Group sequential design power of binary outcome measuring in risk difference

Usage

gs_power_rd(
  p_c = tibble::tibble(stratum = "All", rate = 0.2),
  p_e = tibble::tibble(stratum = "All", rate = 0.15),
  n = tibble::tibble(stratum = "All", n = c(40, 50, 60), analysis = 1:3),
  rd0 = 0,
  ratio = 1,
  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)),
  info_scale = c("h0_h1_info", "h0_info", "h1_info"),
  binding = FALSE,
  test_upper = TRUE,
  test_lower = TRUE,
  r = 18,
  tol = 1e-06
)

Arguments

p_c

Rate at the control group.

p_e

Rate at the experimental group.

n

Sample size.

rd0

Treatment effect under super-superiority designs, the default is 0.

ratio

Experimental:control randomization ratio.

weight

Weighting method, can be "unstratified", "ss", or "invar".

upper

Function to compute upper bound.

lower

Function to compare lower bound.

upar

Parameters passed to upper.

lpar

Parameters passed to lower.

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.

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 a 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.

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).

Value

A list with input parameter, analysis, and bound.

Examples

# Example 1 ----
library(gsDesign)

# unstratified case with H0: rd0 = 0
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 = c(20, 40, 60),
    analysis = 1:3
  ),
  rd0 = 0,
  ratio = 1,
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000309     0.000104  3.71                       0.629
#> 2        2 upper    0.0182       0.00605   2.51                       0.301
#> 3        3 upper    0.0728       0.0250    1.99                       0.195
#> 4        1 lower    0.0571       0.100    -1.28                      -0.217
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n    rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl> <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    20  0.05     0   0.05      0  34.8  34.6     0.333      0.333
#> 2        2    40  0.05     0   0.05      0  69.6  69.3     0.667      0.667
#> 3        3    60  0.05     0   0.05      0 104.  104.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# Example 2 ----
# unstratified case with H0: rd0 != 0
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 = c(20, 40, 60),
    analysis = 1:3
  ),
  rd0 = 0.005,
  ratio = 1,
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000309     0.000116  3.71                       0.571
#> 2        2 upper    0.0182       0.00680   2.51                       0.276
#> 3        3 upper    0.0728       0.0281    1.99                       0.181
#> 4        1 lower    0.0571       0.0949   -1.28                      -0.191
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n    rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl> <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    20  0.05 0.005   0.05  0.005  34.8  34.6     0.333      0.333
#> 2        2    40  0.05 0.005   0.05  0.005  69.6  69.3     0.667      0.667
#> 3        3    60  0.05 0.005   0.05  0.005 104.  104.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# use spending function
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 = c(20, 40, 60),
    analysis = 1:3
  ),
  rd0 = 0.005,
  ratio = 1,
  upper = gs_spending_bound,
  lower = gs_b,
  upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
  lpar = c(qnorm(.1), rep(-Inf, 2))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000309     0.000116  3.71                       0.571
#> 2        2 upper    0.0182       0.00680   2.51                       0.276
#> 3        3 upper    0.0728       0.0281    1.99                       0.181
#> 4        1 lower    0.0571       0.0949   -1.28                      -0.191
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n    rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl> <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    20  0.05 0.005   0.05  0.005  34.8  34.6     0.333      0.333
#> 2        2    40  0.05 0.005   0.05  0.005  69.6  69.3     0.667      0.667
#> 3        3    60  0.05 0.005   0.05  0.005 104.  104.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# Example 3 ----
# stratified case under sample size weighting and H0: rd0 = 0
gs_power_rd(
  p_c = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.15, .2, .25)
  ),
  p_e = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.1, .16, .19)
  ),
  n = tibble::tibble(
    stratum = rep(c("S1", "S2", "S3"), each = 3),
    analysis = rep(1:3, 3),
    n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
  ),
  rd0 = 0,
  ratio = 1,
  weight = "ss",
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000437     0.000104  3.71                       0.456
#> 2        2 upper    0.0237       0.00604   2.51                       0.228
#> 3        3 upper    0.0795       0.0237    1.99                       0.166
#> 4        1 lower    0.0470       0.100    -1.28                      -0.157
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n     rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    38 0.0479     0 0.0479      0  66.3  66.0     0.485      0.485
#> 2        2    66 0.0491     0 0.0491      0 116.  115.      0.846      0.846
#> 3        3    78 0.0492     0 0.0492      0 137.  136.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# Example 4 ----
# stratified case under inverse variance weighting and H0: rd0 = 0
gs_power_rd(
  p_c = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.15, .2, .25)
  ),
  p_e = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.1, .16, .19)
  ),
  n = tibble::tibble(
    stratum = rep(c("S1", "S2", "S3"), each = 3),
    analysis = rep(1:3, 3),
    n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
  ),
  rd0 = 0,
  ratio = 1,
  weight = "invar",
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000443     0.000104  3.71                       0.449
#> 2        2 upper    0.0240       0.00604   2.51                       0.225
#> 3        3 upper    0.0803       0.0237    1.99                       0.164
#> 4        1 lower    0.0467       0.100    -1.28                      -0.155
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n     rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    38 0.0477     0 0.0477      0  68.2  67.9     0.483      0.483
#> 2        2    66 0.0488     0 0.0488      0 119.  119.      0.845      0.845
#> 3        3    78 0.0489     0 0.0489      0 141.  141.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# Example 5 ----
# stratified case under sample size weighting and H0: rd0 != 0
gs_power_rd(
  p_c = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.15, .2, .25)
  ),
  p_e = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.1, .16, .19)
  ),
  n = tibble::tibble(
    stratum = rep(c("S1", "S2", "S3"), each = 3),
    analysis = rep(1:3, 3),
    n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
  ),
  rd0 = 0.02,
  ratio = 1,
  weight = "ss",
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000437     0.000194  3.71                      0.285 
#> 2        2 upper    0.0237       0.0109    2.51                      0.153 
#> 3        3 upper    0.0795       0.0401    1.99                      0.117 
#> 4        1 lower    0.0470       0.0744   -1.28                     -0.0717
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n     rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    38 0.0479  0.02 0.0479   0.02  66.3  66.0     0.485      0.485
#> 2        2    66 0.0491  0.02 0.0491   0.02 116.  115.      0.846      0.846
#> 3        3    78 0.0492  0.02 0.0492   0.02 137.  136.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"       

