gsDesign2 (version 1.1.5)

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

Description

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

Usage

gs_update_ahr(
  x = NULL,
  alpha = NULL,
  ustime = NULL,
  lstime = NULL,
  event_tbl = NULL
)

Value

A list with input parameters, enrollment rate, failure rate, analysis, and bound.

Arguments

x

A design created by either gs_design_ahr() or gs_power_ahr().

alpha

Type I error for the updated design.

ustime

Default is NULL in which case upper bound spending time is determined by timing. Otherwise, this should be a vector of length k (total number of analyses) with the spending time at each analysis.

lstime

Default is NULL in which case lower bound spending time is determined by timing. Otherwise, this should be a vector of length k (total number of analyses) with the spending time at each analysis.

event_tbl

A data frame with two columns: (1) analysis and (2) event, which represents the events observed at each analysis per piecewise interval. This can be defined via the pw_observed_event() function or manually entered. For example, consider a scenario with two intervals in the piecewise model: the first interval lasts 6 months with a hazard ratio (HR) of 1, and the second interval follows with an HR of 0.6. The data frame event_tbl = data.frame(analysis = c(1, 1, 2, 2), event = c(30, 100, 30, 200)) indicates that 30 events were observed during the delayed effect period, 130 events were observed at the IA, and 230 events were observed at the FA.

Examples

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

alpha <- 0.025
beta <- 0.1
ratio <- 1

# Enrollment
enroll_rate <- define_enroll_rate(
  duration = c(2, 2, 10),
  rate = (1:3) / 3)

# Failure and dropout
fail_rate <- define_fail_rate(
  duration = c(3, Inf), fail_rate = log(2) / 9,
  hr = c(1, 0.6), dropout_rate = .0001)

# IA and FA analysis time
analysis_time <- c(20, 36)

# Randomization ratio
ratio <- 1

# ------------------------------------------------- #
# Two-sided asymmetric design,
# beta-spending with non-binding lower bound
# ------------------------------------------------- #
# Original design
x <- gs_design_ahr(
  enroll_rate = enroll_rate, fail_rate = fail_rate,
  alpha = alpha, beta = beta, ratio = ratio,
  info_scale = "h0_info",
  info_frac = NULL, analysis_time = c(20, 36),
  upper = gs_spending_bound,
  upar = list(sf = sfLDOF, total_spend = alpha),
  test_upper = TRUE,
  lower = gs_spending_bound,
  lpar = list(sf = sfLDOF, total_spend = beta),
  test_lower = c(TRUE, FALSE),
  binding = FALSE) %>% to_integer()

planned_event_ia <- x$analysis$event[1]
planned_event_fa <- x$analysis$event[2]


# Updated design with 190 events observed at IA,
# where 50 events observed during the delayed effect.
# IA spending = observed events / final planned events, the remaining alpha will be allocated to FA.
gs_update_ahr(
  x = x,
  ustime = c(190 / planned_event_fa, 1),
  lstime = c(190 / planned_event_fa, 1),
  event_tbl = data.frame(analysis = c(1, 1),
                         event = c(50, 140)))

# Updated design with 190 events observed at IA, and 300 events observed at FA,
# where 50 events observed during the delayed effect.
# IA spending = observed events / final planned events, the remaining alpha will be allocated to FA.
gs_update_ahr(
  x = x,
  ustime = c(190 / planned_event_fa, 1),
  lstime = c(190 / planned_event_fa, 1),
  event_tbl = data.frame(analysis = c(1, 1, 2, 2),
                         event = c(50, 140, 50, 250)))

# Updated design with 190 events observed at IA, and 300 events observed at FA,
# where 50 events observed during the delayed effect.
# IA spending = minimal of planned and actual information fraction spending
gs_update_ahr(
  x = x,
  ustime = c(min(190, planned_event_ia) / planned_event_fa, 1),
  lstime = c(min(190, planned_event_ia) / planned_event_fa, 1),
  event_tbl = data.frame(analysis = c(1, 1, 2, 2),
                         event = c(50, 140, 50, 250)))

# Alpha is updated to 0.05
gs_update_ahr(x = x, alpha = 0.05)