sim.data {WINS}

Function for Data Simulation

Description

A function to simulate a dataset with dependent endpoints. The time-to-event endpoints generated are assumed to have noninformative censoring.

Usage

sim.data(randomseed = 12345, n_trt = 200, n_con = 200, n_ep = 2, n_stratum = 1,
arm.name = c(1,2), ep_type, cdist.rate, sim_method = "copula",
copula_trt = NULL, margins_trt = NULL, paramMargins_trt = NULL,
copula_con = NULL, margins_con = NULL, paramMargins_con = NULL,
rate_trt = NULL, rate_con = NULL, max_accrual_time = NULL)

Arguments

randomseed

The random seed.

n_trt

The number of individuals in the treatment group.

n_con

The number of individuals in the control group.

n_ep

The number of endpoints.

n_stratum

The number of strata. For the simulated dataset, n_stratum is fixed at 1 assuming homogeneous population.

arm.name

A vector for the labels of the two experimental arms, default to be c(1,2). The first label is for the treatment group, and the second label is for the control group.

ep_type

A vector for the outcome type for each endpoint. If scalar, the function will treat all the endpoints as the same type. The types of outcome include:

"tte":

Time-to-event outcome, with the default win strategy: the treatment group wins if min(T_trt, C_trt, C_con + tau) > T_con + tau.

"continuous":

Continuous outcome, with the default win strategy: the treatment group wins if Y_trt > Y_con + tau.

"binary":

Binary outcome coded as 0/1, with the default win strategy: 1 is the winner over 0.

cdist.rate

The censoring time is generated from an exponential distribution. This argument is a vector with the rate of the censoring distribution for each time-to-event endpoint. If scalar, the function will treat all the rate for censoring distribution as the same.

sim_method

Method used to generate multivariate dependence. Possible choices include "copula" and "tte_exponential"

copula_trt

an object of "copula" for the treatment group.

margins_trt

a character vector specifying all the parametric marginal distributions for the treatment group. See details in the R documentation for function "copula::Mvd".

paramMargins_trt

a list for which each element is a list (or numeric vectors) of named components, giving the parameter values of the marginal distributions for the treatment group. See details in the R documentation for function "copula::Mvd".

copula_con

Same argument as "copula_trt" for the control group.

margins_con

Same argument as "margins_trt" for the control group.

paramMargins_con

Same argument as "paramMargins_trt" for the control group.

rate_trt

A vector of the rate in the treatment group for each time-to-event endpoint following an exponential distribution when "sim_method" is set to be the option "tte_exponential".

rate_con

A vector of the rate in the control group for each time-to-event endpoint following an exponential distribution when "sim_method" is set to be the option "tte_exponential".

max_accrual_time

if specified, simulate the study entry time for each individual from uniform distribution U(0,max_accrual_time).

Details

To learn more about "copula", please refer to a discussion on modelling dependence with copulas with the link https://datascienceplus.com/modelling-dependence-with-copulas/. It shows on a high level how copula works, how to use a copula in R using the copula package and then provides a simple example. Moreover, when "sim_method" is set to be the option "tte_exponential", we simulate two endpoints based on the exponential distribution. Dependence between the two simulated endpoints is introduced, as the earlier endpoint takes the min of the two simulated exponential variables.

Value

data

The analysis dataset which contains the following variables:

arm:

A vector for the treatment group (trt = 1 | 2), 1 represents the treatment group and 2 represents the control group.

stratum:

A vector for the stratum number. Alternative names for "stratum" include "group", "level" and "grade".

Delta_j:

A vector for the event status of the j-th endpoint if the endpoint is time-to-event outcome (1=event, 0=censored).

Y_j:

A vector for the outcome of the j-th endpoint, for time-to-event outcome, it would be a vector of simulated time.

Start_time:

A vector for the time when each of the individuals is first accrued to study. Valid only if "max_accrual_time" is not NULL.

Examples

#### Generate with copula: This example is for three endpoints, noted as Y_1, Y_2, and Y_3,
#### with endpoint type as TTE, TTE and continuous.
#### For both the treatment group and the control group, the correlation coefficients
#### cor(Y_1,Y_2), cor(Y_1,Y_3) and cor(Y_2,Y_3) are 0.9, 0.8 and 0.95, respectively.
#### For each treatment group, the marginal distribution for Y_1, Y_2, and Y_3 are Gamma,
#### Beta and Student t specified as a vector in "margins_trt"/"margins_con". The parameters
#### are specified as a list corresponding to the margianl distributions in "paramMargins_trt"
#### or "paramMargins_con".
sim.data <- sim.data(n_trt = 150, n_con = 100, n_ep = 3, arm.name = c("A","B"),
ep_type = c("tte","tte","continuous"), cdist.rate = 0.5, sim_method = "copula",
copula_trt=copula::normalCopula(param=c(0.9,0.8,0.95), dim = 3, dispstr = "un"),
margins_trt=c("gamma", "beta", "t"),
paramMargins_trt=list(list(shape=2, scale=1),list(shape1=2, shape2=2),list(df=5)),
copula_con=copula::normalCopula(param=c(0.9,0.8,0.95), dim = 3, dispstr = "un"),
margins_con=c("gamma", "beta", "t"),
paramMargins_con=list(list(shape=1, scale=1),list(shape1=1, shape2=2),list(df=2)),
max_accrual_time = 5)

win_stat <- win.stat(data = sim.data, ep_type = c("tte","tte","continuous"),
arm.name = c("A","B"), priority = c(1,2,3))

#### Generate two TTE endpoints with the more important TTE endpoint expected to occur later
#### with exponential distribution.
sim.data2 <- sim.data(n_trt = 150, n_con = 100, n_ep = 2, arm.name = c("A","B"),
ep_type = c("tte","tte"), cdist.rate = 0.5, sim_method = "tte_exponential",
rate_trt = c(0.2,0.25),rate_con = c(0.4,0.5), max_accrual_time = 5)

win_stat2 <- win.stat(data = sim.data2, ep_type = c("tte","tte"), arm.name = c("A","B"),
priority = c(1,2))