Group sequential design of binary outcome measuring in risk difference

Usage

gs_design_rd(
  p_c = tibble::tibble(stratum = "All", rate = 0.2),
  p_e = tibble::tibble(stratum = "All", rate = 0.15),
  info_frac = 1:3/3,
  rd0 = 0,
  alpha = 0.025,
  beta = 0.1,
  ratio = 1,
  stratum_prev = NULL,
  weight = c("unstratified", "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("h0_h1_info", "h0_info", "h1_info"),
  binding = FALSE,
  r = 18,
  tol = 1e-06,
  h1_spending = TRUE
)

Arguments

p_c

Rate at the control group.

p_e

Rate at the experimental group.

info_frac

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 unstratified 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

Parameters passed to upper.

lpar

Parameters 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 of FALSE indicates no lower bound; otherwise, a logical vector of the same length as info should indicate which analyses will have a lower bound.

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.

binding

Indicator of whether futility bound is binding; default of FALSE is recommended.

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).

h1_spending

Indicator that lower bound to be set by spending under alternate hypothesis (input fail_rate) if spending is used for lower bound.

Value

A list with input parameters, analysis, and bound.

Details

To be added.

Examples

library(gsDesign)

# Example 1 ----
# unstratified group sequential design
x <- gs_design_rd(
  p_c = tibble::tibble(stratum = "All", rate = .2),
  p_e = tibble::tibble(stratum = "All", rate = .15),
  info_frac = c(0.7, 1),
  rd0 = 0,
  alpha = .025,
  beta = .1,
  ratio = 1,
  stratum_prev = NULL,
  weight = "unstratified",
  upper = gs_b,
  lower = gs_b,
  upar = gsDesign(k = 2, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lpar = c(qnorm(.1), rep(-Inf, 2))
)

y <- gs_power_rd(
  p_c = tibble::tibble(stratum = "All", rate = .2),
  p_e = tibble::tibble(stratum = "All", rate = .15),
  n = tibble::tibble(stratum = "All", n = x$analysis$n, analysis = 1:2),
  rd0 = 0,
  ratio = 1,
  weight = "unstratified",
  upper = gs_b,
  lower = gs_b,
  upar = gsDesign(k = 2, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lpar = c(qnorm(.1), rep(-Inf, 2))
)

# The above 2 design share the same power with the same sample size and treatment effect
x$bound$probability[x$bound$bound == "upper" & x$bound$analysis == 2]
#> [1] 0.9
y$bound$probability[y$bound$bound == "upper" & y$bound$analysis == 2]
#> [1] 0.9

# Example 2 ----
# stratified group sequential design
gs_design_rd(
  p_c = tibble::tibble(
    stratum = c("biomarker positive", "biomarker negative"),
    rate = c(.2, .25)
  ),
  p_e = tibble::tibble(
    stratum = c("biomarker positive", "biomarker negative"),
    rate = c(.15, .22)
  ),
  info_frac = c(0.7, 1),
  rd0 = 0,
  alpha = .025,
  beta = .1,
  ratio = 1,
  stratum_prev = tibble::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)
)
#> $design
#> [1] "rd"
#> 
#> $bound
#> # A tibble: 2 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper       0.616      0.00738  2.44                      0.0339
#> 2        2 upper       0.900      0.0250   2.00                      0.0232
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 2 × 8
#>   analysis     n    rd   rd0  info info0 info_frac info_frac0
#>      <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  
#>