![]() Chapter Contents |
![]() Previous |
![]() Next |
The PHREG Procedure |
Let zl denote the vector of (possibly time-dependent)
explanatory variables for the lth individual.
Let t1 < t2 < ... <tk
denote the k distinct, ordered event times.
Let di denote the multiplicity of failures at
ti; that is,
di is the size of the set
Di of individuals that fail at
ti.
Let si be the sum of the vectors
zl over the individuals who fail at
ti;
that is,
.Using this notation, the likelihood functions used in PROC PHREG
to estimate
are described in the following sections.
The exact likelihood is
The discrete logistic likelihood is
When there are no ties
on the event times
(that is, ),
all four likelihood functions
,
,
, and
reduce to the same expression. In a stratified analysis,
the partial likelihood
is the product of the partial likelihood functions
for the individual strata.
![]() Chapter Contents |
![]() Previous |
![]() Next |
![]() Top |
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.