In keaven/gsDesign2: Group Sequential Design with Non-Constant Effect
knitr::opts_chunk$set(echo = TRUE)
library(gt)
library(dplyr)
library(tidyr)
library(tibble)
library(ggplot2)
library(gsDesign)
devtools::load_all()
Overview
We consider a delayed effect scenario where
- The control group time-to-event distribution is exponential with a median of 15 months.
- The experimental group has a hazard ratio vs. control of 1 for 6 months and 0.6 thereafter.
- Enrollment at a constant rate for 12 months.
- Total study duration from 20 to 48 months.
- Exponential dropout rate of 0.001 per month.
enrollRates <- tibble(Stratum = "All", duration = 12, rate = 1)
failRates <- tibble(Stratum = "All",
duration = c(6, 100),
failRate = log(2) / 15,
hr = c(1, .6),
dropoutRate = 0.001)
enrollRates %>% gt() %>% tab_header(title = "Enrollment Table of Scenario 1")
failRates %>% gt() %>% tab_header(title = "Failure Table of Scenario 1")
For the above scenarios, we investigate the power, sample size and events under 6 tests:
FH05: The Fleming-Harrington with $\rho=0, \gamma=0.5$ test to obtain power of 85\% given 1-sided Type I error of 0.025. FH00: The regular logrank test with $\rho=0, \gamma=0$ under fixed study duration $\in{20, 24, 28, \ldots, 60}$.mc2_test: The Max Combo test including 2 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1)}$.mc2_test: The Max Combo test including 3 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0.5, \tau = -1)}$.mc4_test: The Max Combo test including 4 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0, \tau = -1)}$.MB6: The Magirr-Burman with $\rho=-1, \gamma=0, \tau = 6$ test with fixed study duration $\in{20, 24, 28, \ldots, 60}$.
We then compute power for the logrank test.
The general summary is that the Fleming-Harrington test has a meaningful power gain relative to logrank regardless of the study durations evaluated.
tab <- NULL
for(trial_duration in seq(24, 60, 4)){
# Fleming-Harrington rho=0, gamma=0.5 test
FH05 <- gs_design_wlr(enrollRates = enrollRates,
failRates = failRates,
ratio = 1,
alpha = 0.025, beta = 0.15,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)},
upar = qnorm(.975),
lpar = -Inf,
analysisTimes = trial_duration)
# regular logrank test
FH00 <- gs_power_wlr(enrollRates = FH05$enrollRates,
failRates = failRates,
ratio = 1,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0)},
upar = qnorm(.975),
lpar = -Inf,
analysisTimes = trial_duration,
events = .1)
# max combo test 1
mc2_test <- data.frame(rho = 0, gamma = c(0, .5), tau = -1,
test = 1:2, Analysis = 1, analysisTimes = trial_duration)
MC2 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates,
fh_test = mc2_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# max combo test 2
mc3_test <- data.frame(rho = c(0, 0, .5), gamma = c(0, .5, .5), tau = -1,
test = 1:3, Analysis = 1, analysisTimes = trial_duration)
MC3 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates,
fh_test = mc3_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# max combo test
mc4_test <- data.frame(rho = c(0, 0, .5, .5), gamma = c(0, .5, .5, 0), tau = -1,
test = 1:4, Analysis = 1, analysisTimes = trial_duration)
MC4 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates,
fh_test = mc4_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# Magirr-Burman rho=-1, gamma=0, tau = 6 test
MB6 <- gs_power_wlr(enrollRates = FH05$enrollRates,
failRates = failRates,
ratio = 1,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = -1, gamma = 0, tau = 20)},
upar = qnorm(.975),
lpar = -Inf,
analysisTimes = trial_duration,
events = .1)
tab_new <- tibble(`Study duration` = trial_duration,
N = FH05$analysis$N[1],
Events = FH05$analysi$Events[1],
`Events/N` = Events/N,
# we use the AHR from regular WLR as the AHR of different max combo test
AHR = as.numeric(FH00$analysis$AHR[1]),
`FH(0, 0.5) power` = FH05$bounds$Probability[1],
`FH(0, 0) power` = FH00$bounds$Probability[1],
`MC2 power` = MC2$bounds$Probability[1],
`MC4 power` = MC4$bounds$Probability[1],
`MC3 power` = MC3$bounds$Probability[1],
`MB6 power` = MB6$bounds$Probability[1])
tab <- rbind(tab, tab_new)
}
tab %>%
gt() %>%
fmt_number(columns = c(2, 3), decimals = 1) %>%
fmt_number(columns = 4, decimals = 2) %>%
fmt_number(columns = 5, decimals = 4) %>%
fmt_number(columns = 6:11, decimals = 2)
An Alternative Scenario
Now we consider an alternate scenario where the placebo group starts with the same median, but then has a piecewise change to a median of 30 after 16 months and with a hazard ratio of 0.85 during that late period.
