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 rate. 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.

In the first half of the twentieth century, the rate of death from infectious disease in the United States fell precipitously. Although this decline is well-known and well-documented, there is surprisingly little evidence about whether it took place uniformly across the regions of the United States. We use data on infectious disease deaths from all reporting U.S. cities to describe regional patterns in the decline of urban infectious mortality from 1900 to 1948. We report three main results. First, urban infectious mortality was higher in the South in every year from 1900 to 1948. Second, infectious mortality declined later in southern cities than in cities in the other regions. Third, comparatively high infectious mortality in southern cities was driven primarily by extremely high infectious mortality among African Americans. From 1906 to 1920, African Americans in cities experienced a rate of death from infectious disease that was greater than what urban whites experienced during the 1918 flu pandemic.

In the first half of the twentieth century, deaths from infectious disease, especially among the very young, fell dramatically in American cities. However, as infant mortality fell and life expectancy rose, racial inequality in urban infectious disease mortality grew. In this paper, we show that the fall in mortality and the rise in racial inequality in mortality reflected two countervailing processes. The dramatic decline in infant mortality from waterborne diseases drastically reduced the total urban infectious disease mortality rate of both Black and white Americans while having a comparatively small effect on the total racial disparity in urban infectious disease mortality. In contrast, the unequal fall in tuberculosis mortality, particularly in the prime of life, widened racial inequality in infectious disease mortality in US cities.

In the first half of the twentieth century, racial inequality in the rate of death from infectious disease was immense. In every year from 1906 to 1920, Black Americans in cities died from infectious diseases at a rate higher than that of urban White Americans during the 1918 influenza pandemic. We decompose mortality into three broad causes of death to determine which causes were most influential. Our results suggest that racial inequality in infectious mortality was primarily driven by TB and flu--the two major respiratory causes of death. Waterborne causes, by contrast, played a minor role in explaining the disparity.

COVID-19 mortality increases markedly with age and is also substantially higher among Black, Indigenous, and People of Color (BIPOC) populations in the United States. These two facts can have conflicting implications because BIPOC populations are younger than white populations. In analyses of California and Minnesota—demographically divergent states—we show that COVID vaccination schedules based solely on age benefit the older white populations at the expense of younger BIPOC populations with higher risk of death from COVID-19. We find that strategies that prioritize high-risk geographic areas for vaccination at all ages better target mortality risk than age-based strategies alone, although they do not always perform as well as direct prioritization of high-risk racial/ethnic groups. Vaccination schemas directly implicate equitability of access, both domestically and globally.