#> return(Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> b <- qnorm(spend, lower.tail = FALSE)
#> if (k == 1) {
#> return(b)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> bdelta <- 1
#> j <- 1
#> while (abs(bdelta) > tol) {
#> hg <- hupdate(theta = 0, info = info[k], a = b, b = Inf,
#> thetam1 = 0, im1 = info[k - 1], gm1 = hgm1, r = r)
#> pik <- sum(hg$h)
#> bdelta <- spend - pik
#> dpikdb <- hg$h[1]/hg$w[1]
#> if (bdelta > dpikdb) {
#> bdelta <- 1
#> }
#> else if (bdelta < -dpikdb) {
#> bdelta <- -1
#> }
#> else {
#> bdelta <- bdelta/dpikdb
#> }
#> b <- b - bdelta
#> if (b > extreme_high) {
#> b <- extreme_high
#> }
#> else if (b < extreme_low) {
#> b <- extreme_low
#> }
#> if (abs(bdelta) < tol) {
#> return(b)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> }
#> <bytecode: 0x557dd1cabf28>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> $input$lpar$sf
#> function (alpha, t, param = NULL)
#> {
#> checkScalar(alpha, "numeric", c(0, Inf), c(FALSE, FALSE))
#> checkVector(t, "numeric", c(0, Inf), c(TRUE, FALSE))
#> if (is.null(param) || param < 0.005 || param > 20)
#> param <- 1
#> checkScalar(param, "numeric", c(0.005, 20), c(TRUE, TRUE))
#> t[t > 1] <- 1
#> if (param == 1) {
#> rho <- 1
#> txt <- "Lan-DeMets O'Brien-Fleming approximation"
#> parname <- "none"
#> }
#> else {
#> rho <- param
#> txt <- "Generalized Lan-DeMets O'Brien-Fleming"
#> parname <- "rho"
#> }
#> z <- -qnorm(alpha/2)
#> x <- list(name = txt, param = param, parname = parname, sf = sfLDOF,
#> spend = 2 * (1 - pnorm(z/t^(rho/2))), bound = NULL, prob = NULL)
#> class(x) <- "spendfn"
#> x
#> }
#> <bytecode: 0x557dd108f3d8>
#> <environment: namespace:gsDesign>
#>
#> $input$lpar$total_spend
#> [1] 0.025
#>
#> $input$lpar$param
#> NULL
#>
#> $input$lpar$timing
#> NULL
#>
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] FALSE
#>
#> $input$binding
#> [1] TRUE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 13.7
#> 2 All 2 27.5
#> 3 All 10 41.2
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 6 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.00226 0.0000538 3.87 0.449 0.0000538
#> 2 1 lower 0.000000613 0.0000538 -3.87 2.23 1.00
#> 3 2 upper 0.550 0.00921 2.36 0.730 0.00919
#> 4 2 lower 0.00000125 0.00921 -2.36 1.37 0.991
#> 5 3 upper 0.900 0.0250 2.01 0.794 0.0222
#> 6 3 lower 0.00000128 0.0250 -2.01 1.26 0.978
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 412. 93.4 0.811 0.210 23.0 23.3 0.309
#> 2 2 24 494. 224. 0.715 0.335 54.9 56.1 0.738
#> 3 3 36 494. 303. 0.683 0.381 74.4 75.8 1
#>
#> attr(,"class")
#> [1] "ahr" "gs_design" "list"
# }
# 2-sided asymmetric design with O'Brien-Fleming upper spending
# Pocock lower spending under H1 (NPH)
# \donttest{
gs_design_ahr(
analysis_time = c(12, 24, 36),
binding = TRUE,
upper = gs_spending_bound,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
lower = gs_spending_bound,
lpar = list(sf = gsDesign::sfLDPocock, total_spend = 0.1, param = NULL, timing = NULL),
h1_spending = TRUE
)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.025
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3080415 0.7407917 1.0000000
#>
#> $input$analysis_time
#> [1] 12 24 36
#>
#> $input$upper
#> function (k = 1, par = list(sf = gsDesign::sfLDOF, total_spend = 0.025,
#> param = NULL, timing = NULL, max_info = NULL), hgm1 = NULL,
#> theta = 0.1, info = 1:3, efficacy = TRUE, test_bound = TRUE,
#> r = 18, tol = 1e-06)
