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Expected events observed under piecewise exponential model

Source: R/expected_event.R
expected_event.Rd

Computes expected events over time and by strata under the assumption of piecewise constant enrollment rates and piecewise exponential failure and censoring rates. 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. While the main purpose may be to generate a trial that can be analyzed at a single point in time or using group sequential methods, the routine can also be used to simulate an adaptive trial design. The intent is to enable sample size calculations under non-proportional hazards assumptions for stratified populations.

Usage

expected_event(
  enroll_rate = define_enroll_rate(duration = c(2, 2, 10), rate = c(3, 6, 9)),
  fail_rate = define_fail_rate(duration = c(3, 100), fail_rate = log(2)/c(9, 18),
    dropout_rate = 0.001),
  total_duration = 25,
  simple = TRUE
)

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().

total_duration

Total follow-up from start of enrollment to data cutoff.

simple

If default (TRUE), return numeric expected number of events, otherwise a data frame as described below.

Value

The default when simple = TRUE is to return the total expected number of events as a real number. Otherwise, when simple = FALSE, a data frame is returned with the following variables for each period specified in fail_rate:

  • t: start of period.

  • fail_rate: failure rate during the period.

  • event: expected events during the period.

The records in the returned data frame correspond to the input data frame fail_rate.

Details

More periods will generally be supplied in output than those that are input. The intent is to enable expected event calculations in a tidy format to maximize flexibility for a variety of purposes.

Specification

Examples

library(gsDesign2)

# Default arguments, simple output (total event count only)
expected_event()
#> [1] 57.3537

# Event count by time period
expected_event(simple = FALSE)
#>   t  fail_rate    event
#> 1 0 0.07701635 22.24824
#> 2 3 0.03850818 35.10546

# Early cutoff
expected_event(total_duration = .5)
#> [1] 0.02850923

# Single time period example
expected_event(
  enroll_rate = define_enroll_rate(duration = 10, rate = 10),
  fail_rate = define_fail_rate(duration = 100, fail_rate = log(2) / 6, dropout_rate = .01),
  total_duration = 22,
  simple = FALSE
)
#>   t fail_rate    event
#> 1 0 0.1155245 80.40974

# Single time period example, multiple enrollment periods
expected_event(
  enroll_rate = define_enroll_rate(duration = c(5, 5), rate = c(10, 20)),
  fail_rate = define_fail_rate(duration = 100, fail_rate = log(2) / 6, dropout_rate = .01),
  total_duration = 22, simple = FALSE
)
#>   t fail_rate    event
#> 1 0 0.1155245 118.8484