Group sequential design using MaxCombo test under non-proportional hazards

Usage

gs_design_combo(
  enrollRates = tibble(Stratum = "All", duration = 12, rate = 500/12),
  failRates = tibble(Stratum = "All", duration = c(4, 100), failRate = log(2)/15, hr =
    c(1, 0.6), dropoutRate = 0.001),
  fh_test = rbind(data.frame(rho = 0, gamma = 0, tau = -1, test = 1, Analysis = 1:3,
    analysisTimes = c(12, 24, 36)), data.frame(rho = c(0, 0.5), gamma = 0.5, tau = -1,
    test = 2:3, Analysis = 3, analysisTimes = 36)),
  ratio = 1,
  alpha = 0.025,
  beta = 0.2,
  binding = FALSE,
  upper = gs_b,
  upar = c(3, 2, 1),
  lower = gs_b,
  lpar = c(-1, 0, 1),
  algorithm = mvtnorm::GenzBretz(maxpts = 1e+05, abseps = 1e-05),
  n_upper_bound = 1000,
  ...
)

Arguments

enrollRates: enrollment rates
failRates: failure and dropout rates
fh_test: a data frame to summarize the test in each analysis. Refer examples for its data structure.
ratio: Experimental:Control randomization ratio (not yet implemented)
alpha: One-sided Type I error
beta: Type II error
binding: indicator of whether futility bound is binding; default of FALSE is recommended
upper: Function to compute upper bound
upar: Parameter passed to upper()
lower: Function to compute lower bound
lpar: Parameter passed to lower()
algorithm: an object of class GenzBretz, Miwa or TVPACK specifying both the algorithm to be used as well as the associated hyper parameters.
n_upper_bound: a numeric value of upper limit of sample size
...: additional parameters transfer to mvtnorm::pmvnorm

Examples

# The example is slow to run
library(dplyr)
library(mvtnorm)
library(gsDesign)
library(tibble)

enrollRates <- tibble(
  Stratum = "All", 
  duration = 12, 
  rate = 500/12)
  
failRates <- tibble(
  Stratum = "All",
  duration = c(4, 100),
  failRate = log(2) / 15,  # median survival 15 month
  hr = c(1, .6),
  dropoutRate = 0.001)
  
fh_test <- rbind( 
  data.frame(rho = 0, gamma = 0, tau = -1,
             test = 1, Analysis = 1:3, analysisTimes = c(12, 24, 36)),
  data.frame(rho = c(0, 0.5), gamma = 0.5, tau = -1,
             test = 2:3, Analysis = 3, analysisTimes = 36))

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)

# -------------------------#
#       example 1          #
# ------------------------ #
if (FALSE) {
# User defined boundary
gs_design_combo(
  enrollRates,
  failRates,
  fh_test,
  alpha = 0.025, beta = 0.2,
  ratio = 1,
  binding = FALSE,       
  upar = x$upper$bound,
  lpar = x$lower$bound)
}

# -------------------------#
#       example 2          #
# ------------------------ #
# Boundary derived by spending function
gs_design_combo(
  enrollRates,
  failRates,
  fh_test,
  alpha = 0.025, 
  beta = 0.2,
  ratio = 1,
  binding = FALSE,                 
  upper = gs_spending_combo,
  upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025),   # alpha spending
  lower = gs_spending_combo,
  lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.2),     # beta spending
)
#> The AHR reported in the `analysis` table is under the log-rank test.
#> $enrollRates
#> # A tibble: 1 × 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All           12  25.1
#> 
#> $failRates
#> # A tibble: 2 × 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            4   0.0462   1         0.001
#> 2 All          100   0.0462   0.6       0.001
#> 
#> $bounds
#>   Analysis Bound  Probability Probability0          Z    Nominal p
#> 1        1 Upper 2.088476e-08 3.299865e-10  6.1753973 3.299865e-10
#> 2        1 Lower 3.269581e-04 0.000000e+00 -2.7160104 9.966963e-01
#> 3        2 Upper 2.203836e-01 2.565830e-03  2.7986508 2.565830e-03
#> 4        2 Lower 8.468455e-02 0.000000e+00  0.6533392 2.567688e-01
#> 5        3 Upper 7.999980e-01 2.492783e-02  2.0975425 1.797279e-02
#> 6        3 Lower 2.000048e-01 0.000000e+00  2.0975425 1.797279e-02
#> 
#> $analysis
#>   Analysis Time        N    Events        EF       AHR
#> 1        1   12 301.3099  64.71791 0.3241690 0.8418858
#> 2        2   24 301.3099 148.41524 0.7434051 0.7164215
#> 3        3   36 301.3099 199.64248 1.0000000 0.6831740
#> 
#> attr(,"class")
#> [1] "combo"     "gs_design" "list"