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Dataplot Vol 1 Vol 2

KAPLAN MEIER PLOT

Name:
    KAPLAN MEIER PLOT
Type:
    Graphics Command
Purpose:
    Generates a Kaplan Meier plot.
Description:
    In reliability analysis, many data sets consists of a set of failure times, which may be truncated at some limit value. The cumulative distribution function (CDF) is defined as:

      F(t) = prob(T < t)

    where T is the lifetime of a randomly selected unit.

    Given n units, which are ordered from smallest to largest, t1, t2, ... , tn where ti can represent either a failure time or a censoring time (i.e., the unit was removed from the test before failing), then the Kaplan Meier estimates are given by:

      \( \hat{R}(t_i) = \prod_{\begin{array}{c} j=1 \\ j \in S \end{array}}^{i}{\frac{n-j}{n-j+1}} \)

    where S is the set of all subscripts j such that tj) is a failure time (i.e., S excludes the censoring times). That is, for index i, the product is for all indices less than or equal to i that represent actual failure times.

    The Kaplan-Meier plot is a plot of \( \hat{R}(t_i) \) versus the failure time.

    Once \( \hat{R} \) is computed, then the CDF estimates are

      F(ti) = 1 - R(ti)

    That is, the Kaplan-Meier estimates are a way to estimate the CDF function when you have censored data.

    The Kaplan-Meier estimate of the last failure time is zero, which results in a CDF value of 1. Since the reliability (= 1 - CDF) for standard reliability models asymptotically approaches 1 as time approaches infinity, a modified Kaplan-Meier estimate has been developed:

      \( \hat{R}(t_i) = \frac{n+0.7}{n+0.4} \prod_{\begin{array}{c} j=1 \\ j \in S \end{array}}^{i}{\frac{n-j}{n-j+1}} \)

    Generally, the modified form of the Kaplan-Meier plot is preferred.

    The Kaplan-Meier plot can be thought of as an alternative to the empirical CDF plot that can handle data with both failure and censoring times.

    In Dataplot, a tag variable identifies whether the corresponding points in the response variable represent failure times or censoring times. A value of 1 indicates a failure time and a value of 0 indicates a censoring time.

Syntax 1:
    KAPLAN MEIER PLOT <y> <tag>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable containing failure times;
                <tag> is a tag variable indicating whether the times in <y> are failure times or censoring times;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax plots the unmodified Kaplan-Meier estimates.

Syntax 2:
    MODIFIED KAPLAN MEIER PLOT <y> <tag>             <SUBSET/EXCEPT/FOR qualification>
    where <y> is a response variable containing failure times;
                <tag> is a tag variable indicating whether the times in <y> are failure times or censoring times;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    This syntax plots the modified Kaplan-Meier estimates.

Examples:
    KAPLAN MEIER PLOT Y1 CENSOR
    MODIFIED KAPLAN MEIER PLOT Y1 CENSOR
Note:
    By default, the vertical axis of the Kaplan-Meier plot represents reliability (or survival). Some analysts prefer to plot the CDF on the vertical axis (i.e., 1 - Rhat).

    Enter the following command to plot 1 - Rhat:

      SET KAPLAN MEIER CDF

    Enter the following command to reset the default (plot Rhat):

      SET KAPLAN MEIER RELIABILITY
Note:
    If you want the numeric values of the Kaplan-Meier estimates, do the following:

      MODIFIED KAPLAN-MEIER PLOT Y CENSOR
      LET RELI = YPLOT
      LET FAILTIME = XPLOT

    The variables RELI and FAILTIME can then be used in subsequent analysis and output.

Default:
    None
Synonyms:
    None
Related Commands: Applications:
    Reliability
Implementation Date:
    1998/8
Program:
    SKIP 25
    READ HAHN.DAT MILES TAG
    TITLE MODIFIED KAPLAN MEIER PLOT OF HAHN.DAT
    Y1LABEL SURVIVAL
    X1LABEL FAILURE TIME
    XLIMITS 0 150000
    MODIFIED KAPLAN MEIER PLOT MILES TAG

    plot generated by sample program

Date created: 06/05/2001
Last updated: 12/04/2023

Please email comments on this WWW page to alan.heckert@nist.gov.