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

Description

This package offers a collection of functions to fit quantiles regression models for censored residual lifetimes. It provides various options for regression parameters estimation: the induced smoothing approach (smooth), and L1-minimization (non-smooth). It also implements the estimation methods for standard errors of the regression parameters estimates based on an efficient partial multiplier bootstrap method and robust sandwich estimator. Furthermore, a simultaneous procedure of estimating regression parameters and their standard errors via an iterative updating procedure is implemented (iterative). See Kim, K. (2022) "Smoothed quantile regression for censored residual life", <arXiv:2205.00413>.

Author(s)

Maintainer: Kyu Hyun Kim kyuhyunkim07@yonsei.ac.kr

Authors:

• Sangwook Kang

• Sy Han Chiou

See Also

Useful links:

• https://github.com/Kyuhyun07/qris

Surv function imported from survival

Description

This function is imported from the survival package. See Surv.

Value

An object of class Surv. There are methods for print, is.na, and subscripting survival objects. Surv objects are implemented as a matrix of 2 or 3 columns that has further attributes. These include the type (left censored, right censored, counting process, etc.) and labels for the states for multi-state objects. Any attributes of the input arguments are also preserved in inputAttributes. This may be useful for other packages that have attached further information to data items such as labels; none of the routines in the survival package make use of these values, however. In the case of is.Surv, a logical value TRUE if x inherits from class "Surv", otherwise an FALSE.

Draw 95% confidence interval by a quantile regression estimator of residual lifetime from survival data

Description

Draw 95% confidence interval by a quantile regression estimator of residual lifetime from survival data

Usage

## S3 method for class 'qris'
plot(
  x,
  t0s = NULL,
  Qs = NULL,
  nB = NULL,
  vari = NULL,
  byQs = FALSE,
  ggextra = NULL,
  ...
)

Arguments

Value

A list contains ggplot object and the information to generate it.

Examples

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

library(qris)
fm <- Surv(time, status) ~ age + sex
fit <- qris(fm, data = lung2, t0 = 30, Q = 0.5, nB = 50, "nonsmooth", "fmb")

## Plot with default values; Qs <- 1:9 / 10 and t0s = fit2$para$t0 (in this case 30)
plot(fit)

## Plot with without 95% CI is much faster
plot(fit, nB = 0)

## Plot feature can update qris calls 
fit <- plot(fit, Qs = 3:6 / 10, t0s = 1:6 * 10)

## Faster after updating the qris call
plot(fit, byQs = FALSE)
plot(fit, byQs = TRUE)

plot(fit, byQs = FALSE, vari = c("sex", "age"))
plot(fit, byQs = TRUE, vari = c("sex", "age"))

## Extra ggplot components
library(ggplot2)
plot(fit, byQs = FALSE, vari = c("sex", "age"), ggextra = theme(legend.position = "none"))

Prediction for Quantile Regression Model Fitted on Residual life

Description

Prediction based on fitted quantile regression model

Usage

## S3 method for class 'qris'
predict(object, newdata, ...)

Arguments

Value

A vector of prediction

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

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)

Auxiliary for Controlling qris

Description

Auxiliary function as user interface for qris fitting.

Usage

qris.control(maxiter = 10, tol = 0.001, trace = FALSE)

Arguments

Details

When trace is TRUE, output for each iteration is printed to the screen.

Value

A list with the arguments as components.

See Also

qris

Extend a "qris" object to a specified range of tau or t_0 values.

Description

Extend a "qris" object to a specified range of tau or t_0 values.

Usage

qris.extend(x, t0s = NULL, Qs = NULL, nB = NULL, vari = NULL)

Arguments

Residuals for Quantile Regression Model Fitted on Residual life

Description

Residual based on fitted quantile regression model

Usage

## S3 method for class 'qris'
residuals(object, newdata, ...)

Arguments

Value

A vector of residual