CUMULATIVE HAZARD
Name:
Type:
Purpose:
Compute the cumulative hazard for a set of failure times.
Description:
The hazard is constructed as follows:
 Sort and rank the N failure times from shortest to
longest failure time. Note that the hazard can
accomodate data where the time may be a censoring
time rather than a failure time (i.e., the unit was
taken out of service before it failed).
 Calculate a hazard value at each of the failure
times. Note that the hazard is only caclulated at
failure times, not censoring times. The hazard is:
where K is the rank of the failure time. This
expresses the hazard as a percentage. You can express
the hazard as a proportion by omitting the
multiplication by 100.
 The cumulative hazard is the cumulative sum of the
hazard. That is, the cumulative hazard at the failure
time with rank K is the sum of the hazards of all
failure times with ranks less than or equal to K.
Syntax:
LET <y> = CUMULATIVE HAZARD <x> <tag>
<SUBSET/EXCEPT/FOR qualification>
where <x> is the variable containing the failure
times;
<tag> is a variable that indicates whether the
corresponding element of <x> is a failure
time or a censoring time;
<y> is a variable (of length 1 less than
<x1>) where the cumulative hazards are
saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
A value of 0 for <tag> is used to signify a censoring
time and a value of 1 for <tag> is used to signify a
failure time. Dataplot uses 0.5 as the cutoff. That is,
any value greater than or equal to 0.5 is interpreted as a
failure time.
Examples:
LET Y = CUMULATIVE HAZARD X CENSOR
LET Y = CUMULATIVE HAZARD X CENSOR SUBSET CENSOR = 1
Note:
Hazards are only computed for failure times (i.e., where
= 1), not censoring times. The saved cumulative
hazards () are set to 0 for censoring times. If you just
want to keep the cumulative hazards at failure times, do
something like:
LET Y = CUMULATIVE HAZARD X CENSOR
RETAIN Y SUBSET CENSOR = 1
The censoring times do affect the value of the cumulative
hazard since they are used in determining the rank. If you
only want the failure times to be used in the calculation of
the cumulative hazard, do something like the following:
LET Y = CUMULATIVE HAZARD X CENSOR SUBSET CENSOR = 1
RETAIN Y SUBSET CENSOR = 1
Default:
Synonyms:
Related Commands:
HAZARD

= Compute the hazard for a variable.

HAZARD PLOT

= Generate a hazard plot.

PROBABILITY PLOT

= Generate a probability plot.

WEIBULL PLOT

= Generate a Weibull plot.

INTERARRIVAL TIME

= Compute the interarrival times of a variable.

Applications:
Implementation Date:
Program:
SKIP 25
READ HAHN.DAT Y TAG
LET TAG = 0 SUBSET TAG = 2
LET Z = CUMULATIVE HAZARD Y TAG
Date created: 6/5/2001
Last updated: 4/4/2003
Please email comments on this WWW page to
alan.heckert@nist.gov.
