Hmisc (version 5.3-1)

loess.surv: Loess/Lowess Smoother for Censored Data

Description

Estimates the probability of surviving past time `u` (i.e. the probability that the event has not occurred by `u`) as a smooth function of a continuous predictor `x`, when the response is right-censored. This is a modification of the `loess.surv` function accompanying van Klaveren et al. (2026); see References.

Usage

loess.surv(
  x,
  S,
  u,
  xout = seq(min(x), max(x), length.out = 200),
  span = 0.75,
  formula.cens = ~1,
  smoother = c("lowess", "loess"),
  pl = FALSE,
  add = FALSE
)

Value

A list with components

x

the values `xout` at which the smooth was evaluated

y

estimated probability of surviving past `u` at each `x`, in \([0, 1]\)

Arguments

x

Numeric vector, the predictor to be smoothed against.

S

A [survival::Surv()] object (right-censored) containing the follow-up times and event indicators, with the same length as `x`.

u

Numeric scalar, the time point at which the survival probability is to be estimated.

xout

Numeric vector of `x` values at which to evaluate the smooth. Defaults to 200 equally spaced points over the range of `x`.

span

Smoothing span: the `f` argument of [stats::lowess()] or the `span` argument of [stats::loess()]. Default 0.75.

formula.cens

One-sided formula giving the right-hand side of the Cox model used for the censoring distribution, e.g. `~ x` or `~ strata(g)`. Default `~ 1` assumes censoring is independent of covariates. Variables must be found in the calling environment.

smoother

Which smoother to use: `"lowess"` (default, with `iter = 0`) or `"loess"`.

pl

Logical. If `TRUE`, plot the IPCW-inflated event indicators (unless `add = TRUE`) and draw the estimated survival curve.

add

Logical. If `TRUE` and `pl = TRUE`, add the curve (in red) to an existing plot instead of starting a new one.

Details

Observations are reweighted by inverse probability of censoring weighting (IPCW). Let \(Y_u = \min(Y, u)\). A Cox model for the censoring distribution is fitted to \((Y_u, \text{censored before } u)\), yielding for each subject the probability `K` that the event time was observed (estimated as the exponential of minus the expected number of censoring events). The indicator of an observed event before `u` is then divided by `K`, and this inflated indicator is smoothed against `x`. The smooth estimates the cumulative incidence at `u`, and the function returns \(1 - \) that estimate, curtailed to \([0, 1]\).

With the default `smoother = "lowess"`, [stats::lowess()] is used with iterations turned off (`iter = 0`); this appears to perform better than [stats::loess()] and is much faster. The lowess fit is interpolated to `xout` with [stats::approx()]. Note that `xout` values outside the range of `x` give `NA` with `smoother = "lowess"`.

Relative to the original function, this version returns estimated survival probabilities rather than cumulative incidences, and curtails estimates to lie in \([0, 1]\).

`NA`s are excluded from `x` and `S` before calculations commence.

References

van Klaveren D, Austin PC, Serruys PW, van Calster B, Harrell FE (2026). Locally estimated scatterplot smoothing for censored survival data. *Statistics in Medicine*. tools:::Rd_expr_doi("10.1002/sim.70783")

See Also

[stats::lowess()], [stats::loess()], [survival::coxph()]

Examples

if (FALSE) {
require(survival)
set.seed(1)
n  <- 500
x  <- runif(n)
tt <- rexp(n, rate = exp(x - 0.5))
cc <- rexp(n, rate = 0.3)
S  <- Surv(pmin(tt, cc), tt <= cc)
r  <- loess.surv(x, S, u = 1, pl = TRUE)
r2 <- loess.surv(x, S, u = 1, smoother = "loess", formula.cens = ~ x)
}