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

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

gs_design_ahr(
  enrollRates = tibble::tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6,
    9)),
  failRates = tibble::tibble(Stratum = "All", duration = c(3, 100), failRate =
    log(2)/c(9, 18), hr = c(0.9, 0.6), dropoutRate = rep(0.001, 2)),
  ratio = 1,
  alpha = 0.025,
  beta = 0.1,
  IF = NULL,
  analysisTimes = 36,
  binding = FALSE,
  upper = gs_b,
  upar = gsDesign(k = 3, test.type = 1, n.I = c(0.25, 0.75, 1), sfu = sfLDOF, sfupar =
    NULL)$upper$bound,
  lower = gs_b,
  lpar = c(qnorm(0.1), -Inf, -Inf),
  h1_spending = TRUE,
  test_upper = TRUE,
  test_lower = TRUE,
  r = 18,
  tol = 1e-06
)

Arguments

enrollRates	enrollment rates
failRates	failure and dropout rates
ratio	Experimental:Control randomization ratio (not yet implemented)
alpha	One-sided Type I error
beta	Type II error
IF	Targeted information fraction at each analysis
analysisTimes	Minimum time of analysis
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()
h1_spending	Indicator that lower bound to be set by spending under alternate hypothesis (input failRates) if spending is used for lower bound
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
r	Integer, at least 2; default of 18 recommended by Jennison and Turnbull
tol	Tolerance parameter for boundary convergence (on Z-scale)

Value

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

Details

Need to be added

Examples

library(gsDesign)
#> Loading required package: ggplot2
library(gsDesign2)
library(dplyr)
# call with defaults
gs_design_ahr()
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  13.2
#> 2 All            2  26.4
#> 3 All           10  39.7
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 1 x 11
#>   Analysis Bound  Time     N Events     Z Probability   AHR theta  info info0
#>      <dbl> <chr> <dbl> <dbl>  <dbl> <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper    36  476.   292.  1.96         0.9 0.683 0.381  71.7  73.0
#> 

# Single analysis
gs_design_ahr(analysisTimes = 40)
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  11.9
#> 2 All            2  23.8
#> 3 All           10  35.6
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 1 x 11
#>   Analysis Bound  Time     N Events     Z Probability   AHR theta  info info0
#>      <dbl> <chr> <dbl> <dbl>  <dbl> <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper    40  428.   280.  1.96         0.9 0.678 0.389  68.8  69.9
#> 

# Multiple analysisTimes
gs_design_ahr(analysisTimes = c(12,24,36))
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  14.0
#> 2 All            2  27.9
#> 3 All           10  41.9
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 6 x 11
#>   Analysis Bound  Time     N Events       Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl> <dbl>  <dbl>   <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper    12  419.   95.0    4.33    0.000454 0.811 0.210  23.4  23.8
#> 2        2 Upper    24  503.  229.     2.34    0.566    0.715 0.335  55.9  57.1
#> 3        3 Upper    36  503.  309.     2.01    0.900    0.683 0.381  75.8  77.1
#> 4        1 Lower    12  419.   95.0   -1.28    0.0108   0.811 0.210  23.4  23.8
#> 5        2 Lower    24  503.  229.  -Inf       0.0108   0.715 0.335  55.9  57.1
#> 6        3 Lower    36  503.  309.  -Inf       0.0108   0.683 0.381  75.8  77.1
#> 

# Specified information fraction
gs_design_ahr(IF = c(.25,.75,1), analysisTimes = 36)
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  14.2
#> 2 All            2  28.4
#> 3 All           10  42.5
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 6 x 11
#>   Analysis Bound  Time     N Events       Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl> <dbl>  <dbl>   <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper  10.7  371.   78.3    4.33    0.000254 0.823 0.195  19.3  19.6
#> 2        2 Upper  24.4  511.  235.     2.34    0.585    0.714 0.337  57.4  58.7
#> 3        3 Upper  36    511.  313.     2.01    0.900    0.683 0.381  76.9  78.3
#> 4        1 Lower  10.7  371.   78.3   -1.28    0.0163   0.823 0.195  19.3  19.6
#> 5        2 Lower  24.4  511.  235.  -Inf       0.0163   0.714 0.337  57.4  58.7
#> 6        3 Lower  36    511.  313.  -Inf       0.0163   0.683 0.381  76.9  78.3
#> 

