Predict time at which a targeted event count is achieved

expected_time() is made to match input format with ahr() and to solve for the time at which the expected accumulated events is equal to an input target. Enrollment and failure rate distributions are specified as follows. The piecewise exponential distribution allows a simple method to specify a distribution and enrollment pattern where the enrollment, failure and dropout rates changes over time.

Usage

expected_time(
  enroll_rate = define_enroll_rate(duration = c(2, 2, 10), rate = c(3, 6, 9) * 5),
  fail_rate = define_fail_rate(stratum = "All", duration = c(3, 100), fail_rate =
    log(2)/c(9, 18), hr = c(0.9, 0.6), dropout_rate = rep(0.001, 2)),
  target_event = 150,
  ratio = 1,
  interval = c(0.01, 100)
)

Arguments

enroll_rate: An enroll_rate data frame with or without stratum created by define_enroll_rate().
fail_rate: A fail_rate data frame with or without stratum created by define_fail_rate().
target_event: The targeted number of events to be achieved.
ratio: Experimental:Control randomization ratio.
interval: An interval that is presumed to include the time at which expected event count is equal to target_event.

Value

A data frame with Time (computed to match events in target_event), AHR (average hazard ratio), Events (target_event input), info (information under given scenarios), and info0

(information under related null hypothesis) for each value of total_duration input.

Specification

Examples

# Example 1 ----
# default
# \donttest{
expected_time()
#>       time       ahr event     info info0
#> 1 14.90814 0.7865729   150 36.86707  37.5
# }

# Example 2 ----
# check that result matches a finding using AHR()
# Start by deriving an expected event count
enroll_rate <- define_enroll_rate(duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
fail_rate <- define_fail_rate(
  duration = c(3, 100),
  fail_rate = log(2) / c(9, 18),
  hr = c(.9, .6),
  dropout_rate = .001
)
total_duration <- 20
xx <- ahr(enroll_rate, fail_rate, total_duration)
xx
#>   time       ahr    event     info    info0
#> 1   20 0.7377944 208.3641 50.97575 52.09103

# Next we check that the function confirms the timing of the final analysis.
# \donttest{
expected_time(enroll_rate, fail_rate,
  target_event = xx$event, interval = c(.5, 1.5) * xx$time
)
#>   time       ahr    event     info    info0
#> 1   20 0.7377944 208.3641 50.97575 52.09103
# }

# Example 3 ----
# In this example, we verify `expected_time()` by `ahr()`.
# \donttest{
x <- ahr(
  enroll_rate = enroll_rate, fail_rate = fail_rate,
  ratio = 1, total_duration = 20
)

cat("The number of events by 20 months is ", x$event, ".\n")
#> The number of events by 20 months is  208.3641 .

y <- expected_time(
  enroll_rate = enroll_rate, fail_rate = fail_rate,
  ratio = 1, target_event = x$event
)

cat("The time to get ", x$event, " is ", y$time, "months.\n")
#> The time to get  208.3641  is  20 months.
# }