#> {
#> if (length(test_bound) == 1 && k > 1) {
#> test_bound <- rep(test_bound, k)
#> }
#> if (!is.null(par$timing)) {
#> timing <- par$timing
#> }
#> else {
#> if (is.null(par$max_info)) {
#> timing <- info/max(info)
#> }
#> else {
#> timing <- info/par$max_info
#> }
#> }
#> spend <- par$sf(alpha = par$total_spend, t = timing, param = par$param)$spend
#> old_spend <- 0
#> for (i in 1:k) {
#> if (test_bound[i]) {
#> xx <- spend[i] - old_spend
#> old_spend <- spend[i]
#> spend[i] <- xx
#> }
#> else {
#> spend[i] <- 0
#> }
#> }
#> spend <- spend[k]
#> if (!efficacy) {
#> if (spend <= 0) {
#> return(-Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> a <- qnorm(spend) + sqrt(info[k]) * theta[k]
#> if (k == 1) {
#> return(a)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> adelta <- 1
#> j <- 0
#> while (abs(adelta) > tol) {
#> hg <- hupdate(theta = theta[k], info = info[k], a = -Inf,
#> b = a, thetam1 = theta[k - 1], im1 = info[k -
#> 1], gm1 = hgm1, r = r)
#> i <- length(hg$h)
#> pik <- sum(hg$h)
#> adelta <- spend - pik
#> dplo <- hg$h[i]/hg$w[i]
#> if (adelta > dplo) {
#> adelta <- 1
#> }
#> else if (adelta < -dplo) {
#> adelta <- -1
#> }
#> else {
#> adelta <- adelta/dplo
#> }
#> a <- a + adelta
#> if (a > extreme_high) {
#> a <- extreme_high
#> }
#> else if (a < extreme_low) {
#> a <- extreme_low
#> }
#> if (abs(adelta) < tol) {
#> return(a)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> else {
#> if (spend <= 0) {
#> return(Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> b <- qnorm(spend, lower.tail = FALSE)
#> if (k == 1) {
#> return(b)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> bdelta <- 1
#> j <- 1
#> while (abs(bdelta) > tol) {
#> hg <- hupdate(theta = 0, info = info[k], a = b, b = Inf,
#> thetam1 = 0, im1 = info[k - 1], gm1 = hgm1, r = r)
#> pik <- sum(hg$h)
#> bdelta <- spend - pik
#> dpikdb <- hg$h[1]/hg$w[1]
#> if (bdelta > dpikdb) {
#> bdelta <- 1
#> }
#> else if (bdelta < -dpikdb) {
#> bdelta <- -1
#> }
#> else {
#> bdelta <- bdelta/dpikdb
#> }
#> b <- b - bdelta
#> if (b > extreme_high) {
#> b <- extreme_high
#> }
#> else if (b < extreme_low) {
#> b <- extreme_low
#> }
#> if (abs(bdelta) < tol) {
#> return(b)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> }
#> <bytecode: 0x557dd1cabf28>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> $input$upar$sf
#> function (alpha, t, param = NULL)
#> {
#> checkScalar(alpha, "numeric", c(0, Inf), c(FALSE, FALSE))
#> checkVector(t, "numeric", c(0, Inf), c(TRUE, FALSE))
#> if (is.null(param) || param < 0.005 || param > 20)
#> param <- 1
#> checkScalar(param, "numeric", c(0.005, 20), c(TRUE, TRUE))
#> t[t > 1] <- 1
#> if (param == 1) {
#> rho <- 1
#> txt <- "Lan-DeMets O'Brien-Fleming approximation"
#> parname <- "none"
#> }
#> else {
#> rho <- param
#> txt <- "Generalized Lan-DeMets O'Brien-Fleming"
#> parname <- "rho"
#> }
#> z <- -qnorm(alpha/2)
#> x <- list(name = txt, param = param, parname = parname, sf = sfLDOF,
#> spend = 2 * (1 - pnorm(z/t^(rho/2))), bound = NULL, prob = NULL)
#> class(x) <- "spendfn"
#> x
#> }
#> <bytecode: 0x557dd108f3d8>
#> <environment: namespace:gsDesign>
#>
#> $input$upar$total_spend
#> [1] 0.025
#>
#> $input$upar$param
#> NULL
#>
#> $input$upar$timing
#> NULL
#>
#>
#> $input$lower
#> function (k = 1, par = list(sf = gsDesign::sfLDOF, total_spend = 0.025,
#> param = NULL, timing = NULL, max_info = NULL), hgm1 = NULL,