enrollRates <- tibble(Stratum = "All", duration = 12, rate = 1)
failRates <- tibble(Stratum = "All",
duration = c(6, 10, 100),
# in Scenario 1: failRate = log(2) / 15,
failRate = log(2) / c(15, 15, 30),
# in Scenario 1: hr = c(1, .6)
hr = c(1, .6, .85),
dropoutRate = 0.001)
enrollRates %>% gt() %>% tab_header(title = "Enrollment Table of Scenario 2")
failRates %>% gt() %>% tab_header(title = "Failure Table of Scenario 2")
tab <- NULL
for(trial_duration in seq(20, 60, 4)){
# Fleming-Harrington rho=0, gamma=0.5 test
FH05 <- gs_design_wlr(enrollRates = enrollRates,
failRates = failRates,
ratio = 1,
alpha = 0.025, beta = 0.15,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)},
upper = gs_b,
upar = qnorm(.975),
lower = gs_b,
lpar = -Inf,
analysisTimes = trial_duration)
# regular logrank test
FH00 <- gs_power_wlr(enrollRates = FH05$enrollRates,
failRates = failRates,
ratio = 1,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0)},
upper = gs_b,
upar = qnorm(.975),
lower = gs_b,
lpar = -Inf,
analysisTimes = trial_duration,
events = .1)
# max combo test
mc2_test <- data.frame(rho = 0, gamma = c(0, .5), tau = -1,
test = 1:2, Analysis = 1, analysisTimes = trial_duration)
MC2 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates,
fh_test = mc2_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# max combo test
mc3_test <- data.frame(rho = c(0,0,.5), gamma = c(0, .5, .5), tau = -1,
test = 1:3, Analysis = 1, analysisTimes = trial_duration)
MC3 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates,
fh_test = mc3_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# max combo test
mc4_test <- data.frame(rho = c(0,0,.5,.5), gamma = c(0, .5, .5, 0), tau = -1,
test = 1:4, Analysis = 1, analysisTimes = trial_duration)
MC4 <- gs_power_combo(enrollRates = FH05$enrollRates,
failRates = failRates, fh_test = mc4_test,
upper = gs_spending_combo,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_spending_combo,
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01))
# Magirr-Burman rho=-1, gamma=0, tau = 6 test
MB6 <- gs_power_wlr(enrollRates = FH05$enrollRates,
failRates = failRates,
ratio = 1,
weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = -1, gamma = 0, tau = 6)},
upar = qnorm(.975),
lpar = -Inf,
analysisTimes = trial_duration,
events = .1)
tab_new <- tibble(`Study duration` = trial_duration,
N = FH05$analysis$N[1],
Events = FH05$analysi$Events[1],
`Events/N` = Events/N,
# we use the AHR from regular WLR as the AHR of different max combo test
AHR = as.numeric(FH00$analysis$AHR[1]),
`FH(0, 0.5) power` = FH05$bounds$Probability[1],
`FH(0, 0) power` = FH00$bounds$Probability[1],
`MC2 power` = MC2$bounds$Probability[1],
`MC4 power` = MC4$bounds$Probability[1],
`MC3 power` = MC3$bounds$Probability[1],
`MB6 power` = MB6$bounds$Probability[1])
tab <- rbind(tab, tab_new)
}
tab %>%
gt() %>%
fmt_number(columns = c(2, 3), decimals = 1) %>%
fmt_number(columns = 4, decimals = 2) %>%
fmt_number(columns = 5, decimals = 4) %>%
fmt_number(columns = 6:11, decimals = 2)
keaven/gsDesign2 documentation built on Oct. 13, 2022, 8:42 p.m.
