# Life Tables

There are many situations in which you would want to examine the
distribution of times between two events, such as length of employment
(time between being hired and leaving the company). However, this
kind of data usually includes some cases for which the second event
isn't recorded (for example, people still working for the company
at the end of the study). This can happen for several reasons: for
some cases, the event simply doesn't occur before the end of the study;
for other cases, we lose track of their status sometime before the
end of the study; still other cases may be unable to continue for
reasons unrelated to the study (such as an employee becoming ill and
taking a leave of absence). Collectively, such cases are known as **censored
cases**, and they make this kind of study inappropriate for traditional
techniques such as *t* tests or linear regression.

A statistical technique useful for this type of data is called
a follow-up **life table**. The basic idea of the life table is
to subdivide the period of observation into smaller time intervals.
For each interval, all people who have been observed at least that
long are used to calculate the probability of a terminal event occurring
in that interval. The probabilities estimated from each of the intervals
are then used to estimate the overall probability of the event occurring
at different time points.

**Example.** Is a new nicotine patch therapy better than traditional
patch therapy in helping people to quit smoking? You could conduct
a study using two groups of smokers, one of which received the traditional
therapy and the other of which received the experimental therapy.
Constructing life tables from the data would allow you to compare
overall abstinence rates between the two groups to determine if the
experimental treatment is an improvement over the traditional therapy.
You can also plot the survival or hazard functions and compare them
visually for more detailed information.

**Statistics.** Number entering, number leaving, number exposed
to risk, number of terminal events, proportion terminating, proportion
surviving, cumulative proportion surviving (and standard error), probability
density (and standard error), and hazard rate (and standard error)
for each time interval for each group; median survival time for each
group; and Wilcoxon (Gehan) test for comparing survival distributions
between groups. Plots: function plots for survival, log survival,
density, hazard rate, and one minus survival.

Life Tables Data Considerations

**Data.** Your time variable should be quantitative. Your status
variable should be dichotomous or categorical, coded as integers,
with events being coded as a single value or a range of consecutive
values. Factor variables should be categorical, coded as integers.

**Assumptions.** Probabilities for the event of interest should
depend only on time after the initial event--they are assumed to be
stable with respect to absolute time. That is, cases that enter the
study at different times (for example, patients who begin treatment
at different times) should behave similarly. There should also be
no systematic differences between censored and uncensored cases. If,
for example, many of the censored cases are patients with more serious
conditions, your results may be biased.

**Related procedures.** The Life Tables procedure uses an actuarial
approach to this kind of analysis (known generally as Survival Analysis).
The Kaplan-Meier Survival Analysis procedure uses a slightly different
method of calculating life tables that does not rely on partitioning
the observation period into smaller time intervals. This method is
recommended if you have a small number of observations, such that
there would be only a small number of observations in each survival
time interval. If you have variables that you suspect are related
to survival time or variables that you want to control for (covariates),
use the Cox Regression procedure. If your covariates can have different
values at different points in time for the same case, use Cox Regression
with Time-Dependent Covariates.

Creating Life Tables

This feature requires SPSS® Statistics Standard Edition or the Advanced Statistics Option.

- From the menus choose:
- Select one numeric survival variable.
- Specify the time intervals to be examined.
- Select a status variable to define cases for which the terminal event has occurred.
- Click Define Event to specify the value of the status variable that indicates that an event occurred.

Optionally, you can select a first-order factor variable. Actuarial tables for the survival variable are generated for each category of the factor variable.

You can also select a second-order *by factor* variable. Actuarial
tables for the survival variable are generated for every combination
of the first- and second-order factor variables.

This procedure pastes SURVIVAL command syntax.