#> theta = 0.1, info = 1:3, efficacy = TRUE, test_bound = TRUE,
#> r = 18, tol = 1e-06)
#> {
#> if (length(test_bound) == 1 && k > 1) {
#> test_bound <- rep(test_bound, k)
#> }
#> if (!is.null(par$timing)) {
#> timing <- par$timing
#> }
#> else {
#> if (is.null(par$max_info)) {
#> timing <- info/max(info)
#> }
#> else {
#> timing <- info/par$max_info
#> }
#> }
#> spend <- par$sf(alpha = par$total_spend, t = timing, param = par$param)$spend
#> old_spend <- 0
#> for (i in 1:k) {
#> if (test_bound[i]) {
#> xx <- spend[i] - old_spend
#> old_spend <- spend[i]
#> spend[i] <- xx
#> }
#> else {
#> spend[i] <- 0
#> }
#> }
#> spend <- spend[k]
#> if (!efficacy) {
#> if (spend <= 0) {
#> return(-Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> a <- qnorm(spend) + sqrt(info[k]) * theta[k]
#> if (k == 1) {
#> return(a)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> adelta <- 1
#> j <- 0
#> while (abs(adelta) > tol) {
#> hg <- hupdate(theta = theta[k], info = info[k], a = -Inf,
#> b = a, thetam1 = theta[k - 1], im1 = info[k -
#> 1], gm1 = hgm1, r = r)
#> i <- length(hg$h)
#> pik <- sum(hg$h)
#> adelta <- spend - pik
#> dplo <- hg$h[i]/hg$w[i]
#> if (adelta > dplo) {
#> adelta <- 1
#> }
#> else if (adelta < -dplo) {
#> adelta <- -1
#> }
#> else {
#> adelta <- adelta/dplo
#> }
#> a <- a + adelta
#> if (a > extreme_high) {
#> a <- extreme_high
#> }
#> else if (a < extreme_low) {
#> a <- extreme_low
#> }
#> if (abs(adelta) < tol) {
#> return(a)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> else {
#> if (spend <= 0) {
#> return(Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> b <- qnorm(spend, lower.tail = FALSE)
#> if (k == 1) {
#> return(b)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> bdelta <- 1
#> j <- 1
#> while (abs(bdelta) > tol) {
#> hg <- hupdate(theta = 0, info = info[k], a = b, b = Inf,
#> thetam1 = 0, im1 = info[k - 1], gm1 = hgm1, r = r)
#> pik <- sum(hg$h)
#> bdelta <- spend - pik
#> dpikdb <- hg$h[1]/hg$w[1]
#> if (bdelta > dpikdb) {
#> bdelta <- 1
#> }
#> else if (bdelta < -dpikdb) {
#> bdelta <- -1
#> }
#> else {
#> bdelta <- bdelta/dpikdb
#> }
#> b <- b - bdelta
#> if (b > extreme_high) {
#> b <- extreme_high
#> }
#> else if (b < extreme_low) {
#> b <- extreme_low
#> }
#> if (abs(bdelta) < tol) {
#> return(b)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> }
#> <bytecode: 0x557dd1cabf28>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> $input$lpar$sf
#> function (alpha, t, param)
#> {
#> checkScalar(alpha, "numeric", c(0, Inf), c(FALSE, FALSE))
#> checkVector(t, "numeric", c(0, Inf), c(TRUE, FALSE))
#> t[t > 1] <- 1
#> x <- list(name = "Lan-DeMets Pocock approximation", param = NULL,
#> parname = "none", sf = sfLDPocock, spend = alpha * log(1 +
#> (exp(1) - 1) * t), bound = NULL, prob = NULL)
#> class(x) <- "spendfn"
#> x
#> }
#> <bytecode: 0x557dcb1bda40>
#> <environment: namespace:gsDesign>
#>
#> $input$lpar$total_spend
#> [1] 0.1
#>
#> $input$lpar$param
#> NULL
#>
#> $input$lpar$timing
#> NULL
#>
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] TRUE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 16.5
#> 2 All 2 32.9
#> 3 All 10 49.4
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 6 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.00305 0.0000538 3.87 0.481 0.0000538
#> 2 1 lower 0.0430 0.268 -0.619 1.12 0.732
#> 3 2 upper 0.638 0.00921 2.36 0.750 0.00920
#> 4 2 lower 0.0823 0.874 1.13 0.871 0.129
