TY  - JOUR
A1  - Feehan, Dennis
A1  - Wrigley-Field, Elizabeth
T1  - How do populations aggregate?
Y1  - 2021/02/16
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 363
EP  - 378
DO  - 10.4054/DemRes.2021.44.15
VL  - S8
IS  - 15
UR  - https://www.demographic-research.org/special/8/15/
L1  - https://www.demographic-research.org/special/8/15/s8-15.pdf
L2  - https://www.demographic-research.org/special/8/15/s8-15.pdf
N2  - Background: Understanding the relationship between populations at different scales plays an important
role in many demographic analyses. 

Objective: We show that when a population can be partitioned into subgroups, the death rate for
the entire population can be written as the weighted harmonic mean of the death rates in
each subgroup, where the weights are given by the numbers of deaths in each subgroup.
This decomposition can be generalized to other types of occurrence-exposure rates. Using
different weights, the death rate for the entire population can also be expressed as an
arithmetic mean of the death rates in each subgroup. 

Contribution: We use these relationships as a starting point for investigating how demographers can correctly aggregate rates across non-overlapping subgroups. Our analysis reveals conceptual links between classic demographic models and length-biased sampling. To illustrate how
the harmonic mean can suggest new interpretations of demographic relationships, we
present as an application a new expression for the frailty of the dying, given a standard
demographic frailty model. 

ER  -