gs_power_ahr {gsDesign2}

Group sequential design power using average hazard ratio under non-proportional hazards

Description

Group 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_b,
  upar = gsDesign(k = length(event), test.type = 1, n.I = event, maxn.IPlan = max(event),
    sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lower = gs_b,
  lpar = c(qnorm(0.1), rep(-Inf, 2)),
  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_rate data frame with or without stratum created by define_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 of FALSE indicated no lower bound; otherwise, a logical vector of the same length as info should 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 as info should 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 FALSE is 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, 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.

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.

Value

A tibble with columns Analysis, Bound, Z, Probability, theta, Time, AHR, Events. Contains a row for each analysis and each bound.

Specification

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

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`

gs_power_ahr()

# 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)
)

# Example 3 ----
# 2-sided symmetric O'Brien-Fleming spending bound, driven by event,
# i.e., `event = c(20, 50, 70)`, `analysis_time = NULL`

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)
)

# 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)

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)
)