sim_events_delay {nphRCT}

Simulate survival data from a two-arm trial

Description

Simulate survival data from a two-arm trial with survival times on the control arm and experimental arm simulated from an exponential distribution or piecewise exponential distribution.

Usage

sim_events_delay(event_model, recruitment_model, n_c, n_e, max_cal_t)

Arguments

event_model

List containing information to simulate event times, including:

• duration_c Vector of durations corresponding to each of the periods of the control arm.

• duration_e Vector of durations corresponding to each of the periods of the experimental arm.

• lambda_c Vector of parameters \lambda in the exponential distribution corresponding to each of the periods of the control arm.

• lambda_e Vector of parameters \lambda in the exponential distribution corresponding to each of the periods of the experimental arm.

recruitment_model

List containing information to simulate recruitment times, including:

• rec_model Character string specifying the type of recruitment model. Either the power model "power" or piecewise constant model "pw_constant".

• rec_power Parameter used to model recruitment according to power model, see Details.

• rec_period Parameter used to model recruitment according to power model, see Details.

• rec_rate Parameter used to model recruitment according to piecewise constant model, see Details.

• rec_duration Parameter used to model recruitment according to piecewise constant model, see Details.

n_c

Number of individuals on the control arm

n_e

Number of individuals on the event arm

max_cal_t

Calendar time at which the trial ends, all observations are censored at this time.

Details

Survival times are simulated from an exponential distribution with rate parameter \lambda, f(t)=\lambda exp(-\lambda t). This distribution has a median value of log(2)/\lambda; this can be a useful fact when setting the rates lambda_c and lambda_e. The survival times can be simulated from a piecewise exponential distribution, setting one/multiple durations and \lambda parameters for the control and experimental arms.

Recruitment is modeled using either the power model or the piecewise constant model.

The power model is defined as: P(recruited\_before\_T) = (T / rec\_period) ^ {rec\_power}, where rec\_period is the time at the end of recruitment period, and rec\_power controls the rate of recruitment.

Alternatively, recruitment can be modelled using the piecewise constant model. In the simple case with only one time period defined in rec_duration, the times between each of the individuals entering follow-up are samples from the exponential distribution with rate parameter \lambda, f(t)=\lambda exp(-\lambda t). The number of recruitment times defined in n_c or n_e is returned, regardless of the length of duration rec_duration.

In the case with multiple time periods defined in rec_duration, the number of events in each period is sampled from the Poisson distribution P(K=k)=\lambda^k \exp{(-\lambda}/k!), where k is the number of events. The rate parameter \lambda is equal to rec_rate multiplied by the duration of the time period in rec_duration. The recruitment times are then sampled uniformly from the corresponding time period. In the case that insufficient recruitment times have been simulated by the end of the last time period, the additional recruitment times will be simulated after the end of the last time period.

All observations are censored at the calendar time defined in argument max_cal_t.

Value

Data frame with columns event_time, event_status (1 = event, 0 = censored), and treatment arm indicator group.

Examples

library(nphRCT)
set.seed(1)
sim_data <- sim_events_delay(
  event_model=list(
    duration_c = 36,
    duration_e = c(6,30),
    lambda_c = log(2)/9,
    lambda_e = c(log(2)/9,log(2)/18)
  ),
  recruitment_model=list(
    rec_model="power",
    rec_period = 12,
    rec_power = 1
  ),
  n_c=50,
  n_e=50,
  max_cal_t = 36
)