Quantifying Intrinsic and Extrinsic Contributions to Human Longevity: Application of a Two-Process Vitality Model to the Human Mortality Database
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Demography

December 2016, Volume 53, Issue 6, pp 2105–2119

# Quantifying Intrinsic and Extrinsic Contributions to Human Longevity: Application of a Two-Process Vitality Model to the Human Mortality Database

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- David J. Sharrow Email author
- James J. Anderson

- David J. Sharrow
  - 1
  Email author
- James J. Anderson
  - 1

1. 1.University of Washington Seattle USA

Article

First Online:
  11 November 2016

DOI: 10.1007/s13524-016-0524-4

Cite this article as:
  Sharrow, D.J. & Anderson, J.J. Demography (2016) 53: 2105. doi:10.1007/s13524-016-0524-4

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## Abstract

The rise in human life expectancy has involved declines in intrinsic and extrinsic mortality processes associated, respectively, with senescence and environmental challenges. To better understand the factors driving this rise, we apply a two-process vitality model to data from the Human Mortality Database. Model parameters yield intrinsic and extrinsic cumulative survival curves from which we derive intrinsic and extrinsic expected life spans (ELS). Intrinsic ELS, a measure of longevity acted on by intrinsic, physiological factors, changed slowly over two centuries and then entered a second phase of increasing longevity ostensibly brought on by improvements in old-age death reduction technologies and cumulative health behaviors throughout life. The model partitions the majority of the increase in life expectancy before 1950 to increasing extrinsic ELS driven by reductions in environmental, event-based health challenges in both childhood and adulthood. In the post-1950 era, the extrinsic ELS of females appears to be converging to the intrinsic ELS, whereas the extrinsic ELS of males is approximately 20 years lower than the intrinsic ELS.

### Keywords

Vitality Mortality Survival Epidemiologic transition Life expectancy

An erratum to this article is available at http://dx.doi.org/10.1007/s13524-016-0547-x.

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## Introduction

The rise in human life expectancy over the nineteenth and twentieth centuries for most developed countries is well documented. Omran’s theory of epidemiologic transition and its extensions (McKeown 1976; Olshansky and Ault 1986; Omran 1971; Rogers and Hackenberg 1987; Salomon and Murray 2002) explain this increase as a shift in the cause-of-death structure from infectious and parasitic diseases primarily affecting the very young to a disease burden dominated by noncommunicable ailments affecting people in later stages of life. Alternatively, the rise in human life expectancy can be thought of as having involved declines in intrinsic and extrinsic mortality processes (Olshansky 2010) associated, respectively, with chronic, accumulative physiological deterioration and instantaneous, acute environmental challenges to the vitality of an individual (an abstract measure of survival capacity). Quantifying these sources of change in longevity is useful in determining the contributions from behavior and environment historically and, by extension, in forecasting mortality, a critically important issue for planning health and social services for the world’s aging populations. However, the widely used Gompertz-type models that describe the age pattern of mortality in terms of a single age-specific mortality rate generally disregard these factors. For biodemographers, the challenge is developing frameworks and tractable models for capturing the contributions from these processes in shaping survival patterns in humans and other species (Wachter and Finch 1997).

Li and Anderson (2013) developed a tractable form of this intrinsic-extrinsic framework and applied the model to Swedish population period data concluding that the mid-twentieth century epidemiologic transition involved asynchronous changes in extrinsic and intrinsic adult mortality associated with epidemiologic patterns resulting from environmental and behavioral conditions. Thus far, modeling these processes has been limited to adult populations and there has been no attempt to quantify and compare the mortality partition over the full life span for a large number of populations. However, the model was recently extended to include childhood mortality (Anderson and Li 2015).

In this study, we aim to identify the pattern of change in extrinsic and intrinsic processes in 42 populations over the past two centuries. We do so by fitting a version of the extended vitality model, which characterizes contributions to survival across age and time, to data from the Human Mortality Database (HMD n.d.) and by summarizing the intrinsic and extrinsic survival patterns using the measure of expected life span (ELS).

