km.support: Support values for the Kaplan-Meier product-limit estimator

In conf: Visualization and Analysis of Statistical Measures of Confidence

Support values for the Kaplan-Meier product-limit estimator

Description

Calculate the support values for the Kaplan-Meier product-limit estimator for a particular sample size n using an induction algorithm.

Usage

km.support(n)

Arguments

n	sample size

Details

The Kaplan-Meier product-limit estimator is used to estimate the survivor function for a data set of positive values in the presence of right censoring. The km.support function calculates the support values for the Kaplan-Meier product-limit estimator for a sample of size n using an induction algorithm described in Qin et al. (2023).

The n argument must be a positive integer denoting the sample size. Allowable limits are from 1 to 35. Larger values of n are not allowed because of CPU and memory limitations.

The numerators and denominators are temporarily converted to complex numbers within the km.support function in order to eliminate duplicate support values using the unique function.

Value

The km.support function returns a list with two components.

• num: a vector of integers containing the numerators of the support values

• den: a vector of integers containing the associated denominators of the support values

The support values are not returned in sorted order. Zero and one, which are always a part of the support, are given as 0 / 1 and 1 / 1.

Author(s)

Yuxin Qin ([e-mail]), Heather Sasinowska ([e-mail]), Larry Leemis ([e-mail])

References

Qin, Y., Sasinowska, H., Leemis, L. (2023), "The Probability Mass Function of the Kaplan-Meier Product-Limit Estimator", The American Statistician, Volume 77, Number 1, 102-110.

See Also

survfit

Examples

  #  display unsorted numerators and denominators of support values for n = 4
  km.support(4)
  #  display sorted support values for n = 4 as exact fractions
  n <- 4
  s <- km.support(n)
  i <- order(s$num / s$den)
  m <- length(s$num)
  f <- ""
  for (j in i[2:(m - 1)]) f <- paste(f, s$num[j], "/", s$den[j], ", ", sep = "")
  cat(paste("The ", m, " support values for n = ", n, " are: 0, ", f, "1.\n", sep = ""))
  #  print sorted support values for n = 4 as numerics
  print(s$num[i] / s$den[i])

conf documentation built on Oct. 1, 2023, 1:07 a.m.