FrankFrank.Weibull.MLE: Parameter estimation based on the Frank copula for serial...
In Copula.Markov.survival: Copula Markov Model with Dependent Censoring

Description Usage Arguments Details Value Author(s) Examples

View source: R/FrankFrank.Weibull.MLE.R

Perform two-stage estimation based on the Frank 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). 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).

1 2	FrankFrank.Weibull.MLE(subject, t.event, event, t.death, death, stageI, Weibull.plot, jackknife, plot, GOF, GOF.plot, rep.GOF, digit)

`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 vindicator (=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

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

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 Frank 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

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


FrankFrank.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)