## Methods and Data

### Two-Process Vitality Model

We fit the HMD data with a six-parameter version (Anderson and Li 2015) of the two-process vitality model proposed by Li and Anderson (2013). The model partitions age-dependent mortality into two classes. The intrinsic mortality class describes an individual’s mortality as the absorption of a hidden Markov process characterizing vitality into a zero-vitality boundary representing death. The intrinsic mortality class has been described as a “process point of view” approach (Aalen and Gjessing 2001:2) in that the individual’s loss of vitality is a rudimentary representation of the physiological processes leading to individual senescence. An extrinsic mortality class, which is equivalent to the Strehler and Mildvan (1960) interpretation of Gompertz-type models (Gompertz 1825; Heligman and Pollard 1980; Makeham 1860; Siler 1979), characterizes mortality as external challenges to the average age-dependent level of vitality in the population. Extrinsic death occurs when an environmental challenge instantaneously exhausts remaining vitality. The Li and Anderson (2013) model characterizes intrinsic and extrinsic mortalities during adulthood with four parameters—two for intrinsic mortality, and two for extrinsic mortality—and has been used to describe demographic phenomenon, including the historical pattern of Swedish mortality (Li and Anderson 2013), accelerations of mortality in late-middle life/early old age (Li et al. 2013), and the breakdown of the log-linear relationship of Gompertz mortality parameters in the twentieth century (Li and Anderson 2015). The six-parameter extension (Anderson and Li 2015) includes childhood mortality as a form of extrinsic mortality resulting from childhood challenges acting on an age-increasing deterministic childhood vitality that is separate from age-declining adult vitality. The vitality framework merges Gompertz-type force-of-mortality models with the point-of-view approach; it therefore shifts the focus from explaining how the force of mortality changes with age to how the underlying intrinsic and extrinsic mortality processes change with age.

In the four- and six-parameter versions of the model, the intrinsic and extrinsic processes have limited interactions. Nonlethal extrinsic challenges that do not exceed an individual’s vitality do not change the trajectory of vitality to the absorbing boundary, and lethal extrinsic challenges do not change the distribution of vitality at each age.1

Figure 1 depicts graphically how the six-parameter model controls the rates of intrinsic and extrinsic mortalities.2 In panel a of the figure, the intersection of individual stochastically declining vitality paths with a zero boundary marks intrinsic death. Adult extrinsic death occurs when a challenge exceeds a measure of deterministic age-dependent vitality.3 Juvenile extrinsic death occurs when a challenge exceeds a deterministic juvenile vitality that, unlike the adult deterministic vitality, begins at zero and increases to reflect increasing robustness associated with declining ontogenescent mortality with age among the very young (Levitis 2011; Levitis and Martínez 2013). For simplicity, all juvenile deaths are denoted as extrinsic.
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Fig. 1

Two-process vitality model. Panel a shows the intersection of individual stochastically declining vitality paths with the zero boundary marking intrinsic death. Adult extrinsic death (filled circles) occurs when a challenge (circular plotting symbols) exceeds the deterministic population vitality (solid, declining line). Juvenile extrinsic death (filled triangles) occurs when a challenge (triangular plotting symbols) exceeds deterministic juvenile vitality (solid, increasing line). Panel b shows the two-process vitality model in terms of age-specific survival proportions fit to U.S. males for the period 1935–1939 (observed data shown with circles). Intrinsic survival remains at 1 until later ages; extrinsic challenges dominate in early life, as shown with the extrinsic survival function. Extrinsic survival ignoring childhood mortality is computed with just the adult portion of extrinsic survival shown in Eq. (2). The fitted total survival curve is shown with a dashed black line and is the product of the intrinsic and extrinsic survival functions, as shown in Eq. (3). Both graphs were produced with fitted parameter values for U.S. males for the period 1935–1939: r = 0.011681; s = 0.012588; λ = 0.10575; β = 0.20288; α = 0.13154; γ = 1.7276

Panel b of Fig. 1 depicts the vitality model in terms of age-specific survival proportions. The mathematical development of these elements can be found elsewhere (Anderson and Li 2015; Li and Anderson 2013). Here, we give the equations defining intrinsic and extrinsic components of the survival curve. The intrinsic and extrinsic survival curves can be derived from the distribution of the deaths over age as described in panel a. The parameters of the equations are estimated by fitting the model to survival data (described in the next subsection). Parameters in panel b are estimated by fitting the model to the survival curve for U.S. males for the period 1935–1939.

Intrinsic survival depends on two parameters—r, the mean rate of vitality loss; and s, the variability in the rate of vitality loss:
$$ {l}_x^i=\Phi \left(\frac{1-rx}{s\sqrt{x}}\right)- \exp \left(\frac{2r}{s^2}\right)\Phi \left(\frac{1+rx}{s\sqrt{x}}\right), $$
(1)

where Ф is the cumulative normal distribution, and x is age.

The extrinsic survival curve shown in Eq. (2) depends on five parameters. Adult extrinsic mortality is governed by the mean frequency (λ) and magnitude (β) of extrinsic challenges in adulthood as well as the rate of vitality loss (r). Juvenile extrinsic mortality depends on the juvenile mortality duration in years (α) and the juvenile challenge frequency (γ).
$$ {l}_x^e= \exp \left(-\frac{\upbeta}{r}\times \frac{\lambda \exp \left(-1/\upbeta \right)}{ \exp \left(rx/\upbeta \right)-1}+\upalpha \upgamma \exp \left(-x/\upalpha \right)\right). $$
(2)

The extrinsic challenges are prescribed to have Poisson frequency distributions and exponential magnitude distributions.

