Crude Population RatesΒΆ

Dismod-AT works with life table rates, not crude rates. A crude rate is the number of deaths divided by the number of people exposed to that event. If \(k(t)\) is the birth rate over time, then a crude mortality rate is

\[{}_nM_x = \frac{\int_x^{x+n}k(t-a)l(a)\mu(a)da }{\int_x^{x+n}k(t-a)l(a)da}\]

The life table rate adjusts the crude rate to remove the effect of varying birth rates. In Dismod-AT, the birth rate is normalized to a rate of 1 for all populations. In demographic textbooks, \({}_nm_x\) is called the lifetable mortality rate, and \({}_nM_x\) is called the crude mortality rate.

Note

The bundles aggregate measurements from many sources. Do they use crude population rates or lifetable population rates?

This matters when there is a birth pulse that skews data towards younger or older sides of an age interval. Dismod-AT assumes that the average over an age interval is determined by the lifetable person-years lived.