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

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

gs_power_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,
  events = c(30, 40, 50),
  analysisTimes = NULL,
  binding = FALSE,
  upper = gs_b,
  upar = gsDesign(k = length(events), test.type = 1, n.I = events, maxn.IPlan =
    max(events), sfu = sfLDOF, sfupar = NULL)$upper$bound,
  lower = gs_b,
  lpar = c(qnorm(0.1), rep(-Inf, length(events) - 1)),
  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)
events	Targeted events 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()
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. Contains a row for each analysis and each bound.

Details

Bound satisfy input upper bound specification in upper, upar and lower bound specification in lower, lpar. The AHR() function computes statistical information at targeted event times. The tEvents() function is used to get events and average HR at targeted analysisTimes.

Examples

library(gsDesign2)
gs_power_ahr() %>% filter(abs(Z) < Inf)
#> # A tibble: 4 x 10
#>   Analysis Bound  Time Events     Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl>  <dbl> <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper  14.9   30.0  2.67      0.0219 0.787 0.240  7.37  7.50
#> 2        2 Upper  19.2   40.0  2.29      0.0885 0.744 0.295  9.79 10.0 
#> 3        3 Upper  24.5   50.0  2.03      0.206  0.713 0.339 12.2  12.5 
#> 4        1 Lower  14.9   30.0 -1.28      0.0266 0.787 0.240  7.37  7.50

# 2-sided symmetric O'Brien-Fleming spending bound
gs_power_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))
#> # A tibble: 6 x 10
#>   Analysis Bound  Time Events      Z Probability   AHR theta  info info0
#>      <int> <chr> <dbl>  <dbl>  <dbl>       <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1        1 Upper  14.9   30.0  3.13     0.00656  0.787 0.240  7.37  7.50
#> 2        2 Upper  24     49.1  2.37     0.114    0.715 0.335 12.0  12.3 
#> 3        3 Upper  36     66.2  2.01     0.323    0.683 0.381 16.3  16.6 
#> 4        1 Lower  14.9   30.0 -2.48     0.000871 0.787 0.240  7.37  7.50
#> 5        2 Lower  24     49.1 -1.21     0.00906  0.715 0.335 12.0  12.3 
#> 6        3 Lower  36     66.2 -0.474    0.0250   0.683 0.381 16.3  16.6