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(
enrollRates = tibble::tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6,
9)),
failRates = tibble::tibble(Stratum = "All", duration = c(3, 100), failRate =
log(2)/c(9, 18), hr = c(0.9, 0.6), dropoutRate = rep(0.001, 2)),
ratio = 1,
alpha = 0.025,
beta = 0.1,
IF = NULL,
analysisTimes = 36,
binding = FALSE,
upper = gs_b,
upar = 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,
r = 18,
tol = 1e-06
)Arguments
- enrollRates
enrollment rates
- failRates
failure and dropout rates
- ratio
Experimental:Control randomization ratio (not yet implemented)
- alpha
One-sided Type I error
- beta
Type II error
- IF
Targeted information fraction at each analysis
- analysisTimes
Minimum time of analysis
- binding
indicator of whether futility bound is binding; default of FALSE is recommended
- upper
Function to compute upper bound
- upar
Parameter passed to
upper()- lower
Function to compute lower bound
- lpar
Parameter passed to
lower()- h1_spending
Indicator that lower bound to be set by spending under alternate hypothesis (input
failRates) 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 as
infoshould 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 value FALSE indicated no lower bound; otherwise, a logical vector of the same length as
infoshould indicate which analyses will have a lower bound- r
Integer, at least 2; default of 18 recommended by Jennison and Turnbull
- tol
Tolerance parameter for boundary convergence (on Z-scale)
Examples
library(gsDesign)
library(gsDesign2)
library(dplyr)
# call with defaults
gs_design_ahr()
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 1 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 36 476. 292. 1.96 0.9 0.683 0.381 71.7 73.0
#>
# Single analysis
gs_design_ahr(analysisTimes = 40)
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 1 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 40 428. 280. 1.96 0.9 0.678 0.389 68.8 69.9
#>
# Multiple analysisTimes
gs_design_ahr(analysisTimes = c(12,24,36))
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 12 419. 95.0 4.33 0.000454 0.811 0.210 23.4 23.8
#> 2 2 Upper 24 503. 229. 2.34 0.566 0.715 0.335 55.9 57.1
#> 3 3 Upper 36 503. 309. 2.01 0.900 0.683 0.381 75.8 77.1
#> 4 1 Lower 12 419. 95.0 -1.28 0.0108 0.811 0.210 23.4 23.8
#> 5 2 Lower 24 503. 229. -Inf 0.0108 0.715 0.335 55.9 57.1
#> 6 3 Lower 36 503. 309. -Inf 0.0108 0.683 0.381 75.8 77.1
#>
# Specified information fraction
gs_design_ahr(IF = c(.25,.75,1), analysisTimes = 36)
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 10.7 371. 78.3 4.33 0.000254 0.823 0.195 19.3 19.6
#> 2 2 Upper 24.4 511. 235. 2.34 0.585 0.714 0.337 57.4 58.7
#> 3 3 Upper 36 511. 313. 2.01 0.900 0.683 0.381 76.9 78.3
#> 4 1 Lower 10.7 371. 78.3 -1.28 0.0163 0.823 0.195 19.3 19.6
#> 5 2 Lower 24.4 511. 235. -Inf 0.0163 0.714 0.337 57.4 58.7
#> 6 3 Lower 36 511. 313. -Inf 0.0163 0.683 0.381 76.9 78.3
#>
# multiple analysis times & IF
# driven by times
gs_design_ahr(IF = c(.25,.75,1), analysisTimes = c(12,25,36))
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 12 419. 95.0 4.33 0.000454 0.811 0.210 23.4 23.8
#> 2 2 Upper 25 503. 236. 2.34 0.600 0.711 0.341 57.8 59.1
#> 3 3 Upper 36 503. 308. 2.01 0.900 0.683 0.381 75.8 77.1
#> 4 1 Lower 12 419. 95.0 -1.28 0.0108 0.811 0.210 23.4 23.8
#> 5 2 Lower 25 503. 236. -Inf 0.0108 0.711 0.341 57.8 59.1
#> 6 3 Lower 36 503. 308. -Inf 0.0108 0.683 0.381 75.8 77.1
#>
# driven by IF
gs_design_ahr(IF = c(1/3, .8, 1), analysisTimes = c(12,25,36))
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 12.5 439. 102. 4.33 0.000576 0.806 0.216 25.2 25.6
#> 2 2 Upper 26.4 501. 246. 2.34 0.640 0.706 0.348 60.1 61.4
#> 3 3 Upper 36 501. 307. 2.01 0.900 0.683 0.381 75.4 76.8
#> 4 1 Lower 12.5 439. 102. -1.28 0.00904 0.806 0.216 25.2 25.6
#> 5 2 Lower 26.4 501. 246. -Inf 0.00904 0.706 0.348 60.1 61.4
#> 6 3 Lower 36 501. 307. -Inf 0.00904 0.683 0.381 75.4 76.8
#>
# 2-sided symmetric design with O'Brien-Fleming spending
gs_design_ahr(analysisTimes = 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)
#> $enrollRates
#> # 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
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 12 412. 93.4 3.87 0.00208 0.811 0.210 23.0 23.4
#> 2 2 Upper 24 494. 225. 2.36 0.551 0.715 0.335 54.9 56.2
#> 3 3 Upper 36 494. 303. 2.01 0.900 0.683 0.381 74.5 75.8
#> 4 1 Lower 12 412. 93.4 -3.87 0.000000532 0.811 0.210 23.0 23.4
#> 5 2 Lower 24 494. 225. -2.36 0.00000116 0.715 0.335 54.9 56.2
#> 6 3 Lower 36 494. 303. -2.01 0.00000120 0.683 0.381 74.5 75.8
#>
# 2-sided asymmetric design with O'Brien-Fleming upper spending
# Pocock lower spending under H1 (NPH)
gs_design_ahr(analysisTimes = 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)
#> $enrollRates
#> # A tibble: 3 × 3
#> Stratum duration rate
#> <chr> <dbl> <dbl>
#> 1 All 2 16.5
#> 2 All 2 33.0
#> 3 All 10 49.5
#>
#> $failRates
#> # A tibble: 2 × 5
#> Stratum duration failRate hr dropoutRate
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 All 3 0.0770 0.9 0.001
#> 2 All 100 0.0385 0.6 0.001
#>
#> $bounds
#> # A tibble: 6 × 11
#> Analysis Bound Time N Events Z Probability AHR theta info info0
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 Upper 12 495. 112. 3.87 0.00281 0.811 0.210 27.7 28.1
#> 2 2 Upper 24 594. 270. 2.36 0.639 0.715 0.335 66.0 67.5
#> 3 3 Upper 36 594. 364. 1.98 0.900 0.683 0.381 89.5 91.1
#> 4 1 Lower 12 495. 112. -0.618 0.0426 0.811 0.210 27.7 28.1
#> 5 2 Lower 24 594. 270. 1.13 0.0819 0.715 0.335 66.0 67.5
#> 6 3 Lower 36 594. 364. 1.98 0.100 0.683 0.381 89.5 91.1
#>