The Lexis Diagram |

The above Figure depicts a Lexis diagram, which is a plot of a population's life experience in time vs. age. The graph is sectioned into 1-year by 1-year cells. Each 45° line represents an individual's life, which ends in death (red 'x') or out-migration (solid dot). An individual also may, at some time, migrate into the population (hollow dot).

Demographers often estimate a death rate for each 1×1 cell. Consider the 1×1 cell highlighted
in the above figure, which starts at time *t* and age *x*. If the exact life lines
are known, then exposure in person-years can be calculated by adding up the length of each of the
observed life lines that lie in the cell (of course, the total is divided by
, since the life lines are 45° to the
time axis). The estimate for the death rate for this cell would be the number of deaths (in
this case, one) divided by the person-years of exposure.

However, exact life lines are rarely known. Instead, what are often known are the counts of
individuals alive for each age at exact times *t*, *t* ± 1, *t* ± 2, etc.
In the case of the highlighted cell above, for example, the count at time *t* and age *x*
is 2 (lines *b* and *c*) and the count at time *t* + 1 and age *x*
is 1 (line *a*). The population estimate for the cell is obtained by taking the average
of the two counts. (Incidentally, line *d* does not contribute to this cell's exposure estimate
as it does not cross either of the boundaries at times *t* and *t* + 1.)
The estimate of the death rate in this example, then, is:

1 death ÷ 1.5 person-years = 0.67 deaths per person-year of exposure.

For comparison, a rough estimate of the death rate based on eye-balling the exact lengths of the life lines in the highlighted cell is 0.95 deaths per person-year of exposure.

*Maintained by: Pierre Vachon *