PIC {PICBayes}

PH model for partly interval-censored data

Description

Fit a Bayesian semiparametric PH model to partly interval-censored data.

Usage

PIC(L, R, y, xcov, IC, scale.designX, scaled, binary, order, knots, grids, 
a_eta, b_eta, a_ga, b_ga, beta_iter, beta_cand, beta_sig0, x_user, 
total, burnin, thin, conf.int, seed)

Arguments

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, 3=exact.

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.

binary

The vector indicating whether each covariate is binary: 1=binary, 0=not.

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}.

beta_iter

The number of initial iterations in the Metropolis-Hastings sampling for beta_r.

beta_cand

The sd of the proposal normal distribution in the MH sampling for beta_r.

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.

Details

The baseline cumulative hazard is approximated by a linear combination of I-splines:

sum_{l=1}^{K}(gamma_l*b_l(t)).

The baseline hazard is approximated by a linear combination of basis M-splines:

sum_{l=1}^{K}(gamma_l*M_l(t)).

For a binary prdictor, we sample e^{beta_r}, with Gamma prior.

The regression coefficient beta_r for a continuous predictor is sampled using MH algorithm. During the initial beta_iter iterations, sd of the proposal distribution is beta_cand. Afterwards, proposal sd is set to be the sd of available MCMC draws.

Value

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.

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 functions is estimated.

DIC

Deviance information criterion.

NLLK

Negative log pseudo-marginal likelihood.

Author(s)

Chun Pan

References

Pan, C., Cai, B., and Wang, L. (2020). A Bayesian approach for analyzing partly interval-censored data under the proportional hazards model. Statistical Methods in Medical Research,

DOI: 10.1177/0962280220921552.

Examples

# Number of iterations set to very small for CRAN automatic testing
data(da1)
try1<-PICBayes(formula=Surv(L,R,type='interval2')~x1+x2,data=data.frame(da1),
model='PIC',IC=da1[,6],scale.designX=TRUE,scale=c(1,0),binary=c(0,1),
order=3,knots=c(0,2,6,max(da1[,1:2],na.rm=TRUE)+1),grids=seq(0.1,10.1,by=0.1),
a_eta=1,b_eta=1,a_ga=1,b_ga=1,beta_iter=11,beta_cand=1,beta_sig0=10,
x_user=NULL,total=60,burnin=10,thin=1,conf.int=0.95,seed=1)