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

Usage

gs_design_rd(
  p_c = tibble(Stratum = "All", Rate = 0.2),
  p_e = tibble(Stratum = "All", Rate = 0.15),
  IF = 1:3/3,
  rd0 = 0,
  alpha = 0.025,
  beta = 0.1,
  ratio = 1,
  stratum_prev = NULL,
  weight = c("un-stratified", "ss", "invar"),
  upper = gs_b,
  lower = gs_b,
  upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lpar = c(qnorm(0.1), rep(-Inf, 2)),
  test_upper = TRUE,
  test_lower = TRUE,
  info_scale = c(0, 1, 2),
  binding = FALSE,
  r = 18,
  tol = 1e-06,
  h1_spending = FALSE
)

Arguments

p_c: rate at the control group
p_e: rate at the experimental group
IF: statistical information fraction
rd0: treatment effect under super-superiority designs, the default is 0
alpha: One-sided Type I error
beta: Type II error
ratio: Experimental:Control randomization ratio (not yet implemented)
stratum_prev: randomization ratio of different stratum. If it is un-stratified design then NULL. Otherwise it is a tibble containing two columns (Stratum and prevalence).
weight: the weighting scheme for stratified population
upper: Function to compute upper bound
lower: Function to compute lower bound
upar: Parameter passed to upper()
lpar: Parameter 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
info_scale: the information scale for calculation
binding: indicator of whether futility bound is binding; default of FALSE is recommended
r: Integer, at least 2; default of 18 recommended by Jennison and Turnbull
tol: Tolerance parameter for boundary convergence (on Z-scale)
h1_spending: Indicator that lower bound to be set by spending under alternate hypothesis (input failRates) if spending is used for lower bound

Value

a tibble with columns Analysis, Bound, Z, Probability, theta, Time, AHR, Events

Details

Need to be added

Examples

library(tibble)
library(gsDesign)

# ----------------- #
#    example 1      #
#------------------ #
# un-stratified group sequential design
gs_design_rd(
  p_c = tibble(Stratum = "All", Rate = .2),
  p_e = tibble(Stratum = "All", Rate = .15),
  IF = c(0.7, 1),
  rd0 = 0, 
  alpha = .025,                  
  beta = .1,                    
  ratio = 1,
  stratum_prev = NULL,
  weight = "un-stratified",
  upper = gs_b,
  lower = gs_b,
  upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lpar = c(qnorm(.1), rep(-Inf, 2))
  )
#> $bounds
#> # A tibble: 4 × 7
#>   Analysis Bound Probability Probability0       Z ~Risk difference at …¹ Nomin…²
#>      <int> <chr>       <dbl>        <dbl>   <dbl>                  <dbl>   <dbl>
#> 1        1 Upper  0.297          0.000100    3.71                 0.0582 1.04e-4
#> 2        1 Lower  0.00000389     0.0995     -1.28                -0.0201 9   e-1
#> 3        2 Upper  0.900          0.00602     2.51                 0.0330 6.01e-3
#> 4        2 Lower  0.00000389     0.0995   -Inf                 -Inf      1   e+0
#> # … with abbreviated variable names ¹`~Risk difference at bound`, ²`Nominal p`
#> 
#> $analysis
#> # A tibble: 2 × 8
#>   Analysis     N    rd   rd0  info info0    IF   IF0
#>      <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 2336.  0.05     0 4062. 4044.   0.7   0.7
#> 2        2 3337.  0.05     0 5803. 5778.   1     1  
#> 
#> attr(,"class")
#> [1] "rd"        "gs_design" "list"     
  
# ----------------- #
#     example 2     #
# ----------------- #
# stratified group sequential design
gs_design_rd(
  p_c = tibble(Stratum = c("biomarker positive", "biomarker negative"), Rate = c(.2, .25)),
  p_e = tibble(Stratum = c("biomarker positive", "biomarker negative"), Rate = c(.15,.22)),
  IF = c(0.7, 1),
  rd0 = 0, 
  alpha = .025,                  
  beta = .1,                    
  ratio = 1,
  stratum_prev = tibble(Stratum = c("biomarker positive", "biomarker negative"), prevalence = c(.4, .6)),
  weight = "ss",
  upper = gs_spending_bound,lower = gs_b,
  upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
  lpar = rep(-Inf, 2)
)
#> $bounds
#> # A tibble: 4 × 7
#>   Analysis Bound Probability Probability0       Z ~Risk difference at …¹ Nomin…²
#>      <int> <chr>       <dbl>        <dbl>   <dbl>                  <dbl>   <dbl>
#> 1        1 Upper       0.616      0.00733    2.44                 0.0339 0.00738
#> 2        1 Lower       0          0       -Inf                 -Inf      1      
#> 3        2 Upper       0.900      0.0249     2.00                 0.0232 0.0228 
#> 4        2 Lower       0          0       -Inf                 -Inf      1      
#> # … with abbreviated variable names ¹`~Risk difference at bound`, ²`Nominal p`
#> 
#> $analysis
#> # A tibble: 2 × 8
#>   Analysis     N    rd   rd0  info info0    IF   IF0
#>      <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 3426. 0.038     0 5184. 5172.   0.7   0.7
#> 2        2 4894. 0.038     0 7406. 7388.   1     1  
#> 
#> attr(,"class")
#> [1] "rd"        "gs_design" "list"