Life-Table Method
The life-table estimates are computed by counting the numbers of censored and uncensored observations that fall into each of the time intervals
,
, where
and
. Let
be the number of units entering the interval
, and let
be the number of events occurring in the interval. Let
, and let
, where
is the number of units censored in the interval. The effective sample size of the interval
is denoted by
. Let
denote the midpoint of
.
The conditional probability of an event in
is estimated by
and its estimated standard error is
where
.
The estimate of the survival function at
is
and its estimated standard error is
The density function at
is estimated by
and its estimated standard error is
The estimated hazard function at
is
and its estimated standard error is
Let
be the interval in which
. The median residual lifetime at
is estimated by
and the corresponding standard error is estimated by
Interval Determination
If you want to determine the intervals exactly, use the INTERVALS= option in the PROC LIFETEST statement to specify the interval endpoints. Use the WIDTH= option to specify the width of the intervals, thus indirectly determining the number of intervals. If neither the INTERVALS= option nor the WIDTH= option is specified in the life-table estimation, the number of intervals is determined by the NINTERVAL= option. The width of the time intervals is 2, 5, or 10 times an integer (possibly a negative integer) power of 10. Let
(maximum observed time/number of intervals), and let
be the largest integer not exceeding
. Let
and let
with
being the indicator function. The width is then given by
By default, NINTERVAL=10.