Quantifying the Shape of Aging

Abstract

In Biodemography, aging is typically measured and compared based on aging rates. We argue that this approach may be misleading, because it confounds the time aspect with the mere change aspect of aging. To disentangle these aspects, here we utilize a time-standardized framework and, instead of aging rates, suggest the shape of aging as a novel and valuable alternative concept for comparative aging research. The concept of shape captures the direction and degree of change in the force of mortality over age, which—on a demographic level—reflects aging. We 1) provide a list of shape properties that are desirable from a theoretical perspective, 2) suggest several demographically meaningful and non-parametric candidate measures to quantify shape, and 3) evaluate performance of these measures based on the list of properties as well as based on an illustrative analysis of a simple dataset. The shape measures suggested here aim to provide a general means to classify aging patterns independent of any particular mortality model and independent of any species-specific time-scale. Thereby they support systematic comparative aging research across different species or between populations of the same species under different conditions and constitute an extension of the toolbox available to comparative research in Biodemography.

The emergence of longevous populations

“…We provide answers to these questions by applying a powerful framework that simultaneously examines changes in both the average length of life in a population or species-the "pace" of life-and relative variation in the length of life, i.e., the "shape" of the distribution of ages at death (3)(4)(5). Studying variation in lifespan links to increasing interest in social, economic, and health inequalities and to key sociological findings that relate social factors-including high social status and social integration-to longer, healthier lifespans in human and animal societies (6)(7)(8)(9)(10).…”

Complexity of the Relationship between Life Expectancy and Overlap of Lifespans

“…with the radix l(0) = 1. Incidentally, after developing the measure we foundl 0 equals 116 1 − G 0 , where G 0 is the Gini coefficient, which is commonly used to measure lifespan 117 equality [14,25]. This illustrates the close positive association between the proportion of 118 life shared and lifespan equality.…”

“…Any of these mortality trajectories can result in similar life expectancies 59 from birth. Methods have been developed to distinguish these two aspects of the ageing 60 regime as the "pace and shape" of ageing [12][13][14], where life expectancy is a measure of 61 pace and the relative increase or decrease in mortality across the life course is a measure 62 of shape.…”

A pace and shape perspective on fertility

“…Our measure of the shape of reproductive ageing fits most properties previously defined as important for the shape of mortality (Wrycza et al, 2015). First, shape measures should be dimensionless.…”

“…This structure contrasts the ratio between expected time to birth (P) and potential maximum time to birth (τ) with the same ratio for constant reproduction (0.5). The same structure is predominant in several survival shape measures evaluated by Wrycza et al (2015), Non-monotonous mortality trajectories posed a challenge to previous survival shape measures (Wrycza et al, 2015), because, for example, u-shaped mortality patterns could lead to shape values that indicated negative senescence and falsely classified declining and u-shaped patterns in the same category. Our measures outline a solution: though our method will yield the same shape values for many different reproduction patterns (Figures 1a,b and 2a,b), it is possible to explore and evaluate the shape of these different patterns by looking at partial reproduction curves, (Gini coefficient as measure of survival shape can also be calculated over partial age ranges (Shkolnikov, Andreev, & Begun 2003), but has not been ap-…”