latency: Compute Nonparametric Estimator of the Conditional Latency
In npcure: Nonparametric Estimation in Mixture Cure Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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. If`dataset` 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`.

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

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.

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

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.

controlpars, latencyhboot

## 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))