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knitr::opts_chunk$set(echo = TRUE)
library(gt) library(dplyr) library(tidyr) library(tibble) library(ggplot2) library(gsDesign) devtools::load_all()
Overview
We consider a delayed effect scenario where
- The control group time-to-event distribution is exponential with a median of 15 months.
- The experimental group has a hazard ratio vs. control of 1 for 6 months and 0.6 thereafter.
- Enrollment at a constant rate for 12 months.
- Total study duration from 20 to 48 months.
- Exponential dropout rate of 0.001 per month.
enrollRates <- tibble(Stratum = "All", duration = 12, rate = 1) failRates <- tibble(Stratum = "All", duration = c(6, 100), failRate = log(2) / 15, hr = c(1, .6), dropoutRate = 0.001) enrollRates %>% gt() %>% tab_header(title = "Enrollment Table of Scenario 1") failRates %>% gt() %>% tab_header(title = "Failure Table of Scenario 1")
For the above scenarios, we investigate the power, sample size and events under 6 tests:
FH05: The Fleming-Harrington with $\rho=0, \gamma=0.5$ test to obtain power of 85\% given 1-sided Type I error of 0.025.FH00: The regular logrank test with $\rho=0, \gamma=0$ under fixed study duration $\in{20, 24, 28, \ldots, 60}$.mc2_test: The Max Combo test including 2 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1)}$.mc2_test: The Max Combo test including 3 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0.5, \tau = -1)}$.mc4_test: The Max Combo test including 4 WLR tests, i.e., ${(\rho=0, \gamma=0, \tau = -1), (\rho=0, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0.5, \tau = -1), (\rho=0.5, \gamma=0, \tau = -1)}$.MB6: The Magirr-Burman with $\rho=-1, \gamma=0, \tau = 6$ test with fixed study duration $\in{20, 24, 28, \ldots, 60}$.
We then compute power for the logrank test. The general summary is that the Fleming-Harrington test has a meaningful power gain relative to logrank regardless of the study durations evaluated.
tab <- NULL for(trial_duration in seq(24, 60, 4)){ # Fleming-Harrington rho=0, gamma=0.5 test FH05 <- gs_design_wlr(enrollRates = enrollRates, failRates = failRates, ratio = 1, alpha = 0.025, beta = 0.15, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)}, upar = qnorm(.975), lpar = -Inf, analysisTimes = trial_duration) # regular logrank test FH00 <- gs_power_wlr(enrollRates = FH05$enrollRates, failRates = failRates, ratio = 1, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0)}, upar = qnorm(.975), lpar = -Inf, analysisTimes = trial_duration, events = .1) # max combo test 1 mc2_test <- data.frame(rho = 0, gamma = c(0, .5), tau = -1, test = 1:2, Analysis = 1, analysisTimes = trial_duration) MC2 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc2_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # max combo test 2 mc3_test <- data.frame(rho = c(0, 0, .5), gamma = c(0, .5, .5), tau = -1, test = 1:3, Analysis = 1, analysisTimes = trial_duration) MC3 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc3_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # max combo test mc4_test <- data.frame(rho = c(0, 0, .5, .5), gamma = c(0, .5, .5, 0), tau = -1, test = 1:4, Analysis = 1, analysisTimes = trial_duration) MC4 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc4_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # Magirr-Burman rho=-1, gamma=0, tau = 6 test MB6 <- gs_power_wlr(enrollRates = FH05$enrollRates, failRates = failRates, ratio = 1, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = -1, gamma = 0, tau = 20)}, upar = qnorm(.975), lpar = -Inf, analysisTimes = trial_duration, events = .1) tab_new <- tibble(`Study duration` = trial_duration, N = FH05$analysis$N[1], Events = FH05$analysi$Events[1], `Events/N` = Events/N, # we use the AHR from regular WLR as the AHR of different max combo test AHR = as.numeric(FH00$analysis$AHR[1]), `FH(0, 0.5) power` = FH05$bounds$Probability[1], `FH(0, 0) power` = FH00$bounds$Probability[1], `MC2 power` = MC2$bounds$Probability[1], `MC4 power` = MC4$bounds$Probability[1], `MC3 power` = MC3$bounds$Probability[1], `MB6 power` = MB6$bounds$Probability[1]) tab <- rbind(tab, tab_new) } tab %>% gt() %>% fmt_number(columns = c(2, 3), decimals = 1) %>% fmt_number(columns = 4, decimals = 2) %>% fmt_number(columns = 5, decimals = 4) %>% fmt_number(columns = 6:11, decimals = 2)
An Alternative Scenario
Now we consider an alternate scenario where the placebo group starts with the same median, but then has a piecewise change to a median of 30 after 16 months and with a hazard ratio of 0.85 during that late period.
