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 that enter the interval
, and let
be the number of events that occur 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
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 b be the largest integer not exceeding c. Let
and let
with I being the indicator function. The width is then given by
By default, NINTERVAL=10.