The total survival curve, lx, is the product of the extrinsic and intrinsic survival curves as shown in Eq. (3).
$$ {l}_x={l}_x^i\times {l}_x^e. $$
(3)

Each parameter has a unique age-dependent effect on total survival and the mortality rate (Li and Anderson 2015). The influence of r and s on the mortality rate increases with age, whereas the influence of λ and β decreases with age. The juvenile parameters α and γ influence the mortality rate only in early childhood. These patterns reflect the dominance of juvenile processes in early age, extrinsic processes in middle age, and intrinsic processes in old age.

The ELS for each type of survival (intrinsic or extrinsic) is
$$ EL{S}_{type}={\displaystyle {\int}_0^{\infty }{l}_x^{type}dx.} $$
(4)

ELStype is equivalent to the life expectancy at birth derived from a life table calculated with either \( {l}_x^i \) or \( {l}_x^e \).

### Parameter Estimation

We estimate the parameters defining intrinsic and extrinsic ELS by fitting survival curves with a maximum likelihood estimation routine for the vitality model developed by Salinger et al. (2003) for age interval survival data. The Salinger et al. procedure defines a likelihood function for interval-censored survival data (i.e., deaths are counted at the end of each age interval rather than continuously) and searches the parameter space for the combination of model parameter values that produces the maximum likelihood.4 We carry out parameter estimation with the vitality package in the statistical analysis software R, which provides fitting routines for several models in the vitality family. We use a set of initial parameter values (r = 0.01, s = 0.01, λ = 0.1, β = 0.2, α = 1, γ = 0.01) to ensure convergence and provide a reasonable parameter search start for all life tables in the HMD. Although the model partitions total mortality into two processes, cause-of-death data are not used to fit the model to survival data, and cause-of-death data are not actually available in the HMD.

### Interpreting ELS and Survival From Intrinsic and Extrinsic Components

Although we make a distinction between these two mortality processes, it would be misguided to think that either process is driven solely by intrinsic or by extrinsic causes (Li and Anderson 2013). The process of extrinsic death already relies on a deterministic intrinsic vitality function, and extrinsic challenges could theoretically alter the trajectory of vitality paths. In our case, we do not model the latter process directly. Thus, interpretation of intrinsic survival is rather straightforward. An intrinsic death occurs with the complete loss of vitality after a pattern of chronic, incremental degradation of survival capacity with age. Intrinsic survival, then, is survival unaffected by extrinsic challenges. ELSi can be considered a kind of life expectancy in the absence of extrinsic mortality. Extrinsic death occurs when an acute, environmental challenge instantaneously exhausts remaining vitality. Because the intrinsic survival proportion is 1.0 until old age and the overall survival curve is the product of extrinsic and intrinsic survival curves, lx is entirely governed by extrinsic survival until advanced age (see Fig. 1, panel b).

A final note on interpretation concerns period versus cohort data. For this study, we are primarily concerned with the change in death processes over time and thus utilize period data. Intrinsic parameters estimated from period data represent weighted averages from all the cohorts making up the period and, because they are of biological origin, are expected to change slowly across cohorts. That said, it is entirely possible that period intrinsic ELS could shift abruptly from one period to the next if successive cohorts engage in varying cumulative health behaviors—a phenomenon captured by changes in the s parameter (Li and Anderson 2013). For example, if members of a successive cohort experience early intrinsic mortality from engaging in a harmful cumulative health behavior, such as smoking, the variability in age at intrinsic death will increase (i.e., s increases). Because ELS is simply an average, it is sensitive to the younger ages at death, and period intrinsic ELS can drop sharply under these conditions. Meanwhile, extrinsic parameters, which reflect environmental conditions, can change rapidly across periods (Li and Anderson 2013). Therefore, Li and Anderson proposed that parameters estimated from period data represent the change over time of the underlying processes more accurately than those estimated from cohort data.

### Human Mortality Database (HMD)

We fit the two-process vitality model by sex to a collection of 743 period survival patterns representing 42 populations from the HMD. The HMD is a publically available data set containing mortality data for 37 mostly developed countries with varying lengths of data series. (A list of the countries and data availability used in this analysis can be found in Table 1.) We model the cumulative survival curves (the lx column of the life table) from total population five-year period life tables with single-year age intervals and an open interval of 110+ (x = 0, 1, 2, . . . , 108, 109, 110+). All life tables in this collection are computed from directly observed deaths except at the oldest ages (Wilmoth et al. 2007). The life tables in this collection contain approximately 149 million deaths and roughly 4.6 billion male and 5 billion female person-years of observation.
Table 1

