FrankClayton.Weibull.MLE {Copula.Markov.survival} R Documentation

## Parameter estimation based on the Frank copula for serial dependence and the Clayton copula for dependent censoring with the Weibull distributions

### Description

Perform two-stage estimation based on the Frank copula C_theta for serial dependence and the Clayton copula tilde(C)_alpha for dependent censoring with the marginal distributions Weib(scale1, shape1) and Weib(scale2, shape2). The jackknife method estimates the asymptotic covariance matrix. Parametric bootstrap is applied while doing Kolmogorov-Smirnov tests and Cramer-von Mises test. The guide for using this function shall be explained by Huang (2019), and Huang, Wang and Emura (2020).

### Usage

FrankClayton.Weibull.MLE(subject, t.event, event, t.death, death, stageI, Weibull.plot,
jackknife, plot, GOF, GOF.plot, rep.GOF, digit)

### Arguments

 subject a vector for numbers of subject t.event a vector for event times event a vector for event indicator (=1 if recurrent; =0 if censoring) t.death a vector for death times death a vector for death indicator (=1 if death; =0 if censoring) stageI an option to select MLE or LSE method for the 1st-stage optimization Weibull.plot if TRUE, show the Weibull probability plot jackknife if TRUE, the jackknife method is used for estimate covariance matrix (default = TRUE) plot if TRUE, the plots for marginal distributions are shown (default = FALSE) GOF if TRUE, show the p-values for KS-test and CvM-test GOF.plot if TRUE, show the model diagnostic plot rep.GOF repetition number of parametric bootstrap digit accurate to some decimal places

### Details

When jackknife=FALSE, the corresponding standard error and confidence interval values are shown as NA.

### Value

A list with the following elements:

 Sample_size Sample size N Case Count for event occurences scale1 Scale parameter for Weib(scale1, shape1) shape1 Shape parameter for Weib(scale1, shape1) scale2 Scale parameter for Weib(scale2, shape2) shape2 Shape parameter for Weib(scale2, shape2) theta Copula parameter for the Frank copula C_theta alpha Copula parameter for the Clayton copula tilde(C)_alpha COV Asymptotic covariance estimated by the jackknife method KS Kolmogorov-Smirnov test statistics p.KS P-values for Kolmogorov-Smirnov tests CM Cramer-von Mises test statistics p.CM P-values for Cramer-von Mises tests Convergence Convergence results for each stage Jackknife_error Count for error in jackknife repititions Log_likelihood Log-likelihood values

Xinwei Huang

### Examples

data = FrankClayton.Weibull.data(N = 30, scale1 = 1, shape1 =0.5, theta = 2,
scale2 = 0.45, shape2 = 0.5, alpha = 2, b = 10, l = 300)

FrankClayton.Weibull.MLE(subject = data\$Subject,
t.event = data\$T_ij, event = data\$delta_ij,
t.death = data\$T_i_star, death = data\$delta_i_star,
jackknife= TRUE, plot = TRUE)

[Package Copula.Markov.survival version 1.0.0 Index]