npsurv (version 0.5-0)

plot.Uhaz: Plot Functions for U-shaped Hazard Estimation

Description

Functions for plotting various functions in U-shaped hazard estimation

Usage

# S3 method for Uhaz
plot(x, ...)
# S3 method for uh
plot(x, data, fn=c("haz","grad","surv","den","chaz"), ...)
plothazuh(h, add=FALSE, col="darkblue", lty=1, xlim, ylim,
         lwd=2, pch=19, len=500, vert=FALSE, add.knots=TRUE,
         xlab="Time", ylab="Hazard", ...)
plotchazuh(h, add=FALSE, lwd=2, len=500, col="darkblue",
          pch=19, add.knots=TRUE, vert=FALSE, xlim, ylim, ...)
plotdenuh(h, add=FALSE, lty=1, lwd=2, col="darkblue",
         add.knots=TRUE, pch=19, ylim, len=500, vert=FALSE, ...)
plotsurvuh(h, add=FALSE, lty=1, lwd=2, len=500, vert=FALSE,
          col="darkblue", pch=19, add.knots=TRUE, xlim, ylim, ...)
plotgraduh(h, data, w=1, len=500, xlim, ylim, vert=TRUE,
          add=FALSE, xlab="Time", ylab="Gradient",
          col0="red3", col1="blue3", col2="green3", order=0, ...)

Arguments

x

an object of class Uhaz, i.e., an output of function Uhaz, or an object of class uh..

...

arguments for other graphical parameters (see par).

h

an object of class uh.

data

vector or matrix that stores observations, or an object of class icendata.

w

additional weights/multiplicities for the observations stored in data.

fn

function to be plotted. It can be

= haz, for hazard function;

= chaz, for cumulative hazard function;

= den, for density function;

= surv, for survival function;

= gradient, for gradient functions.

xlim, ylim

numeric vectors of length 2, giving the x and y coordinates ranges.

xlab, ylab

x- or y-axis labels.

add

= TRUE, adds the curve to the existing plot;

= FALSE, plots the curve in a new one.

col

color used for plotting the curve.

lty

line type for plotting the curve.

lwd

line width for plotting the curve.

len

number of points used to plot a curve.

add.knots

logical, indicating if knots are also plotted.

pch

point character/type for plotting knots.

vert

logical, indicating if grey vertical lines are plotted to show the interval that separates the two discrete measures.

col0

color for gradient function 0, i.e., for the hazard-constant part, or alpha.

col1

color for gradient function 1, i.e., for the hazard-decreasing part.

col2

color for gradient function 1, i.e., for the hazard-increasing part.

order

= 0, the gradient functions are plotted;

= 1, their first derivatives are plotted;

= 2, their second derivatives are plotted.

Details

plot.Uhaz and plot.uh are wrapper functions that can be used to invoke plot.hazuh, plot.chazuh, plot.survuh, plot.denuh or plot.graduh.

plothazuh plots a U-shaped hazard function.

plotchazuh plots a cumulative hazard function that has a U-shaped hazard function.

plotsurvuh plots the survival function that has a U-shaped hazard function.

plotdenuh plots the density function that has a U-shaped hazard function.

plotgraduh plots the gradient function that has a U-shaped hazard function.

A U-shaped hazard function is given by

$$h(t) = \alpha + \sum_{j = 1}^k \nu_j(\tau_j - t)_+^p + \sum_{j = 1}^{m} \mu_j (t-\eta_j)_+^p,$$

where \(\alpha,\nu_j,\mu_j \ge 0\), \(\tau_1 < \cdots < \tau_k \le \eta_1 < \cdots < \eta_m,\) and \(p \ge 0\).

References

Wang, Y. and Fani, S. (2018). Nonparametric maximum likelihood computation of a U-shaped hazard function. Statistics and Computing, 28, 187-200.

See Also

icendata, uh, npsurv.

Examples

# NOT RUN {
## Angina Pectoris Survival Data
data(ap)
plot(r<-Uhaz(ap))              # hazard function for a convex hazard
plot(r, fn="c")                # cumulative hazard function
plot(r, fn="s")                # survival function
plot(r, fn="d")                # density function
plot(r, ap, fn="g")            # gradient functions
plot(r, ap, fn="g", order=1)   # first derivatives of gradient functions
plot(r, ap, fn="g", order=2)   # second derivatives of gradient functions

## New Zealand Mortality in 2000
data(nzmort)
i = nzmort$ethnic == "maori"
x = nzmort[i,1:2]                            # Maori mortality
h = Uhaz(x[,1]+0.5, x[,2], deg=2)$h          # smooth U-shaped hazard
plot(h)                        # hazard function
plot(h, fn="d")                # density function
plot(h, fn="s")                # survival function

x2 = nzmort[!i,1:2]                          # Non-Maori mortality
h2 = Uhaz(x2[,1]+0.5, x2[,2], deg=2)$h
plot(h2, fn="s", add=TRUE, col="green3")

# }