ClaytonFrank.Weibull.data {Copula.Markov.survival}

Generate data from the Clayton copula for serial dependence and the Frank copula for dependent censoring with the Weibull distributions

Description

The data generation process is based on the Clayton copula C_theta for serial dependence and the Frank copula tilde(C)_alpha for dependent censoring with the marginal distributions Weib(scale1, shape1) and Weib(scale2, shape2). Censoring percentage can be controlled by constant b. This function is used when doing parametric bootstrap. The guide for using this function shall be explained by Huang (2019), and Huang, Wang and Emura (2020).

Usage

ClaytonFrank.Weibull.data(N, scale1, shape1, theta, scale2, shape2, alpha, b, l)

Arguments

N

sample size

scale1

scale parameter for Weib(scale1, shape1), scale1 > 0

shape1

shape parameter for Weib(scale1, shape1), shape1 > 0

theta

copula parameter for C_theta, theta > 0

scale2

scale parameter for Weib(scale2, shape2), scale2 > 0

shape2

shape parameter for Weib(scale2, shape2), shape2 > 0

alpha

copula parameter for tilde(C)_alpha, alpha \neq 0

b

parameter of Unif(0, b) for controlling censoring percentage

l

length for data generation (default = 300)

Value

A list with the following elements:

Subject

a vector for numbers of subject

T_ij

a vector for event times

delta_ij

a vector for event indicator (=1 if recurrent; =0 if censoring)

T_i_star

a vector for death times

delta_i_star

a vector for death indicator (=1 if death; =0 if censoring)

Author(s)

Xinwei Huang

References

Huang XW, Wang W, Emura T (2020) A copula-based Markov chain model for serially dependent event times with a dependent terminal event. Japanese Journal of Statistics & Data Science. Accepted.

Examples

Y = ClaytonFrank.Weibull.data(N = 100, scale1 = 1, shape1 =0.5, theta = 2,
                              scale2 = 0.45, shape2 = 0.5, alpha = 2, b = 10, l = 300)