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
)

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.

Value

A list with input parameters, enrollment rate, failure rate, analysis, and bound.

Examples

library(gsDesign)
library(gsDesign2)
library(dplyr)

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)))
#> $enroll_rate
#> # A tibble: 3 × 3
#>   stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  10.6
#> 2 All            2  21.2
#> 3 All           10  31.8
#> 
#> $fail_rate
#> # A tibble: 2 × 5
#>   stratum duration fail_rate dropout_rate    hr
#>   <chr>      <dbl>     <dbl>        <dbl> <dbl>
#> 1 All            3    0.0770       0.0001   1  
#> 2 All          Inf    0.0770       0.0001   0.6
#> 
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0        z `~hr at bound` `nominal p`
#>      <int> <chr>       <dbl>        <dbl>    <dbl>          <dbl>       <dbl>
#> 1        1 upper      0.481       0.00414    2.64           0.682     0.00414
#> 2        2 upper      0.906       0.0237     1.98           0.799     0.0237 
#> 3        1 lower      0.0353      0.784      0.787          0.892     0.216  
#> 4        2 lower      0.0353      0.784   -Inf            Inf         1      
#> 
#> $analysis
#>   analysis     time   n event       ahr     theta  info info0 info_frac
#> 1        1 19.91897 382   190 0.6863292 0.3763978 47.50 47.50 0.6109325
#> 2        2 36.06513 382   311 0.6829028 0.3814027 77.75 77.75 1.0000000
#>   info_frac0
#> 1  0.6109325
#> 2  1.0000000
#> 
#> attr(,"class")
#> [1] "non_binding"    "ahr"            "gs_design"      "list"          
#> [5] "updated_design"

# 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)))
#> $enroll_rate
#> # A tibble: 3 × 3
#>   stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  10.6
#> 2 All            2  21.2
#> 3 All           10  31.8
#> 
#> $fail_rate
#> # A tibble: 2 × 5
#>   stratum duration fail_rate dropout_rate    hr
#>   <chr>      <dbl>     <dbl>        <dbl> <dbl>
#> 1 All            3    0.0770       0.0001   1  
#> 2 All          Inf    0.0770       0.0001   0.6
#> 
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0        z `~hr at bound` `nominal p`
#>      <int> <chr>       <dbl>        <dbl>    <dbl>          <dbl>       <dbl>
#> 1        1 upper      0.481       0.00414    2.64           0.682     0.00414
#> 2        2 upper      0.939       0.0239     1.98           0.796     0.0238 
#> 3        1 lower      0.0353      0.784      0.787          0.892     0.216  
#> 4        2 lower      0.0353      0.784   -Inf            Inf         1      
#> 
#> $analysis
#>   analysis     time   n event       ahr     theta info info0 info_frac
#> 1        1 19.91897 382   190 0.6863292 0.3763978 47.5  47.5 0.6109325
#> 2        2 36.06513 382   300 0.6533201 0.4256880 75.0  75.0 1.0000000
#>   info_frac0
#> 1  0.6333333
#> 2  1.0000000
#> 
#> attr(,"class")
#> [1] "non_binding"    "ahr"            "gs_design"      "list"          
#> [5] "updated_design"

# 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)))
#> $enroll_rate
#> # A tibble: 3 × 3
#>   stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  10.6
#> 2 All            2  21.2
#> 3 All           10  31.8
#> 
#> $fail_rate
#> # A tibble: 2 × 5
#>   stratum duration fail_rate dropout_rate    hr
#>   <chr>      <dbl>     <dbl>        <dbl> <dbl>
#> 1 All            3    0.0770       0.0001   1  
#> 2 All          Inf    0.0770       0.0001   0.6
#> 
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0        z `~hr at bound` `nominal p`
#>      <int> <chr>       <dbl>        <dbl>    <dbl>          <dbl>       <dbl>
#> 1        1 upper      0.481       0.00414    2.64           0.682     0.00414
#> 2        2 upper      0.939       0.0239     1.98           0.796     0.0238 
#> 3        1 lower      0.0353      0.784      0.787          0.892     0.216  
#> 4        2 lower      0.0353      0.784   -Inf            Inf         1      
#> 
#> $analysis
#>   analysis     time   n event       ahr     theta info info0 info_frac
#> 1        1 19.91897 382   190 0.6863292 0.3763978 47.5  47.5 0.6109325
#> 2        2 36.06513 382   300 0.6533201 0.4256880 75.0  75.0 1.0000000
#>   info_frac0
#> 1  0.6333333
#> 2  1.0000000
#> 
#> attr(,"class")
#> [1] "non_binding"    "ahr"            "gs_design"      "list"          
#> [5] "updated_design"

# Alpha is updated to 0.05
gs_update_ahr(x = x, alpha = 0.05)
#> $enroll_rate
#> # A tibble: 3 × 3
#>   stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  10.6
#> 2 All            2  21.2
#> 3 All           10  31.8
#> 
#> $fail_rate
#> # A tibble: 2 × 5
#>   stratum duration fail_rate dropout_rate    hr
#>   <chr>      <dbl>     <dbl>        <dbl> <dbl>
#> 1 All            3    0.0770       0.0001   1  
#> 2 All          Inf    0.0770       0.0001   0.6
#> 
#> $bound
#> # A tibble: 4 × 7
#>   analysis bound probability probability0        z `~hr at bound` `nominal p`
#>      <int> <chr>       <dbl>        <dbl>    <dbl>          <dbl>       <dbl>
#> 1        1 upper      0.518        0.0150    2.17           0.737      0.0150
#> 2        2 upper      0.933        0.0487    1.69           0.826      0.0455
#> 3        1 lower      0.0413       0.684     0.478          0.935      0.316 
#> 4        2 lower      0.0413       0.684  -Inf            Inf          1     
#> 
#> $analysis
#>   analysis     time   n event       ahr     theta  info info0 info_frac
#> 1        1 19.91897 382   202 0.7322996 0.3115656 50.50 50.50 0.6495177
#> 2        2 36.06513 382   311 0.6829028 0.3814027 77.75 77.75 1.0000000
#>   info_frac0
#> 1  0.6495177
#> 2  1.0000000
#> 
#> attr(,"class")
#> [1] "non_binding"    "ahr"            "gs_design"      "list"          
#> [5] "updated_design"