PROC LIFETEST: Life-Table Method :: SAS/STAT(R) 9.2 User's Guide, Second Edition

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 $\text{[math]}$ , $\text{[math]}$ , where $\text{[math]}$ and $\text{[math]}$ . Let $\text{[math]}$ be the number of units entering the interval $\text{[math]}$ , and let $\text{[math]}$ be the number of events occurring in the interval. Let $\text{[math]}$ , and let $\text{[math]}$ , where $\text{[math]}$ is the number of units censored in the interval. The effective sample size of the interval $\text{[math]}$ is denoted by $\text{[math]}$ . Let $\text{[math]}$ denote the midpoint of $\text{[math]}$ .

The conditional probability of an event in $\text{[math]}$ is estimated by

$\text{[math]}$

and its estimated standard error is

$\text{[math]}$

where $\text{[math]}$ .

The estimate of the survival function at $\text{[math]}$ is

$\text{[math]}$

and its estimated standard error is

$\text{[math]}$

The density function at $\text{[math]}$ is estimated by

$\text{[math]}$

and its estimated standard error is

$\text{[math]}$

The estimated hazard function at $\text{[math]}$ is

$\text{[math]}$

and its estimated standard error is

$\text{[math]}$

Let $\text{[math]}$ be the interval in which $\text{[math]}$ . The median residual lifetime at $\text{[math]}$ is estimated by

$\text{[math]}$

and the corresponding standard error is estimated by

$\text{[math]}$

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 $\text{[math]}$ (maximum observed time/number of intervals), and let $\text{[math]}$ be the largest integer not exceeding $\text{[math]}$ . Let $\text{[math]}$ and let

$\text{[math]}$

with $\text{[math]}$ being the indicator function. The width is then given by

$\text{[math]}$

By default, NINTERVAL=10.

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