sm.survival function

Nonparametric regression with survival data.

This function creates a smooth, nonparametric estimate of the quantile of the distribution of survival data as a function of a single covariate. A weighted product-limit estimate of the survivor function is obtained by smoothing across the covariate scale. A small amount of smoothing is then also applied across the survival time scale in order to achieve a smooth estimate of the quantile.

sm.survival(x, y, status, h , hv = 0.05, p = 0.5, status.code = 1, ...)

Arguments

• x: a vector of covariate values.

• y: a vector of survival times.

• status: an indicator of a complete survival time or a censored value. The value of status.code defines a complete survival time.

• h: the smoothing parameter applied to the covariate scale. A normal kernel function is used and h is its standard deviation.

• hv: a smoothing parameter applied to the weighted to the product-limit estimate derived from the smoothing procedure in the covariate scale. This ensures that a smooth estimate is obtained.

• p: the quantile to be estimated at each covariate value.

• status.code: the value of status which defines a complete survival time.

• ...: other optional parameters are passed to the sm.options

  function, through a mechanism which limits their effect only to this call of the function; those relevant for this function are add, eval.points, ngrid, display, xlab, ylab, lty; see the documentation of sm.options for their description.

Returns

a list containing the values of the estimate at the evaluation points and the values of the smoothing parameters for the covariate and survival time scales.

Side Effects

a plot on the current graphical device is produced, unless the option display="none" is set.

Details

see Section 3.5 of the reference below.

References

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis:

the Kernel Approach with S-Plus Illustrations.

Oxford University Press, Oxford.

See Also

sm.regression, sm.options

Examples

x <- runif(50, 0, 10)
y <- rexp(50, 2)
z <- rexp(50, 1)
status <- rep(1, 50)
status[z<y] <- 0
y <- pmin(z, y)
sm.survival(x, y, status, h=2)