#> 5 3 upper 0.900 0.0250 1.98 0.813 0.0240
#> 6 3 lower 0.100 0.975 1.97 0.813 0.0243
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 494. 112. 0.811 0.210 27.6 28.0 0.309
#> 2 2 24 593. 269. 0.715 0.335 65.9 67.3 0.738
#> 3 3 36 593. 364. 0.683 0.381 89.3 90.9 1
#>
#> attr(,"class")
#> [1] "ahr" "gs_design" "list"
# }
# Example 7 ----
# \donttest{
gs_design_ahr(
alpha = 0.0125,
analysis_time = c(12, 24, 36),
upper = gs_spending_bound,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.0125, param = NULL, timing = NULL),
lower = gs_b,
lpar = rep(-Inf, 3)
)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.0125
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3080415 0.7407917 1.0000000
#>
#> $input$analysis_time
#> [1] 12 24 36
#>
#> $input$upper
#> function (k = 1, par = list(sf = gsDesign::sfLDOF, total_spend = 0.025,
#> param = NULL, timing = NULL, max_info = NULL), hgm1 = NULL,
#> theta = 0.1, info = 1:3, efficacy = TRUE, test_bound = TRUE,
#> r = 18, tol = 1e-06)
#> {
#> if (length(test_bound) == 1 && k > 1) {
#> test_bound <- rep(test_bound, k)
#> }
#> if (!is.null(par$timing)) {
#> timing <- par$timing
#> }
#> else {
#> if (is.null(par$max_info)) {
#> timing <- info/max(info)
#> }
#> else {
#> timing <- info/par$max_info
#> }
#> }
#> spend <- par$sf(alpha = par$total_spend, t = timing, param = par$param)$spend
#> old_spend <- 0
#> for (i in 1:k) {
#> if (test_bound[i]) {
#> xx <- spend[i] - old_spend
#> old_spend <- spend[i]
#> spend[i] <- xx
#> }
#> else {
#> spend[i] <- 0
#> }
#> }
#> spend <- spend[k]
#> if (!efficacy) {
#> if (spend <= 0) {
#> return(-Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> a <- qnorm(spend) + sqrt(info[k]) * theta[k]
#> if (k == 1) {
#> return(a)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> adelta <- 1
#> j <- 0
#> while (abs(adelta) > tol) {
#> hg <- hupdate(theta = theta[k], info = info[k], a = -Inf,
#> b = a, thetam1 = theta[k - 1], im1 = info[k -
#> 1], gm1 = hgm1, r = r)
#> i <- length(hg$h)
#> pik <- sum(hg$h)
#> adelta <- spend - pik
#> dplo <- hg$h[i]/hg$w[i]
#> if (adelta > dplo) {
#> adelta <- 1
#> }
#> else if (adelta < -dplo) {
#> adelta <- -1
#> }
#> else {
#> adelta <- adelta/dplo
#> }
#> a <- a + adelta
#> if (a > extreme_high) {
#> a <- extreme_high
#> }
#> else if (a < extreme_low) {
#> a <- extreme_low
#> }
#> if (abs(adelta) < tol) {
#> return(a)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> else {
#> if (spend <= 0) {
#> return(Inf)
#> }
#> if (length(theta) == 1)
#> theta <- rep(theta, length(info))
#> b <- qnorm(spend, lower.tail = FALSE)
#> if (k == 1) {
#> return(b)
#> }
#> mu <- theta[k] * sqrt(info[k])
#> extreme_low <- mu - 3 - 4 * log(r)
#> extreme_high <- mu + 3 + 4 * log(r)
#> bdelta <- 1
#> j <- 1
#> while (abs(bdelta) > tol) {
#> hg <- hupdate(theta = 0, info = info[k], a = b, b = Inf,
#> thetam1 = 0, im1 = info[k - 1], gm1 = hgm1, r = r)
#> pik <- sum(hg$h)
#> bdelta <- spend - pik
#> dpikdb <- hg$h[1]/hg$w[1]
#> if (bdelta > dpikdb) {
#> bdelta <- 1
#> }
#> else if (bdelta < -dpikdb) {
#> bdelta <- -1
#> }
#> else {
#> bdelta <- bdelta/dpikdb
#> }
#> b <- b - bdelta
#> if (b > extreme_high) {
#> b <- extreme_high
#> }
#> else if (b < extreme_low) {
#> b <- extreme_low
#> }
#> if (abs(bdelta) < tol) {
#> return(b)
#> }
#> j <- j + 1
#> if (j > 20) {
#> stop(paste("gs_spending_bound(): bound_update did not converge for lower bound calculation, analysis",
#> k, " !"))
