The Lexis Diagram Back Home

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 11 cell. Consider the 11 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 root 2, 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