trans.haz {SurvSparse}

Transformed hazards model with sparse longitudinal covariates

Description

Statistical inference on transformed hazards model with sparse longitudinal covariates. Kernel-weighted log-likelihood and sieve maximum log-likelihood estimation are combined to conduct statistical inference on the hazards function.

Usage

trans.haz(data, n, nknots, norder, tau, s, h)

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.

nknots

An object of class integer. The number of knots for B-spline.

norder

An object of class integer. The order of B-spline.

tau

An object of class numeric. The maximum follow-up time.

s

An object of class numeric. The parameter for Box-Cox transformation.

h

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

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.

References

Sun, D. et al. (2023) <arXiv:2308.15549>

Examples

library(dplyr)
library(gaussquad)
library(nleqslv)
library(MASS)
n=200
lqrule64 <- legendre.quadrature.rules(64)[[64]]
simdata <- function(  beta ) {
cen=1
nstep=20
Sigmat_z <- exp(-abs(outer(1:nstep, 1:nstep, "-")) / nstep)
z  <-  2*(pnorm(c(mvrnorm(  1, rep(0,20), Sigmat_z  )))-0.5)
left_time_points <- (0:(nstep - 1)) / nstep
z_fun <- stepfun(left_time_points, c(0,z  ))
h_fun <- function(x) { beta  * 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, censoring = cen  )  )
  }
beta=1
data <- replicate( n, simdata( beta ), simplify = FALSE ) %>% bind_rows(.id = "id")
trans.haz(data,n,3,3,1,s=0,n^(-0.35))