Package 'qris'

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 [email protected]

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

x	is an "qris" object or a data.frame returned by plot.qris.
t0s	is a vector of range of t0 to plot; when not specified, the default value is from 0 to presently defined $t_0$
Qs	is a vector of range of Q to plot; when not specified, the default value is from 5% to presently defined $Q$
nB	is the number of multiplier bootstrapping for standard error estimation.
vari	is a character string to choose variables to draw the regression coefficient.
byQs	put Q's on x-axis; only used when both t0's and Q's are specified.
ggextra	is a list that contains additional components to apply to the ggplot output. The ggplot2 library must be loaded in order to utilize this feature.
...	for future extension

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

object	is a qris object
newdata	is a data frame for an optional new data to do predictions. If omitted, the fitted values based on the original data and fit will be returned.
...	for future extension

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

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)

---

Auxiliary for Controlling qris

Description

Auxiliary function as user interface for qris fitting.

Usage

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

Arguments

maxiter	max number of iteration.
tol	tolerance of convergence
trace	a binary variable, determine whether to save output for each iteration.

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

x	is an qris object or a data.frame returned by plot.qris
t0s	is a vector of range of t0 to plot; when not specified, the default value is from 0 to presently defined $t_0$
Qs	is a vector of range of Q to plot; when not specified, the default value is from 5% to presently defined $Q$
nB	is the number of multiplier bootstrapping for standard error estimation.
vari	is a character string to choose variables to draw the regression coefficient.

---

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

object	is a qris object
newdata	is a data frame for an optional new data to do predictions. If omitted, the fitted values based on the original data and fit will be returned.
...	for future extension

Value

A vector of residual

---