Group sequential design power using average hazard ratio under non-proportional hazards
Source:R/gs_power_ahr.R
gs_power_ahr.RdGroup sequential design power using average hazard ratio under non-proportional hazards.
Usage
gs_power_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 = rep(0.001, 2)),
event = c(30, 40, 50),
analysis_time = NULL,
upper = gs_spending_bound,
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
lower = gs_b,
lpar = rep(-Inf, 3),
test_lower = TRUE,
test_upper = TRUE,
ratio = 1,
binding = FALSE,
info_scale = c("h0_h1_info", "h0_info", "h1_info"),
r = 18,
tol = 1e-06,
interval = c(0.01, 1000)
)Arguments
- enroll_rate
An
enroll_ratedata frame with or without stratum created bydefine_enroll_rate().- fail_rate
Failure and dropout rates.
- event
Targeted event at each analysis.
- analysis_time
Minimum time of analysis.
- upper
Function to compute upper bound.
- upar
Parameters passed to
upper.- lower
Function to compute lower bound.
- lpar
Parameters passed to
lower.- test_lower
Indicator of which analyses should include an lower bound; single value of
TRUE(default) indicates all analyses; single value ofFALSEindicated no lower bound; otherwise, a logical vector of the same length asinfoshould indicate which analyses will have a 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.- ratio
Experimental:Control randomization ratio (not yet implemented).
- binding
Indicator of whether futility bound is binding; default of
FALSEis recommended.- 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.
Value
A tibble with columns Analysis, Bound, Z, Probability,
theta, Time, AHR, Events.
Contains a row for each analysis and each bound.
Details
Bound satisfy input upper bound specification in
upper, upar, and lower bound specification in lower, lpar.
ahr() computes statistical information at targeted event times.
The expected_time() function is used to get events and average HR at
targeted analysis_time.
Examples
library(gsDesign2)
library(dplyr)
# Example 1 ----
# The default output of `gs_power_ahr()` is driven by events,
# i.e., `event = c(30, 40, 50)`, `analysis_time = NULL`
# \donttest{
gs_power_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
#>
#> $input$event
#> [1] 30 40 50
#>
#> $input$analysis_time
#> NULL
#>
#> $input$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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <environment: namespace:gsDesign>
#>
#> $input$upar$total_spend
#> [1] 0.025
#>
#>
#> $input$lower
#> function (par = NULL, k = NULL, ...)
#> {
#> if (is.null(k)) {
#> return(par)
#> }
#> else {
#> return(par[k])
#> }
#> }
#> <bytecode: 0x56342efe38e8>
#> <environment: namespace:gsDesign2>
#>
#> $input$lpar
#> [1] -Inf -Inf -Inf
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$ratio
#> [1] 1
#>
#> $input$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 3
#> 2 All 2 6
#> 3 All 10 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: 3 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.0231 0.00381 2.67 0.374 0.00381
#> 2 2 upper 0.0897 0.0122 2.29 0.481 0.0110
#> 3 3 upper 0.207 0.0250 2.03 0.559 0.0211
#>
#> $analysis
#> analysis time n event ahr theta info info0
#> 1 1 14.90817 108 30.00008 0.7865726 0.2400702 7.373433 7.50002
#> 2 2 19.16437 108 40.00000 0.7442008 0.2954444 9.789940 10.00000
#> 3 3 24.54264 108 50.00000 0.7128241 0.3385206 12.227632 12.50000
#> info_frac info_frac0
#> 1 0.6030140 0.6000016
#> 2 0.8006407 0.8000001
#> 3 1.0000000 1.0000000
#>
#> attr(,"class")
#> [1] "non_binding" "ahr" "gs_design" "list"
# }
# Example 2 ----
# 2-sided symmetric O'Brien-Fleming spending bound, driven by analysis time,
# i.e., `event = NULL`, `analysis_time = c(12, 24, 36)`
gs_power_ahr(
analysis_time = c(12, 24, 36),
event = NULL,
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)
)
#> $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
#>
#> $input$event
#> NULL
#>
#> $input$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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <environment: namespace:gsDesign>
#>
#> $input$lpar$total_spend
#> [1] 0.025
#>
#> $input$lpar$param
#> NULL
#>
#> $input$lpar$timing
#> NULL
#>
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$ratio
#> [1] 1
#>
#> $input$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 3
#> 2 All 2 6
