gs_design_wlr {gsDesign2}

Group sequential design using weighted log-rank test under non-proportional hazards

Description

Group sequential design using weighted log-rank test under non-proportional hazards

Usage

gs_design_wlr(
  enroll_rate = define_enroll_rate(duration = c(2, 2, 10), rate = c(3, 6, 9)),
  fail_rate = tibble(stratum = "All", duration = c(3, 100), fail_rate = log(2)/c(9, 18),
    hr = c(0.9, 0.6), dropout_rate = rep(0.001, 2)),
  weight = wlr_weight_fh,
  approx = "asymptotic",
  alpha = 0.025,
  beta = 0.1,
  ratio = 1,
  info_frac = NULL,
  info_scale = c("h0_h1_info", "h0_info", "h1_info"),
  analysis_time = 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),
  test_upper = TRUE,
  test_lower = TRUE,
  h1_spending = TRUE,
  r = 18,
  tol = 1e-06,
  interval = c(0.01, 1000)
)

Arguments

enroll_rate

Enrollment rates.

fail_rate

Failure and dropout rates.

weight

Weight of weighted log rank test:

• "1" = unweighted.

• "n" = Gehan-Breslow.

• "sqrtN" = Tarone-Ware.

• "FH_p[a]_q[b]" = Fleming-Harrington with p=a and q=b.

approx

Approximate estimation method for Z statistics.

• "event_driven" = only work under proportional hazard model with log rank test.

• "asymptotic".

alpha

One-sided Type I error.

beta

Type II error.

ratio

Experimental:Control randomization ratio (not yet implemented).

info_frac

Targeted information fraction at each analysis.

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.

analysis_time

Minimum time of analysis.

binding

Indicator of whether futility bound is binding; default of FALSE is recommended.

upper

Function to compute upper bound.

upar

Parameters passed to upper.

lower

Function to compute lower bound.

lpar

Parameters passed to lower.

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 info should 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 info should indicate which analyses will have a lower bound.

h1_spending

Indicator that lower bound to be set by spending under alternate hypothesis (input fail_rate) if spending is used for lower bound.

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, r will 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 list with input parameters, enrollment rate, analysis, and bound.

Specification

The contents of this section are shown in PDF user manual only.

Examples

library(dplyr)
library(mvtnorm)
library(gsDesign)
library(gsDesign2)

# set enrollment rates
enroll_rate <- define_enroll_rate(duration = 12, rate = 500 / 12)

# set failure rates
fail_rate <- define_fail_rate(
  duration = c(4, 100),
  fail_rate = log(2) / 15, # median survival 15 month
  hr = c(1, .6),
  dropout_rate = 0.001
)

# Example 1 ----
# Boundary is fixed
x <- gsSurv(
  k = 3,
  test.type = 4,
  alpha = 0.025, beta = 0.2,
  astar = 0, timing = 1,
  sfu = sfLDOF, sfupar = 0,
  sfl = sfLDOF, sflpar = 0,
  lambdaC = 0.1,
  hr = 0.6, hr0 = 1,
  eta = 0.01, gamma = 10,
  R = 12, S = NULL,
  T = 36, minfup = 24,
  ratio = 1
)

gs_design_wlr(
  enroll_rate = enroll_rate,
  fail_rate = fail_rate,
  ratio = 1,
  alpha = 0.025, beta = 0.2,
  weight = function(x, arm0, arm1) {
    wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)
  },
  upper = gs_b,
  upar = x$upper$bound,
  lower = gs_b,
  lpar = x$lower$bound,
  analysis_time = c(12, 24, 36)
)

# Example 2 ----
# Boundary derived by spending function
gs_design_wlr(
  enroll_rate = enroll_rate,
  fail_rate = fail_rate,
  ratio = 1,
  alpha = 0.025, beta = 0.2,
  weight = function(x, arm0, arm1) {
    wlr_weight_fh(x, arm0, arm1, rho = 0, gamma = 0.5)
  },
  upper = gs_spending_bound,
  upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),
  lower = gs_spending_bound,
  lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.2),
  analysis_time = c(12, 24, 36)
)