Beran function

Estimation of the conditional distribution function of the response, given the covariate under random censoring.

Computes the conditional survival probability P(T > y|Z = z)

Beran(
  time,
  status,
  covariate,
  delta,
  x,
  y,
  kernel = "gaussian",
  bw,
  lower.tail = FALSE
)

Arguments

• time: The survival time of the process.
• status: Censoring indicator of the total time of the process; 0 if the total time is censored and 1 otherwise.
• covariate: Covariate values for obtaining estimates for the conditional probabilities.
• delta: Censoring indicator of the covariate.
• x: The first time (or covariate value) for obtaining estimates for the conditional probabilities. If missing, 0 will be used.
• y: The total time for obtaining estimates for the conditional probabilities.
• kernel: A character string specifying the desired kernel. See details below for possible options. Defaults to "gaussian" where the gaussian density kernel will be used.
• bw: A single numeric value to compute a kernel density bandwidth.
• lower.tail: logical; if FALSE (default), probabilities are c("$P(T > y|Z =\n$", "$z)$") otherwise, $P(T <= y|Z = z)$.

Details

Possible options for argument window are "gaussian", "epanechnikov", "tricube", "boxcar", "triangular", "quartic" or "cosine".

Examples

obj <- with(colonCS, survCS(time1, event1, Stime, event))

#P(T>y|age=45)
library(KernSmooth)
h <- dpik(colonCS$age)
Beran(time = obj$Stime, status = obj$event, covariate = colonCS$age,
x = 45, y = 730, bw = h)

#P(T<=y|age=45)
Beran(time = obj$Stime, status = obj$event, covariate = colonCS$age,
x = 45, y = 730, bw = h, lower.tail = TRUE)

References

R. Beran. Nonparametric regression with randomly censored survival data. Technical report, University of California, Berkeley, 1981.

Author(s)

Luis Meira-Machado and Marta Sestelo