#> 3 All 10 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: 6 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000370 0.0000538 3.87 0.178 0.0000538
#> 2 1 lower 0.0000612 0.000343 -3.40 4.55 1.00
#> 3 2 upper 0.116 0.00921 2.36 0.506 0.00919
#> 4 2 lower 0.00907 0.115 -1.20 1.42 0.885
#> 5 3 upper 0.324 0.0250 2.01 0.608 0.0222
#> 6 3 lower 0.0250 0.324 -0.473 1.12 0.682
#>
#> $analysis
#> analysis time n event ahr theta info info0 info_frac
#> 1 1 12 90 20.40451 0.8107539 0.2097907 5.028327 5.101127 0.3090946
#> 2 2 24 108 49.06966 0.7151566 0.3352538 11.999266 12.267415 0.7376029
#> 3 3 36 108 66.23948 0.6833395 0.3807634 16.267921 16.559870 1.0000000
#> info_frac0
#> 1 0.3080415
#> 2 0.7407917
#> 3 1.0000000
#>
#> attr(,"class")
#> [1] "ahr" "gs_design" "list"
# Example 3 ----
# 2-sided symmetric O'Brien-Fleming spending bound, driven by event,
# i.e., `event = c(20, 50, 70)`, `analysis_time = NULL`
# \donttest{
gs_power_ahr(
analysis_time = NULL,
event = c(20, 50, 70),
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)
)
#> $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
#>
#> $input$event
#> [1] 20 50 70
#>
#> $input$analysis_time
#> NULL
#>
#> $input$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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <environment: namespace:gsDesign>
#>
#> $input$lpar$total_spend
#> [1] 0.025
#>
#> $input$lpar$param
#> NULL
#>
#> $input$lpar$timing
#> NULL
#>
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$ratio
#> [1] 1
#>
#> $input$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 3
#> 2 All 2 6
#> 3 All 10 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: 6 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.000198 0.0000275 4.03 0.163 0.0000275
#> 2 1 lower 0.0000312 0.000181 -3.57 4.98 1.00
#> 3 2 upper 0.110 0.00800 2.41 0.502 0.00799
#> 4 2 lower 0.00782 0.109 -1.23 1.42 0.891
#> 5 3 upper 0.352 0.0250 2.00 0.617 0.0226
#> 6 3 lower 0.0250 0.352 -0.393 1.10 0.653
#>
#> $analysis
#> analysis time n event ahr theta info info0
#> 1 1 11.87087 88.8378 20 0.8119328 0.2083377 4.929331 5.0
#> 2 2 24.54264 108.0000 50 0.7128241 0.3385206 12.227632 12.5
#> 3 3 39.39207 108.0000 70 0.6785816 0.3877506 17.218358 17.5
#> info_frac info_frac0
#> 1 0.2862834 0.2857143
#> 2 0.7101509 0.7142857
#> 3 1.0000000 1.0000000
#>
#> attr(,"class")
#> [1] "ahr" "gs_design" "list"
# }
# Example 4 ----
# 2-sided symmetric O'Brien-Fleming spending bound,
# driven by both `event` and `analysis_time`, i.e.,
# both `event` and `analysis_time` are not `NULL`,
# then the analysis will driven by the maximal one, i.e.,
# Time = max(analysis_time, calculated Time for targeted event)
# Events = max(events, calculated events for targeted analysis_time)
# \donttest{
gs_power_ahr(
analysis_time = c(12, 24, 36),
event = c(30, 40, 50),
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)
)
#> $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
#>
#> $input$event
#> [1] 30 40 50
#>
#> $input$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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <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: 0x56342efe2a08>
#> <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: 0x56342d0cba30>
#> <environment: namespace:gsDesign>
#>
#> $input$lpar$total_spend
#> [1] 0.025
#>
#> $input$lpar$param
#> NULL
#>
#> $input$lpar$timing
#> NULL
#>
#>
#> $input$test_lower
#> [1] TRUE
#>
#> $input$test_upper
#> [1] TRUE
#>
#> $input$ratio
#> [1] 1
#>
#> $input$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 3
#> 2 All 2 6
#> 3 All 10 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: 6 × 7
#> analysis bound probability probability0 z `~hr at bound` `nominal p`
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 upper 0.00706 0.000867 3.13 0.316 0.000867
#> 2 1 lower 0.000935 0.00658 -2.48 2.49 0.993
#> 3 2 upper 0.115 0.00921 2.37 0.505 0.00892
#> 4 2 lower 0.00912 0.113 -1.21 1.42 0.888
#> 5 3 upper 0.324 0.0250 2.01 0.607 0.0222
#> 6 3 lower 0.0251 0.323 -0.474 1.12 0.682
#>
#> $analysis
#> analysis time n event ahr theta info info0
#> 1 1 14.90817 108 30.00008 0.7865726 0.2400702 7.373433 7.50002
#> 2 2 24.00000 108 49.06966 0.7151566 0.3352538 11.999266 12.26741
#> 3 3 36.00000 108 66.23948 0.6833395 0.3807634 16.267921 16.55987
#> info_frac info_frac0
#> 1 0.4532499 0.4529033
#> 2 0.7376029 0.7407917
#> 3 1.0000000 1.0000000
#>
#> attr(,"class")
#> [1] "ahr" "gs_design" "list"
# }