# The LIFETEST Procedure

#### 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 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

##### 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 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.