simu.trial: Simulate Survival Trial Data

Description

simu.trial simulates survival data allowing flexible input of design parameters. It supports both event-driven design and fixed study duration design.

Usage

simu.trial(
  type = c("event", "time"),
  trial_param,
  bsl_dist = c("weibull", "loglogistic", "mix-weibull"),
  bsl_param,
  drop_param0,
  drop_param1 = drop_param0,
  entry_pdf0 = function(x) {
     (1/trial_param[2]) * (x >= 0 & x

Value

A list containing the following components

data: a dataframe (simulated dataset) with columns:

id: identifier number from 1:n, n is the total sample size
group: group variable with 1 indicating treatment and 0 indicating control
aval: observed survival time, the earliest time among event time, drop-out time and end of study time
cnsr: censoring indicator with 1 indicating censor and 0 indicating event
cnsr.desc: description of the cnsr status, including three options- drop-out, event and end of study. Both drop-out and end of study are considered as censor.
event: event indicator with 1 indicating event and 0 indicating censor
entry.time: time when the patient is enrolled in the study

a list of summary information of the trial including

type: a character indicating input design type - event or time

entrytime

a number indicating input enrollment period

maxob

a number indicating the maximum study duration. For time type of design, the value is equal to the enrollment period plus the follow-up period. For event type of design, the value is the calendar time of the last event.

Arguments

type: indicates whether event-driven trial ("event) or fixed study duration trial ("time"), Option: c("event", "time")
trial_param: a vector of length 3 with components for required subject size, enrollment time and required number of events ("event" type trial)/follow-up time ("time" type trial)
bsl_dist: indicates the survival distribution for control group, option: c("weibull", "loglogistic",mix-weibull)
bsl_param: a vector of length 2 with the shape and rate (scale) parameter for the weibull or loglogistic survival distribution of control group. A vector of length 3 with shape, rate and cure rate for the mix-weibull distribution. See details.
drop_param0: a vector of length 2 with shape and scale parameter for the weibull distribution of drop-out time for control group
drop_param1: a vector of length 2 with shape and scale parameter for the weibull distribution of drop-out time for treatment group
entry_pdf0: a function describing the pdf of the entry time for control. Default: uniform enrollment
entry_pdf1: a function describing the pdf of the entry time for treatment.
enrollmentType: default value is NULL, indicating a entry time follows specified distribution. Specify "piecewise uniform", indicating entry time follows piecewise uniform
entryP: if enrollmentType is piecewise uniform. entryP should be provided with a list containing the enrollment rate at each interval
HR_fun: a function describing the hazard ratio function between treatment and control group
ratio: allocation ratio between treatment and control group. For example, ratio=2 if 2:1 allocation is used.
cureModel: specifies the cure model. "PHCM" and "PHCRM".
cureRate1: specifies the cure rate for the susceptible population in the experimental group if the cure model is PHCM.
HR_data: a matrix consisting of covariates values
upInt: a value indicating the upper bound used in the uniroot function. See details. Default: 100
summary: a logical indicating whether basic information summary is printed to the console or not, Default: TRUE

Details

The loglogistic distribution for the event time has the survival function \(S(x)=b^a/(b^a+x^a)\) and hazard function \(\lambda(x)=a/b(x/b)^{a-1}/(1+(t/b)^a)\), where \(a\) is the shape parameter and \(b\) is the scale parameter. The weibull distribution for event time and drop-out time has the survival function \(S(x)=exp(-(xb)^a)\) and hazard function \(\lambda(x)=ab(xb)^{a-1}\), where \(a\) is the shape parameter and \(b\) is the rate parameter. The median of weibull distribution is \((ln(2)^{1/a}/b)\). If drop out or loss to follow-up are do not need to be considered, a very small rate parameter \(b\) can be chosen such that the median time is greatly larger than the study duration. The default entry time is uniformly distributed within the enrollment period by default. Other options are allowed through providing the density function.

The simu.trial function simulates survival times for control and treatment groups separately. The control survival times are drawn from standard parametric distribution (Weibull, Loglogistic). Let \(\lambda_1(t)\) and \(\lambda_0(t)\) denote the hazard function for treatment and control. It is assumed that \(\lambda_1(t)/\lambda_0(t)=g(t)\), where \(g(t)\) is the user-defined function, describing the change of hazard ratio over time. In case of proportional hazards, \(g(t)\) is a constant. The survival function for treatment group is \(S_1(t)=exp(-\int_0^t g(s)\lambda_0(s)ds)\). The Survival time T is given by \(T=S_1^(-1)(U)\), where U is drawn from uniform (0,1). More details can be found in Bender, et al. (2005). Function uniroot from stats package is used to generate the random variable. The argument upInt in simu.trial function corresponds to the upper end point of the search interval and it can be adjusted by user if the default value 100 is not appropriate. More details can be found in help file of uniroot function.

References

Bender, R., Augustin, T., & Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in medicine, 24(11), 1713-1723.

Examples

Run this code

# total sample size
N <- 300
# target event
E <- 100
# allocation ratio
RR <- 2
# enrollment time
entry <- 12
# follow-up time
fup <- 18
# shape and scale parameter of weibull for entry time
b_weibull <- c(1,log(2)/18)
# shape and scale parameter of weibull for drop-out time
drop_weibull <- c(1,log(2)/30)
# hazard ratio function (constant)
HRf <- function(x){0.8*x^0}

### event-driven trial
set.seed(123445)
data1 <- simu.trial(type="event",trial_param=c(N,entry,E),bsl_dist="weibull",
                    bsl_param=b_weibull,drop_param0=drop_weibull,HR_fun=HRf,
                    ratio=RR)

### fixed study duration
set.seed(123445)
data2 <- simu.trial(type="time",trial_param=c(N,entry,fup),bsl_dist="weibull",
                    bsl_param=b_weibull,drop_param0=drop_weibull,HR_fun=HRf,
                    ratio=RR)

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