Generate Correlated PFS and OS Using Gumbel Copula

Generate correlated PFS and OS endpoints using the Gumbel copula. Marginally, both PFS and OS follow exponential distributions. This function can be used as custom generator in the function endpoint().

Note that the Gumbel copula is applied to the survival functions of OS and time-to-progression (TTP). PFS is defined as min(TTP, OS), which also follows an exponential distribution.

For more information, refer to this vignette.

Usage

CorrelatedPfsAndOs2(
  n,
  median_pfs,
  median_os,
  kendall,
  pfs_name = "pfs",
  os_name = "os"
)

Arguments

n

integer. Number of observations.

median_pfs

numeric. Median of PFS.

median_os

numeric. Median of OS.

kendall

numeric. Kendall's tau between observed, uncensored PFS and OS. Must be positive and usually away from zero. Note that this argument is not the Kendall's tau between TTP and OS.

pfs_name

column name of PFS in returned data frame. It must be consistent with name in the function endpoint().

os_name

column name of OS in returned data frame. It must be consistent with name in the function endpoint().

Value

A data frame of n rows and four columns, including PFS, OS and their event indicators. The event indicators are all 1s. The column names are <pfs_name>, <pfs_name>_event, <os_name>, and <os_name>_event.

Examples

pfs_and_os <- endpoint(name = c('PFS', 'Os'),
                       type = c('tte', 'tte'),
                       generator = CorrelatedPfsAndOs2,
                       median_pfs = 5,
                       median_os = 11,
                       kendall = .6,
                       pfs_name = 'PFS',
                       os_name = 'Os')

pfs_and_os # run it in console to see summary report
#> Summary generated.

## for validation purpose only
## not the recommended way to use TrialSimulator
dat <- pfs_and_os$test_generator(n = 1e4)
cor(dat[, 1:2], method = 'kendall') ## close to 0.6
#>           PFS        Os
#> PFS 1.0000000 0.6012212
#> Os  0.6012212 1.0000000