qris: Estimate a quantile regression estimator of residual lifetime...

In qris: Quantile Regression Model for Residual Lifetime Using an Induced Smoothing Approach

Estimate a quantile regression estimator of residual lifetime from survival data

Description

Using three estimation methods (1) L1-minimization(non-smooth estimating equation (2) Induced smoothing approach (smooth estimating equation (3) Iterative procedure with induced smoothing approach (smooth estimating equation

Usage

qris(
  formula,
  data,
  t0 = 0,
  Q = 0.5,
  nB = 100,
  method = c("smooth", "iterative", "nonsmooth"),
  se = c("fmb", "pmb"),
  init = c("rq", "noeffect"),
  verbose = FALSE,
  control = qris.control()
)

Arguments

formula	is a formula expression, of the form response ~ predictors. The response is a Surv object with right censoring.
data	is an optional data.frame in which to interpret the variables occurring in the formula.
t0	is the follow-up time (or basetime of analysis). The default followup time is set to 0.
Q	is the quantile. The default quantile is set to 0.5.
nB	is number of multiplier bootstrapping for V matrix estimation. The default number of bootstrapping is set to 100.
method	is an option for specifying the methods of parameters estimation; smooth is the default in which parameters estimates and their standard errors are obtained via induced smoothed estimating equations. nonsmooth uses a L1-minimization method for non-smooth object functions in coefficient estimation. iterative simultaneously estimates parameters and their standard errors based on the iterative updates for the parameter estimates.
se	is an option for specifying the methods of standard errors estimation; The available options are pmb and fmb. The pmb is the default option. It estimates the standard errors via partial multiplier bootstrapping and is only available when method = "smooth" or method = "iterative". The fmb uses a full multiplier bootstrapping in standard errors estimation.
init	is an option for specifying the initial values of the parameters estimates. Available options are rq and noeffect. These options correspond to the estimates from the quantreg::rq() and a zero vector, respectively. Alternatively, user defined numerical vector is also allowed.
verbose	Shows computation status.
control	controls maximum number of iteration, tolerance of convergence and whether to display output for each iteration when method = "iterative".

Value

An object of class "qris" contains model fitting results. The "qris" object is a list containing at least the following components:

coefficient

a vector of point estimates

stderr

a vector of standard error of point estimates

vcov

a matrix of the estimated variance-covariance matrix

maxiter

a number of iteration until convergence (only for iterative procedure)

Examples

## ######################################### 
## Simulated data
## #########################################
data.gen <- function(n) {
  r0 <- .2 * sqrt(log(2))
  r1 <- .1 * sqrt(log(2))
  dat <- data.frame(censoring = runif(n, 0, 24.35),
                    Time0 = sqrt(-log(1 - runif(n))),
                    X = rbinom(n, 1, .5))
  dat$Time0 <- ifelse(dat$X > 0, dat$Time0 / r1, dat$Time0 / r0)
  dat$Time <- pmin(dat$Time0, dat$censoring)
  dat$status <- 1 * (dat$Time0 < dat$censoring)
  subset(dat, select = c(Time, status, X))
}

set.seed(1)
dat <- data.gen(200)
fm <- Surv(Time, status) ~ X
fit1 <- qris(fm, data = dat, t0 = 1, Q = 0.5, nB = 100, "smooth", "pmb", c(1,1))
fit2 <- qris(fm, data = dat, t0 = 1, Q = 0.5, nB = 100, "nonsmooth", "fmb", "rq")
fit3 <- qris(fm, data = dat, t0 = 1, Q = 0.5, nB = 100, "iterative", "fmb", "rq",
             control = qris.control(maxit = 20, tol = 1e-3, trace = TRUE))

summary(fit1)
summary(fit2)
summary(fit3)

## #########################################
## Real data application
## #########################################
data(cancer, package = "survival")
lung2 <- subset(lung, select = c(time, status, age, sex))
## tidy up the data
lung2$status <- lung2$status - 1
lung2$sex <- lung2$sex - 1

fm <- Surv(time, status) ~ age + sex
fit1 <- qris(fm, data = lung2, t0 = 0, Q = 0.5, nB = 100, "iterative", "pmb", "rq")
fit2 <- qris(fm, data = lung2, t0 = 30, Q = 0.5, nB = 100, "nonsmooth", "fmb", c(1, 0, 1))
fit3 <- qris(fm, data = lung2, t0 = 100, Q = 0.5, nB = 100,"smooth", "pmb", "rq")

summary(fit1)
summary(fit2)
summary(fit3)

plot(fit2, Qs = 4:6 / 10)

qris documentation built on May 29, 2024, 8 a.m.