enrollRates <- tibble(Stratum = "All", duration = 12, rate = 1) failRates <- tibble(Stratum = "All", duration = c(6, 10, 100), # in Scenario 1: failRate = log(2) / 15, failRate = log(2) / c(15, 15, 30), # in Scenario 1: hr = c(1, .6) hr = c(1, .6, .85), dropoutRate = 0.001) enrollRates %>% gt() %>% tab_header(title = "Enrollment Table of Scenario 2") failRates %>% gt() %>% tab_header(title = "Failure Table of Scenario 2")
tab <- NULL for(trial_duration in seq(20, 60, 4)){ # Fleming-Harrington rho=0, gamma=0.5 test FH05 <- gs_design_wlr(enrollRates = enrollRates, failRates = failRates, ratio = 1, alpha = 0.025, beta = 0.15, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)}, upper = gs_b, upar = qnorm(.975), lower = gs_b, lpar = -Inf, analysisTimes = trial_duration) # regular logrank test FH00 <- gs_power_wlr(enrollRates = FH05$enrollRates, failRates = failRates, ratio = 1, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0)}, upper = gs_b, upar = qnorm(.975), lower = gs_b, lpar = -Inf, analysisTimes = trial_duration, events = .1) # max combo test mc2_test <- data.frame(rho = 0, gamma = c(0, .5), tau = -1, test = 1:2, Analysis = 1, analysisTimes = trial_duration) MC2 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc2_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # max combo test mc3_test <- data.frame(rho = c(0,0,.5), gamma = c(0, .5, .5), tau = -1, test = 1:3, Analysis = 1, analysisTimes = trial_duration) MC3 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc3_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # max combo test mc4_test <- data.frame(rho = c(0,0,.5,.5), gamma = c(0, .5, .5, 0), tau = -1, test = 1:4, Analysis = 1, analysisTimes = trial_duration) MC4 <- gs_power_combo(enrollRates = FH05$enrollRates, failRates = failRates, fh_test = mc4_test, upper = gs_spending_combo, upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025), lower = gs_spending_combo, lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.01)) # Magirr-Burman rho=-1, gamma=0, tau = 6 test MB6 <- gs_power_wlr(enrollRates = FH05$enrollRates, failRates = failRates, ratio = 1, weight = function(x, arm0, arm1){wlr_weight_fh(x, arm0, arm1, rho = -1, gamma = 0, tau = 6)}, upar = qnorm(.975), lpar = -Inf, analysisTimes = trial_duration, events = .1) tab_new <- tibble(`Study duration` = trial_duration, N = FH05$analysis$N[1], Events = FH05$analysi$Events[1], `Events/N` = Events/N, # we use the AHR from regular WLR as the AHR of different max combo test AHR = as.numeric(FH00$analysis$AHR[1]), `FH(0, 0.5) power` = FH05$bounds$Probability[1], `FH(0, 0) power` = FH00$bounds$Probability[1], `MC2 power` = MC2$bounds$Probability[1], `MC4 power` = MC4$bounds$Probability[1], `MC3 power` = MC3$bounds$Probability[1], `MB6 power` = MB6$bounds$Probability[1]) tab <- rbind(tab, tab_new) } tab %>% gt() %>% fmt_number(columns = c(2, 3), decimals = 1) %>% fmt_number(columns = 4, decimals = 2) %>% fmt_number(columns = 5, decimals = 4) %>% fmt_number(columns = 6:11, decimals = 2)
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