# Example 6 ----
# stratified case under inverse variance weighting and H0: rd0 != 0
gs_power_rd(
  p_c = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.15, .2, .25)
  ),
  p_e = tibble::tibble(
    stratum = c("S1", "S2", "S3"),
    rate = c(.1, .16, .19)
  ),
  n = tibble::tibble(
    stratum = rep(c("S1", "S2", "S3"), each = 3),
    analysis = rep(1:3, 3),
    n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
  ),
  rd0 = 0.03,
  ratio = 1,
  weight = "invar",
  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))
)
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0     z `~risk difference at bound`
#>      <int> <chr>       <dbl>        <dbl> <dbl>                       <dbl>
#> 1        1 upper    0.000443     0.000267  3.71                      0.197 
#> 2        2 upper    0.0240       0.0145    2.51                      0.113 
#> 3        3 upper    0.0803       0.0518    1.99                      0.0906
#> 4        1 lower    0.0467       0.0632   -1.28                     -0.0275
#> # ℹ 1 more variable: `nominal p` <dbl>
#> 
#> $analysis
#> # A tibble: 3 × 10
#>   analysis     n     rd   rd0 theta1 theta0  info info0 info_frac info_frac0
#>      <int> <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl> <dbl>     <dbl>      <dbl>
#> 1        1    38 0.0477  0.03 0.0477   0.03  68.2  67.9     0.483      0.483
#> 2        2    66 0.0488  0.03 0.0488   0.03 119.  119.      0.845      0.845
#> 3        3    78 0.0489  0.03 0.0489   0.03 141.  141.      1          1    
#> 
#> attr(,"class")
#> [1] "non_binding" "rd"          "gs_design"   "list"