Kernel estimate of hazard function for right-censored data
Description
Kernel estimate of (unconditional) hazard function for right-censored data. Options include two methods for bandwidth selection.
Usage
khazard(times, delta, h = NULL, t = NULL, t.length = 100,
tmin = NULL, tmax = NULL, kernel = "epanechnikov",
type = "interior", parallel = FALSE, value = "CVML",
h.method = "crossval", optim.method = "optimize",
tol = ifelse(h.method == "crossval", 10^(-6), 1), run = 2, ...)
Arguments
times
vector of observed times
delta
vector of censoring indicator. 0 - censored, 1 - uncensored (dead)
h
bandwidth (scalar or vector). If missing, h is found using some bandwidth selection method.
t
vector of time points at which estimate is evaluated
t.length
number of grid points
tmin, tmax
minimum/maximum values for grid
kernel
kernel function, possible values are: "epanechnikov" (default), "gaussian", "rectangular", "quartic".
type
Type of kernel estimate. Possible types are: "exterior", "interior" (default).
parallel
allows parallel computation. Default is FALSE.
value
If h parameter is vector, this option controls output values. If "CVML" (default), the crossvalidation or log-likelihood values only are calculated. If "hazard", the hazard functions only are calculated. If "both" the crossvalidation or log-likelihood values and hazard function are calculated.
h.method
method for bandwidth selection. Possible methods are: "crossval" (default), "maxlike".
optim.method
method for numerical optimization of the crossvalidation or log-likelihood function. Possible methods are: "optimize" (default), "ga".
tol
the desired accuracy of optimization algorithm
run
the number of consecutive generations without any improvement in the best fitness value before the GA is stopped.
...
additional arguments of GA algorithm
Details
External type of kernel estimator is defined as the ratio of kernel estimator of the subdensity of the uncensored observations to the survival function of the observable time. Internal type of kernel estimator is based on a convolution of the kernel function with a nonparametric estimator of the cumulative hazard function (Nelson-Aalen estimator).
Value
Returns an object of class 'khazard' which is a list with fields
time.points
vector of time points at which estimate is evaluated
hazard
data frame of time points, hazard function values and bandwidth
h
bandwidth
CVML
value of crossvalidation or log-likelihood at h
details
description of used methods
GA.result
output of ga, object of class ga-class
References
Selingerova, I., Dolezelova, H., Horova, I., Katina, S., and Zelinka, J. (2016). Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches. PloS one, 11(2), e0148733.
See Also
plot.khazard , ga , optimize
Examples
library(survival)
fit<-khazard(times = lung$time,delta = lung$status-1)
Kernel estimate of conditional hazard function for right-censored data
Description
Kernel estimate of conditional hazard function for right-censored data with one covariate. Options include two methods for bandwidth selection.
Usage
khazardcond(times, delta, covariate, h = NULL, t = NULL, x = NULL,
tx = NULL, t.length = 100, x.length = 100, tmin = NULL,
tmax = NULL, xmin = NULL, xmax = NULL, kernel = "epanechnikov",
type = "interior", type.w = "nw", parallel = FALSE,
h.method = "crossval", optim.method = "ga", tol = ifelse(h.method
== "crossval", 10^(-6), 1), run = 2, ...)
Arguments
times
vector of observed times
delta
vector of censoring indicator. 0 - censored, 1 - uncensored (dead)
covariate
vector of covariate
h
bandwidth vector of length 2, first element is bandwidth for time and second for covariate. If missing, h is found using some bandwidth selection method.
t
vector of time points at which estimate is evaluated
x
vector of covariate points at which estimate is evaluated
tx
data frame of t and x at which estimate is evaluated
t.length
number of grid points of time
x.length
number of grid points of covariate
tmin, tmax
minimum/maximum values for grid of time
xmin, xmax
minimum/maximum values for grid of covariate
kernel
kernel function, possible values are: "epanechnikov" (default), "gaussian", "rectangular", "quartic".
type
Type of kernel estimate. Possible types are: "exterior", "interior" (default).
type.w
Type of weights. Default are Nadaraya-Watson weights.
parallel
allows parallel computation. Default is FALSE.
h.method
method for bandwidth selection. Possible methods are: "crossval" (default), "maxlike".
optim.method
method for numerical optimization of the crossvalidation or log-likelihood function. Possible methods are: "ga"(default).
tol
the desired accuracy of optimization algorithm
run
the number of consecutive generations without any improvement in the best fitness value before the GA is stopped.
...
additional arguments of GA algorithm
Details
External type of kernel estimator is defined as the ratio of kernel estimator of the conditional subdensity of the uncensored observations to the conditional survival function of the observable time. Internal type of kernel estimator is based on a convolution of the kernel function with a nonparametric estimator of the cumulative conditional hazard function.
Value
Returns an object of class 'khazardcond' which is a list with fields
time.points
vector of time points at which estimate is evaluated
covariate.points
vector of covariate points at which estimate is evaluated
hazard
matrix of hazard function values on grid or data.frame of time and covariate points and appropriate hazard values if hx is defined
h
bandwidth vector
CVML
value of crossvalidation or log-likelihood at h
details
description of used methods
GA.result
output of ga, object of class ga-class
References
Selingerova, I., Dolezelova, H., Horova, I., Katina, S., and Zelinka, J. (2016). Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches. PloS one, 11(2), e0148733.
See Also
Examples
library(survival)
fit<-khazardcond(times = lung$time,delta = lung$status-1,covariate = lung$age,h=c(200,20))
Plot of kernel hazard estimate from an object of class khazard
Description
Plot of kernel hazard estimate from an object of class khazard
Usage
## S3 method for class 'khazard'
plot(x, h = NULL, ylim, type, xlab, ylab, main, ...)
Arguments
x
Object of class khazard
h
bandwidth for which hazard function estimate will be plot if x$h is vector
ylim
Limits for the y axis.
type
type argument for plot.
xlab
Label for the x axis.
ylab
Label for the y axis.
main
Title of plot.
...
Additional arguments.
See Also
Examples
library(survival)
fit<-khazard(times = lung$time,delta = lung$status-1)
plot(fit)
fit<-khazard(times = lung$time,delta = lung$status-1,h=c(100,150,200,250), value="both")
plot(fit,h=200)
Plot of kernel conditional hazard estimate from an object of class khazardcond
Description
Plot of kernel conditional hazard estimate from an object of class khazardcond
Usage
## S3 method for class 'khazardcond'
plot(x, type = "persp", zlim, xlab, ylab, zlab,
main, ...)
Arguments
x
Object of class khazardcond
type
type of plot. Possible types are: "persp" (default), "persp3d", "contour".
zlim
Limits for the z axis.
xlab
Label for the x axis.
ylab
Label for the y axis.
zlab
Label for the z axis.
main
Title of plot.
...
Additional arguments.
See Also
Examples
library(survival)
fit<-khazardcond(times = lung$time,delta = lung$status-1,covariate = lung$age,h=c(200,20))
plot(fit)