Academic journal article Demographic Research

An Integrated Approach to Cause-of-Death Analysis: Cause-Deleted Life Tables and Decompositions of Life Expectancy

Academic journal article Demographic Research

An Integrated Approach to Cause-of-Death Analysis: Cause-Deleted Life Tables and Decompositions of Life Expectancy

Article excerpt

Abstract

This article integrates two methods that analyze the implications of various causes of death for life expectancy. One of the methods attributes changes in life expectancy to various causes of death; the other method examines the effect of removing deaths from a particular cause on life expectancy. This integration is accomplished by new formulas that make clearer the interactions among causes of death in determining life expectancy. We apply our approach to changes in life expectancy in the United States between 1970 and 2000. We demonstrate, and explain analytically, the paradox that cancer is responsible for more years of life lost in 2000 than in 1970 despite the fact that declines in cancer mortality contributed to advances in life expectancy between 1970 and 2000.

1. Introduction

When measured for a particular period, life expectancy at birth is a summary measure of the mortality conditions of that period. Estimating the role of causes of death in determining the level of life expectancy, and changes therein, is an active area of demographic research. Two broad research approaches have been employed: analyzing the life-shortening effect of causes of death if a cause were eliminated; and attributing changes or differences in life expectancy to various causes of death. The first approach is focused on a single population and has led to the development of single decrement (often, "cause-deleted") life tables. The second approach is comparative and has lead to the development of decomposition methods that assign responsibility for mortality variation to particular causes of death.

The approaches are related but the relations have not been demonstrated. In this paper, we develop new expressions for decomposition methods and show that they are related in a straightforward way to expressions characterizing cause-deleted tables. We apply the analytic framework to data for the United States between 1970 and 2000.

2. Background

Although demographers have long used life tables to analyze mortality from all causes combined, the development of life tables that highlight the role of various causes of death is more recent (Brownlee 1919; Fisher, Vigfusson, and Dickson 1922; Pearl 1922; Greville 1948; Jordan 1952; Chiang 1968; Spiegelman 1968, Preston, Keyfitz, and Schoen 1972). The first official decennial life table by cause of death for the United States was published in the late 1960's (United States. Dept. of Health, Education, and Welfare 1968).

One of the most important products of such life tables is the estimated gain in life expectancy at birth if a particular cause of death were eliminated, i.e., if the death rate from that cause were arbitrarily set to zero while death rates from all other causes remained the same. To recapitulate the mathematics of such a calculation, suppose that there are n mutually exclusive and exhaustive causes of death operating in a population at time t. The probability of surviving from birth to age a at time t if the only cause of death operating were cause i is

...

where µ^sub i^(s; t) is the death rate from cause i in the age interval s to s+ds. In the life table for all causes of death combined, the equivalent survival function is

...

For simplicity, let p(a; t) = p(a).

If we assume the n causes of death to be independent, p(a) = p1(a).p2(a).: : :.pn(a). Let ... be the probability of surviving from all causes except cause i at age a. Given the force of mortality, µ(s), life expectancy at birth is computed as

...

If there are n mutually exclusive and exhaustive causes of death operating in a population then life expectancy is computed as

...

Let Di(0) be the years of life gained at birth if cause of death i were eliminated. Then Di(0) is computed as:

... (1)

It is important to note that the calculations made by assuming a particular cause of death is "eliminated" are best interpreted as an accounting exercise rather than an epidemiologic prediction. …

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