#> }
#> }
#> }
#> }
#> <bytecode: 0x557dd1cabf28>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> $input$upar$sf
#> function (alpha, t, param = NULL)
#> {
#> checkScalar(alpha, "numeric", c(0, Inf), c(FALSE, FALSE))
#> checkVector(t, "numeric", c(0, Inf), c(TRUE, FALSE))
#> if (is.null(param) || param < 0.005 || param > 20)
#> param <- 1
#> checkScalar(param, "numeric", c(0.005, 20), c(TRUE, TRUE))
#> t[t > 1] <- 1
#> if (param == 1) {
#> rho <- 1
#> txt <- "Lan-DeMets O'Brien-Fleming approximation"
#> parname <- "none"
#> }
#> else {
#> rho <- param
#> txt <- "Generalized Lan-DeMets O'Brien-Fleming"
#> parname <- "rho"
#> }
#> z <- -qnorm(alpha/2)
#> x <- list(name = txt, param = param, parname = parname, sf = sfLDOF,
#> spend = 2 * (1 - pnorm(z/t^(rho/2))), bound = NULL, prob = NULL)
#> class(x) <- "spendfn"
#> x
#> }
#> <bytecode: 0x557dd108f3d8>
#> <environment: namespace:gsDesign>
#>
#> $input$upar$total_spend
#> [1] 0.0125
#>
#> $input$upar$param
#> NULL
#>
#> $input$upar$timing
#> NULL
#>
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -Inf -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 16.1
#> 2 All 2 32.2
#> 3 All 10 48.3
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 3 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000619 0.00000679 4.35 0.435 0.00000679
#> 2 2 upper 0.505 0.00371 2.68 0.719 0.00371
#> 3 3 upper 0.900 0.0125 2.28 0.785 0.0114
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 483. 109. 0.811 0.210 27.0 27.4 0.309
#> 2 2 24 579. 263. 0.715 0.335 64.3 65.8 0.738
#> 3 3 36 579. 355. 0.683 0.381 87.2 88.8 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
gs_design_ahr(
alpha = 0.0125,
analysis_time = c(12, 24, 36),
upper = gs_b,
upar = gsDesign::gsDesign(
k = 3, test.type = 1, n.I = c(.25, .75, 1),
sfu = sfLDOF, sfupar = NULL, alpha = 0.0125
)$upper$bound,
lower = gs_b,
lpar = rep(-Inf, 3)
)
#> $input
#> $input$enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 3
#> 2 All 2 6
#> 3 All 10 9
#>
#> $input$fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $input$alpha
#> [1] 0.0125
#>
#> $input$beta
#> [1] 0.1
#>
#> $input$ratio
#> [1] 1
#>
#> $input$info_frac
#> [1] 0.3080415 0.7407917 1.0000000
#>
#> $input$analysis_time
#> [1] 12 24 36
#>
#> $input$upper
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$upar
#> [1] 4.859940 2.658446 2.280095
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x557dd1ca8fd8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -Inf -Inf -Inf
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$h1_spending
#> [1] TRUE
#>
#> $input$binding
#> [1] FALSE
#>
#> $input$info_scale
#> [1] "h0_h1_info"
#>
#> $input$r
#> [1] 18
#>
#> $input$tol
#> [1] 1e-06
#>
#>
#> $enroll_rate
#> # A tibble: 3 × 3
#> stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 16.1
#> 2 All 2 32.2
#> 3 All 10 48.3
#>
#> $fail_rate
#> # A tibble: 2 × 5
#> stratum duration fail_rate dropout_rate hr
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.001 0.9
#> 2 All 100 0.0385 0.001 0.6
#>
#> $bound
#> # A tibble: 3 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.0000938 0.000000587 4.86 0.395 0.000000587
#> 2 2 upper 0.513 0.00393 2.66 0.721 0.00393
#> 3 3 upper 0.900 0.0125 2.28 0.785 0.0113
#>
#> $analysis
#> # A tibble: 3 × 9
#> analysis time n event ahr theta info info0 info_frac
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 12 483. 110. 0.811 0.210 27.0 27.4 0.309
#> 2 2 24 580. 263. 0.715 0.335 64.4 65.9 0.738
#> 3 3 36 580. 356. 0.683 0.381 87.3 88.9 1
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# }