The crossover between life expectancies at birth and at age one: The imbalance in the life table

Abstract The single most used demographic measure to describe population health is life expectancy at birth, but life expectancies at ages other than zero are also used in the study of human longevity. Our intuition tells us that the longest life expectancy is that of a newborn. However, historically, the expectation of life at age one (e^sub 1^) has exceeded the expectation of life at birth (e^sub 0^). The crossover between e^sub 0^ and e^sub 1^ only occurred in the developed world in the second half of the twentieth century. Life tables for populations that have not achieved this crossing between life expectancy at birth and at age one are referred to here as imbalanced. This crossover occurs when infant mortality is equal to the inverse of life expectancy at age one. This simple relation between mortality at age zero and mortality after age one divides the world into countries that have achieved the crossover in life expectancies and those that have not. It is a within-population comparison of mortality at infancy and after age one. However, results of these within-population comparisons can be used for comparison between populations. For countries that have already achieved this crossing in life expectancies, the sex differential in the timing of the crossing is marked: Females attain the crossing before males for every single population and in some cases by up to 18 years earlier. However, for most developing countries, life expectancy at age one is still higher than life expectancy at birth, in some cases by several years. Subpopulation comparisons for the US show that black Americans are near to transitioning out of the imbalanced life table situation while the white population has already done so. (ProQuest: ... denotes formulae omitted.) 1. Introduction Since the 1920s and 1930s, the summary indicator most widely used to describe population health is life expectancy at birth, e0 (Robine 2006; Dublin 1923; Dublin and Lotka 1934). Period life expectancy at birth is defined as the average number of years that a newborn would live given a set of death rates observed in a calendar year (Preston, Heuveline, and Guillot 2001). Changes in mortality in the first year of life strongly affect life expectancy at birth, and it has been suggested that the time series of e0 alone is not well suited for studying the length of life in aging populations (Kannisto 2001). This could be circumvented if both infant mortality and life expectancy at age one are used as comparative measures of the level of mortality in a population (Kintner 2004). Infant mortality levels can be compared over time, or over subpopulations defined in terms of sex, race, nationality, education, social class, etc. (Frisbie et al. 2004; Martin et al. 2005; Hummer et al. 2007). Another comparison can be made by observing the relation between the level of infant mortality in a population and its mortality at adult ages (Finch and Crimmins 2004; Galobardes, Lynch, and Smith 2004). In this study we address an alternative comparison by analyzing the crossover between life expectancy at birth and at age one, which relates the information of infant mortality to mortality at other ages. For high-income countries, the e0 calculated from period life tables is currently higher than the life expectancy at any other age. In historical populations as well as in most developing countries, however, high rates of infant and early childhood mortality result in lower values of life expectancy at birth than at other ages. In such populations, those surviving the hazards of early childhood have a higher life expectancy than newborns and the highest life expectancy occurs not at birth but at a later age. Let an imbalance in a life table be defined as a situation where levels of life expectancy at a younger age x, ex, are lower than at an older age y, ey, this can be expressed as ex