gsDesign2 (version 1.1.8)

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)

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)

# ------------------------------------------------- #
# Two-sided asymmetric stratified design,
# beta-spending with non-binding lower bound
# ------------------------------------------------- #
enroll_rate <- define_enroll_rate(stratum = c("A", "B"), duration = c(12, 12), rate = c(1, 1))

# We assumme there are 2 strata, "A" and "B".
# For each stratum, there are delayed effect for the first 3 months.
# After the delayed effect, the HR is 0.8 for stratum A and 0.5 for stratum B.
fail_rate <- define_fail_rate(stratum = c("A", "A", "B", "B"),
                              duration = c(3, Inf, 3, Inf),
                              fail_rate = log(2) / c(9, 9, 9, 15),
                              hr = c(1, 0.8, 1, 0.5),
                              dropout_rate = rep(0.001, 4))

# The original design assumes there are 2 IAs and 1 FA cutting by calendar time.
# The efficacy testing is conducted at IA2 and FA.
# The futility testing is conducted at IA1.
x <- gs_design_ahr(enroll_rate = enroll_rate,
                  fail_rate = fail_rate,
                  alpha = 0.0125,
                  beta = 0.1,
                  analysis = c(20, 28, 36),
                  upper = "gs_spending_bound",
                  upar = list(sf = "sfLDOF", total_spend = 0.0125),
                  lower = "gs_spending_bound",
                  lpar = list(sf = "sfHSD", total_spend = 0.1, param = -8),
                  test_upper = c(FALSE, TRUE, TRUE),
                  test_lower = c(TRUE, FALSE, FALSE)) |> to_integer()

# At time of analysis
# For IA1,
# - There are 70 events observed during the delayed effect period for stratum A.
# - There are 150 events observed after the delayed effect period for stratum A.
# - There are 75 events observed during the delayed effect period for stratum B.
# - There are 90 events observed after the delayed effect period for stratum B.
# For IA2,
# - There are 75 events observed during the delayed effect period for stratum A.
# - There are 210 events observed after the delayed effect period for stratum A.
# - There are 76 events observed during the delayed effect period for stratum B.
# - There are 136 events observed after the delayed effect period for stratum B.
# For FA,
# - There are 77 events observed during the delayed effect period for stratum A.
# - There are 245 events observed after the delayed effect period for stratum A.
# - There are 77 events observed during the delayed effect period for stratum B.
# - There are 170 events observed after the delayed effect period for stratum B.
event_tbl <- data.frame(analysis = c(1, 1, 1, 1,
                                    2, 2, 2, 2,
                                    3, 3, 3, 3),
                       stratum = c("A", "A", "B", "B", # IA1
                                   "A", "A", "B", "B", # IA2
                                   "A", "A", "B", "B"),# FA
                                 # event per interval per stratum at IA1
                       event = c(70, 150, 75, 90,
                                 # event per interval per stratum at IA2
                                 75, 210, 76, 136,
                                 # event per interval per stratum at FA
                                 77, 245, 77, 170))
observed_event <- (event_tbl |> dplyr::group_by(analysis) |> dplyr::summarize(x = sum(event)))$x

ustime <- pmin(x$analysis$event,
               observed_event) / x$analysis$event[3]
ustime[3] <- 1
lstime <- ustime

xu <- gs_update_ahr(x = x,
                    alpha = 0.015,
                    ustime = ustime,
                    lstime = lstime,
                    event_tbl = event_tbl
                    )