km.outcomes: Outcomes for the Kaplan-Meier product-limit estimator
In conf: Visualization and Analysis of Statistical Measures of Confidence

km.outcomes

R Documentation

Outcomes for the Kaplan-Meier product-limit estimator

Description

Generates a matrix containing all possible outcomes (all possible sequences of failure times and right-censoring times) of the value of the Kaplan-Meier product-limit estimator for a particular sample size n.

Usage

km.outcomes(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.outcomes function generates a matrix with all possible combinations of observed failures and right censored values and the resulting support values for the Kaplan-Meier product-limit estimator for a sample of size n.

The n argument must be a positive integer denoting the sample size. Allowable limits are from 1 to 24. Larger values of n are not allowed because of CPU and memory limitations.

In order to keep the support values as exact fractions, the numerators and denominators are stored separately in the a matrix in the columns named num and den. The support values are stored as numeric values in the column named S(t).

Value

The km.outcomes function returns a matrix with 2ⁿ⁺¹-1 rows and n + 4 columns. The location l indicates the position where the time of interest falls within the observed events. The meaning of the columns is as follows.

l: number of observed events (failures times or censoring times) between times 0 and the observation time;
d1, d2, ..., dn: equals 0 if the event corresponds to a censored observation, equals 1 if the event corresponds to a failure;
S(t): numeric value of the associated support value;
num: numerator of the support value as a fraction;
den: denominator of the support value as a fraction.

Author(s)

Yuxin Qin (yqin08@wm.edu), Heather Sasinowska (hdsasinowska@wm.edu), Larry Leemis (leemis@math.wm.edu)

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.