latency {npcure}

Compute Nonparametric Estimator of the Conditional Latency

Description

This function computes the nonparametric estimator of the conditional latency function proposed by López-Cheda et al. (2017).

Usage

latency(x, t, d, dataset, x0, h, local = TRUE, testimate = NULL,
conflevel = 0L, bootpars = if (conflevel == 0 && !missing(h)) NULL else
controlpars())

Arguments

x

If dataset is missing, a numeric object giving the covariate values. If dataset is a data frame, it is interpreted as the name of the variable corresponding to the covariate in the data frame.

t

If dataset is missing, a numeric object giving the observed times. If dataset is a data frame, it is interpreted as the name of the variable corresponding to the observed times in the data frame.

d

If dataset is missing, an integer object giving the values of the uncensoring indicator. Censored observations must be coded as 0, uncensored ones as 1. Ifdataset is a data frame, it is interpreted as the name of the variable corresponding to the uncensoring indicator.

dataset

An optional data frame in which the variables named in x, t and d are interpreted. If it is missing, x, t and d must be objects of the workspace.

x0

A numeric vector of covariate values where the latency estimates will be computed.

h

A numeric vector of bandwidths. If it is missing the default is to use the local bootstrap bandwidth computed by the latencyhboot function.

local

A logical value, TRUE by default, specifying whether local or global bandwidths are used.

testimate

A numeric vector specifying the times at which the latency is estimated. By default it is NULL, and then the latency is estimated at the times given by t.

conflevel

A value controlling whether bootstrap confidence intervals (CI) of the latency are to be computed. With the default value, 0L, the CIs are not computed. If a numeric value between 0 and 1 is passed, it specifies the confidence level of the CIs.

bootpars

A list of parameters controlling the bootstrap when computing the CIs of the latency: B, the number of bootstrap resamples, and nnfrac, the fraction of the sample size that determines the order of the nearest neighbor used for choosing a pilot bandwidth. If h is missing the list of parameters is extended to be the same used for computing the bootstrap bandwidth (see the help of latencyhboot for details). The default is the value returned by the controlpars function called without arguments. In case the CIs are not computed and h is not missing the default is NULL.

Details

The function computes the nonparametric estimator of the conditional latency S_0(t | X = x_0) = P(Y>t | Y<\infty, X=x_0) proposed by López-Cheda et al. (2017). It is only available for a continuous covariate X.

Value

An object of S3 class 'npcure'. Formally, a list of components:

type

The constant string "latency".

local

The value of the local argument.

h

The value of the h argument, unless this is missing, in which case its value is that of the cross-validation bandwidth.

x0

The value of the x0 argument.

testim

The numeric vector of time values where the latency function is estimated.

S

A list whose components are the estimates of the latency function for each one of the covariate values, i.e., those specified by the x0 argument. The latency estimates are given at the times determined by the testimate argument.

conf

A list of components lower and upper giving the lower and the upper limits of the confidence intervals, respectively.

Author(s)

Ignacio López-de-Ullibarri [aut, cre], Ana López-Cheda [aut], Maria Amalia Jácome [aut]

References

López-Cheda, A., Jácome, M. A., Cao, R. (2017). Nonparametric latency estimation for mixture cure models. Test, 26: 353–376. https://doi.org/10.1007/s11749-016-0515-1.

See Also

controlpars, latencyhboot

Examples

## Some artificial data
set.seed(123)
n <- 50
x <- runif(n, -2, 2) ## Covariate values
y <- rweibull(n, shape = .5*(x + 4)) ## True lifetimes
c <- rexp(n) ## Censoring values
p <- exp(2*x)/(1 + exp(2*x)) ## Probability of being susceptible
u <- runif(n)
t <- ifelse(u < p, pmin(y, c), c) ## Observed times
d <- ifelse(u < p, ifelse(y < c, 1, 0), 0) ## Uncensoring indicator
data <- data.frame(x = x, t = t, d = d)

## Latency estimates for covariate value 0.5...
x0 <- .5

## ... (a) with global bandwidths 0.5, 1, 2.
## By default, estimates are computed at the time values of 't'
S1 <- latency(x, t, d, data, x0 = x0, h = c(.5, 1, 2), local = FALSE)
plot(S1$testim, S1$S$h0.5$x0.5, type = "s", xlab = "Time", ylab =
"Latency", ylim = c(0, 1))
lines(S1$testim, S1$S$h1$x0.5, type = "s", lty = 2)
lines(S1$testim, S1$S$h2$x0.5, type = "s", lty = 3)
## The true latency curve is plotted as reference
lines(S1$testim, pweibull(S1$testim, shape = .5*(x0 + 4), lower.tail =
FALSE), col = 2)
legend("topright", c(paste("Estimate, ", c("h = 0.5", "h = 1",
"h = 2")), "True"), lty = c(1:3, 1), col = c(rep(1, 3), 2))

## As before, but with estimates computed at times 0.1, 0.2,..., 1
S2 <- latency(x, t, d, data, x0 = x0, h = c(.5, 1, 2), local = FALSE,
testimate = .1*(1:10))

## ... (b) with local bandwidth 2.
S3 <- latency(x, t, d, data, x0 = x0, h = 2, local = TRUE)
#### Note that with only one covariate value the results with
#### 'local = FALSE' and 'local = TRUE' coincide, but the output formats
#### differ slightly. Compare with
S3 <- latency(x, t, d, data, x0 = x0, h = 2, local = FALSE)

## ... (c) with local bootstrap bandwidth
b  <- latencyhboot(x, t, d, data, x0 = x0)
S4 <- latency(x, t, d, data, x0 = x0, h = b$h)

## ... (d) when the bandwidth is not specified, the bootstrap bandwidth
#### selector given by the 'latencyhboot' function is used by default.
#### The computation of 95% confidence intervals based on 1999 bootstrap
#### resamples is also illustrated
S5 <- latency(x, t, d, data, x0 = x0, conflevel = .95, bootpars =
controlpars(B = 1999))
plot(S5$testim, S5$S$x0, type = "s", xlab = "Time", ylab = "Latency",
ylim = c(0, 1))
lines(S5$testim, S5$conf$x0$lower, type = "s", lty = 2)
lines(S5$testim, S5$conf$x0$upper, type = "s", lty = 2)
lines(S5$testim, pweibull(S5$testim, shape = .5*(x0 + 4), lower.tail =
FALSE), col = 2)
legend("topright", c("Estimate", "95% CI limits", "True"), lty = c(1,
2, 1), col = c(1, 1, 2))


## Example with the dataset 'bmt' of the 'KMsurv' package
## to study the survival of the uncured patients aged 25 and 40
data("bmt", package = "KMsurv")
x0 <- c(25, 40)
S <- latency(z1, t2, d3, bmt, x0 = x0, conflevel = .95)
## Plot of predicted latency curves and confidence intervals
plot(S$testim, S$S$x25, type = "s", xlab = "Time (days)",
ylab = "Latency", ylim = c(0,1))
lines(S$testim, S$conf$x25$lower, type = "s", lty = 2)
lines(S$testim, S$conf$x25$upper, type = "s", lty = 2)
lines(S$testim, S$S$x40, type = "s", lty = 1, col = 2)
lines(S$testim, S$conf$x40$lower, type = "s", lty = 2, col = 2)
lines(S$testim, S$conf$x40$upper, type = "s", lty = 2, col = 2)
legend("topright", c("Age 25: Estimate", "Age 25: 95% CI limits",
"Age 40: Estimate","Age 40: 95% CI limits"), lty = 1:2,
col = c(1, 1, 2, 2))