clusterIC_trt_DP: PH model with random intercept and random treatment for...
In PICBayes: Bayesian Models for Partly Interval-Censored Data

Description Usage Arguments Details Value Author(s)

Fit a Bayesian semiparametric PH model with random intercept and random treatment for clustered general interval-censored data. Each random effect follows a Dirichlet process mixture distribution.

clusterIC_trt_DP(L, R, y, xcov, IC, scale.designX, scaled, xtrt, area, binary, 
I, order, knots, grids, a_eta, b_eta, a_ga, b_ga, a_alpha, b_alpha, H, 
a_tau_star, b_tau_star, a_alpha_trt, b_alpha_trt, H_trt, a_tau_trt_star, 
b_tau_trt_star, beta_iter, phi_iter, beta_cand, phi_cand, beta_sig0, x_user, 
total, burnin, thin, conf.int, seed)

`L`	The vector of left endpoints of the observed time intervals.
`R`	The vector of right endponts of the observed time intervals.
`y`	The vector of censoring indicator: 0=left-censored, 1=interval-censored, 2=right-censored.
`xcov`	The covariate matrix for the p predictors.
`IC`	The vector of general interval-censored indicator: 1=general interval-censored, 0=exact.
`scale.designX`	The TRUE or FALSE indicator of whether or not to scale the design matrix X.
`scaled`	The vector indicating whether each covariate is to be scaled: 1=to be scaled, 0=not.
`xtrt`	The covariate that has a random effect.
`area`	The vector of cluster ID.
`binary`	The vector indicating whether each covariate is binary.
`I`	The number of clusters.
`order`	The degree of basis I-splines: 1=linear, 2=quadratic, 3=cubic, etc.
`knots`	A sequence of knots to define the basis I-splines.
`grids`	A sequence of points at which baseline survival function is to be estimated.
`a_eta`	The shape parameter of Gamma prior for `gamma_l`.
`b_eta`	The rate parameter of Gamma prior for `gamma_l`.
`a_ga`	The shape parameter of Gamma prior for `e^{beta_r}`.
`b_ga`	The rate parameter of Gamma prior for `e^{beta_r}`.
`a_alpha`	The shape parameter of Gamma prior for `alpha`.
`b_alpha`	The rate parameter of Gamma prior for `alpha`.
`H`	The number of distinct components in DP mixture prior under blocked Gibbs sampler.
`a_tau_star`	The shape parameter of `G_0` in DP mixture prior.
`b_tau_star`	The rate parameter of `G_0` in DP mixture prior.
`a_alpha_trt`	The shape parameter of Gamma prior for `alpha_trt`.
`b_alpha_trt`	The rate parameter of Gamma prior for `alpha_trt`.
`H_trt`	The number of distinct components in DP mixture prior under blocked Gibbs sampler for random treatment.
`a_tau_trt_star`	The shape parameter of `G_0` in DP mixture prior for random treatment.
`b_tau_trt_star`	The rate parameter of `G_0` in DP mixture prior for random treatment.
`beta_iter`	The number of initial iterations in the Metropolis-Hastings sampling for `beta_r`.
`phi_iter`	The number of initial iterations in the Metropolis-Hastings sampling for `phi_i`.
`beta_cand`	The sd of the proposal normal distribution in the initial MH sampling for `beta_r`.
`phi_cand`	The sd of the proposal normal distribution in the initial MH sampling for `phi_i`.
`beta_sig0`	The sd of the prior normal distribution for `beta_r`.
`x_user`	The user-specified covariate vector at which to estimate survival function(s).
`total`	The number of total iterations.
`burnin`	The number of burnin.
`thin`	The frequency of thinning.
`conf.int`	The confidence level of the CI for `beta_r`.
`seed`	A user-specified random seed.

Both random intercept and random treatment follow its own DP mixture prior. DP mixture prior:

phi_i~N(0,tau_{i}^{-1})

tau_{i}~G

G~DP(alpha,G_{0})

G_{0}=Gamma(a_tau_star,b_tau_star)

tau_{h}^{*}~G_{0}, h=1,...,H

The blocked Gibbs sampler proposed by Ishwaran and James (2001) is used to sample from the posteriors under the DP mixture prior.

a list containing the following elements:

`N`	The sample size.
`parbeta`	A `total` by `p` matrix of MCMC draws of `beta_r`, r=1, ..., p.
`parsurv0`	A `total` by `length(grids)` matrix, each row contains the baseline survival at `grids` from one iteration.
`parsurv`	A `total` by `length(grids)*G` matrix, each row contains the survival at `grids` from one iteration. G is the number of sets of user-specified covariate values.
`paralpha`	A `total` by 1 vector of MCMC draws of `alpha`.
`paralpha_trt`	A `total` by 1 vector of MCMC draws of `alpha_trt`.
`parphi`	A `total` by `I` matrix of MCMC draws of `phi_i`, i=1,...,I.
`parphi_trt`	A `total` by `I` matrix of MCMC draws of `phi_trt_i`, i=1,...,I.
`partau_star`	A `total` by H matrix of MCMC draws of `tau_star`.
`partau_trt_star`	A `total` by H_trt matrix of MCMC draws of `tau_trt_star`.
`coef`	A vector of regression coefficient estimates.
`coef_ssd`	A vector of sample standard deviations of regression coefficient estimates.
`coef_ci`	The credible intervals for the regression coefficients.
`S0_m`	The estimated baseline survival at `grids`.
`S_m`	The estimated survival at `grids` with user-specified covariate values `x_user`.
`grids`	The sequance of points where baseline survival function is estimated.
`DIC`	Deviance information criterion.
`NLLK`	Negative log pseudo-marginal likelihood.