# multiple analysis times & IF
# driven by times
gs_design_ahr(IF = c(.25,.75,1), analysisTimes = c(12,25,36))
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  14.0
#> 2 All            2  27.9
#> 3 All           10  41.9
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 6 x 11
#>   Analysis Bound  Time     N Events       Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl> <dbl>  <dbl>   <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper    12  419.   95.0    4.33    0.000454 0.811 0.210  23.4  23.8
#> 2        2 Upper    25  503.  236.     2.34    0.600    0.711 0.341  57.8  59.1
#> 3        3 Upper    36  503.  308.     2.01    0.900    0.683 0.381  75.8  77.1
#> 4        1 Lower    12  419.   95.0   -1.28    0.0108   0.811 0.210  23.4  23.8
#> 5        2 Lower    25  503.  236.  -Inf       0.0108   0.711 0.341  57.8  59.1
#> 6        3 Lower    36  503.  308.  -Inf       0.0108   0.683 0.381  75.8  77.1
#> 
# driven by IF
gs_design_ahr(IF = c(1/3, .8, 1), analysisTimes = c(12,25,36))
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  13.9
#> 2 All            2  27.8
#> 3 All           10  41.7
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 6 x 11
#>   Analysis Bound  Time     N Events       Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl> <dbl>  <dbl>   <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper  12.5  439.   102.    4.33    0.000576 0.806 0.216  25.2  25.6
#> 2        2 Upper  26.4  501.   246.    2.34    0.640    0.706 0.348  60.1  61.4
#> 3        3 Upper  36    501.   307.    2.01    0.900    0.683 0.381  75.4  76.8
#> 4        1 Lower  12.5  439.   102.   -1.28    0.00904  0.806 0.216  25.2  25.6
#> 5        2 Lower  26.4  501.   246. -Inf       0.00904  0.706 0.348  60.1  61.4
#> 6        3 Lower  36    501.   307. -Inf       0.00904  0.683 0.381  75.4  76.8
#> 

# 2-sided symmetric design with O'Brien-Fleming spending
gs_design_ahr(analysisTimes = c(12, 24, 36),
              binding = TRUE,
              upper = gs_spending_bound,
              upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL, theta=0),
              lower = gs_spending_bound,
              lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL, theta=0),
              h1_spending = FALSE)
#> $enrollRates
#> # A tibble: 3 x 3
#>   Stratum duration  rate
#>   <chr>      <dbl> <dbl>
#> 1 All            2  13.8
#> 2 All            2  27.5
#> 3 All           10  41.3
#> 
#> $failRates
#> # A tibble: 2 x 5
#>   Stratum duration failRate    hr dropoutRate
#>   <chr>      <dbl>    <dbl> <dbl>       <dbl>
#> 1 All            3   0.0770   0.9       0.001
#> 2 All          100   0.0385   0.6       0.001
#> 
#> $bounds
#> # A tibble: 6 x 11
#>   Analysis Bound  Time     N Events     Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl> <dbl>  <dbl> <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper    12  413.   93.5  3.87 0.00208     0.811 0.210  23.0  23.4
#> 2        2 Upper    24  495.  225.   2.36 0.551       0.715 0.335  55.0  56.2
#> 3        3 Upper    36  495.  304.   2.01 0.900       0.683 0.381  74.6  75.9
#> 4        1 Lower    12  413.   93.5 -3.87 0.000000531 0.811 0.210  23.0  23.4
#> 5        2 Lower    24  495.  225.  -2.36 0.00000116  0.715 0.335  55.0  56.2
#> 6        3 Lower    36  495.  304.  -2.01 0.00000119  0.683 0.381  74.6  75.9
#>