tv.co.Cox {SurvSparse}

Multiplicative hazards model with sparse longitudinal covariates

Description

Regression analysis of multiplicative hazards model with sparse longitudinal covariates. The kernel weighting approach is employed to impute the missing value and localize the estimating equation. A wild bootstrap-based simultaneous confidence band for the nonparametric function is also provided.

Usage

tv.co.Cox(data, n, l, times, bd, scb)

Arguments

data

An object of class tibble. The structure of the tibble must be: tibble(id = id, X = failure time, covariates = observation for covariates, obs_times = observation times, delta = censoring indicator).

n

An object of class integer. The sample size.

l

An object of class vector. The selection vector. For example, for the p dimensional regression coefficient function, if we want to construct simultaneous confidence band for the first regression coefficient function, we can take l=c(1,0,...,0).

times

An object of class vector. The interest time.

bd

An object of class vector. If use auto bandwidth selection, the structure of the vector must be: bd=c(the maximum bandwidth, the minimum bandwidth, the number of bandwidth divided). If use fixed bandwidth, bd is the chosen bandwidth.

scb

An object of class vector. If need to construct the simultaneous confidence band, the structure of the vector must be: c(desirable confidence level, repeat times). Otherwise, scb=0.

Value

a list with the following elements:

est

The estimation for the corresponding parameters.

se

The estimation for the standard error of the estimated parameters.

scb

The quantile used to construct simultaneous confidence band.

References

Sun, Z. and Cao, H. (2023) <arXiv:2310.15877>

Examples

library(dplyr)
library(gaussquad)
library(MASS)
library(nleqslv)
n=500
beta<-function(t){
  0.5*(t+0.5)^2
}
lqrule64 <- legendre.quadrature.rules(64)[[64]]
simdata <- function(  beta ) {
cen=1
nstep=20
Sigmat_z <- exp(-abs(outer(1:nstep, 1:nstep, "-")) / nstep)
z  <-c(mvrnorm(  1, rep(0,20), Sigmat_z  ))
left_time_points <- (0:(nstep - 1)) / nstep
z_fun <- stepfun(left_time_points, c(0,z  ))
h_fun <- function(x) { beta(x) * z_fun(x)  }
lam_fun <- function(tt) 2 * exp(h_fun(tt))
u <- runif(1)
fail_time <- nleqslv(0, function(ttt)
legendre.quadrature(lam_fun, lower = 0,upper = ttt, lqrule64) + log(u))$x
X <- min(fail_time, cen)
obs=rpois(1,  5)+1
tt= sort(runif(obs, min = 0, max = 1))
obs_times <- tt[which(tt<=cen)]
if (length(obs_times) == 0)
 obs_times <- cen
 covariates_obscov <-z_fun(obs_times)
 return( tibble(X = X,delta = fail_time < cen,
  covariates = covariates_obscov,obs_times = obs_times   )  ) }


data <- replicate(  n, simdata( beta ), simplify = FALSE ) %>% bind_rows(.id = "id")
tv.co.Cox(data,n,l,0.2,bd=c(n^(-0.4),n^(-0.4)),scb=0)