Volume 44 - Article 15 | Pages 363–378  

How do populations aggregate?

By Dennis Feehan, Elizabeth Wrigley-Field

This article is part of the ongoing Special Collection 8 "Formal Relationships"

Abstract

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.

Author's Affiliation

• Dennis Feehan - University of California, Berkeley, United States of America EMAIL
• Elizabeth Wrigley-Field - University of Minnesota Twin Cities, United States of America EMAIL

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