Survival data included for analysis

Country/Population | Years | Country/Population | Years
--- | --- | --- | ---
Australia | 1925–2005 | Latvia | 1960–2005
Austria | 1950–2005 | Lithuania | 1960–2005
Belarus | 1960–2005 | Luxembourg | 1960–2005
Belgium | 1845–2005 | Netherlands | 1850–2005
Bulgaria | 1950–2005 | New Zealand: Maori | 1950–2000
Canada | 1925–2005 | New Zealand: National | 1950–2000
Chile | 1995–2000 | New Zealand: Non-Maori | 1905–2000
Czech Republic | 1950–2005 | Northern Ireland | 1925–2005
Denmark | 1835–2005 | Norway | 1850–2005
England & Wales | 1845–2005 | Poland | 1960–2005
Estonia | 1960–2005 | Portugal | 1940–2005
Finland | 1880–2005 | Russia | 1960–2005
France | 1820–2005 | Scotland | 1855–2005
Germany | 1990–2005 | Slovakia | 1950–2005
Germany: East | 1960–2005 | Slovenia | 1985–2005
Germany: West | 1960–2005 | Spain | 1910–2005
Hungary | 1950–2005 | Sweden | 1755–2005
Iceland | 1840–2005 | Switzerland | 1880–2005
Ireland | 1950–2005 | Taiwan | 1970–2005
Italy | 1875–2005 | Ukraine | 1960–2005
Japan | 1950–2005 | USA | 1935–2005

Notes: The “Years” column shows the range of start years. No country had a discontinuity in its data series. Australia, for example, has 17 five-year periods (1925–1929, 1930–1934, . . . , 2005–2009).

## Results

We quantify the contributions from each source of mortality as the ELS from the intrinsic and extrinsic survival curves. Again, the ELS is simply the life expectancy at birth derived from a life table based on either the intrinsic or extrinsic survival curve calculated with Eqs. (1) and (2), respectively. Figure 2 plots the two ELS by five-year period for all 42 populations along with the observed life expectancy at birth (diamond-shaped plotting symbols). This figure also shows the extrinsic ELS when ignoring childhood mortality (triangle plotting symbols). The extrinsic ELS without childhood mortality is also derived from an extrinsic survival curve, but this curve is computed by setting γ = 0 in Eq. (2) (see Fig. 1, panel b). The means across the five-year periods for each ELS are shown with solid lines.
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Fig. 2

Extrinsic and intrinsic ELS for HMD (n = 743 for each sex) life tables for males (left panel) and females (right panel). Intrinsic ELS and extrinsic ELS are the life expectancies at birth derived from life tables calculated with extrinsic and intrinsic survival curves, respectively. Vitality parameters are estimated for six-parameter model. Extrinsic ELS without childhood mortality is derived in the same fashion as other ELS, but the extrinsic survival curve is generated with the four-parameter model. Observed life expectancy at birth is also shown, and the average over each five-year period for each ELS or life expectancy is shown with a solid line

The majority of the increase in life expectancy before 1950 can be attributed to increasing extrinsic ELS (ELSe). For most populations in this data set and for both sexes, ELSe rises linearly from roughly 1875 until about 1950, presumably driven by reductions in acute health challenges. Table 2 shows the per year gains in mean observed life expectancy at birth and the mean intrinsic (ELSi) and extrinsic ELS (solid lines in Fig. 2) for three periods of equal length. For both sexes, the first period (1830–1890) shows small improvements in life expectancy driven by relatively modest improvement in extrinsic survival. Life expectancy grows most rapidly during the second period leading up to 1950, which is dominated by substantial progress in extrinsic survival. Major extrinsic challenges to human health also explain a few momentary depressions in overall period life expectancy at birth; extrinsic ELS dips in 1915–1919 for both sexes, likely as a consequence of World War I and the worldwide flu pandemic, and extrinsic ELS also temporarily declines for males around World War II. A final trend in extrinsic mortality supports the epidemiologic transition as classically understood. Just as much of the increase in life expectancy can be attributed to declines in extrinsic mortality, much of the increase in ELSe can be attributed to the reduction of childhood extrinsic challenges. In Fig. 2, this trend is evident in the merging of the “Extrinsic” (circles) and “Extrinsic (adult only)” (triangles) clouds. The “Extrinsic (adult only)” cloud shows extrinsic ELS as if there were no childhood mortality (i.e., the cumulative survival proportion during childhood remains 1; see Fig. 1, panel b). In the most recent period, the diminishing difference between extrinsic ELS with and without childhood mortality results from the dramatic reduction in mortality from acute challenges in the early years of life. With the substantial reduction in juvenile extrinsic mortality over the past few decades, the vast majority of extrinsic mortality now occurs in adulthood.
Table 2

Change per year in mean life expectancy at birth (e0), mean extrinsic ELS (ELSe), and mean intrinsic ELS (ELSi) for three 60-year periods for both sexes

| Female | Male
--- | --- | ---
| e0 | ELSi | ELSe | e0 | ELSi | ELSe
1830–1890 | 0.111 | 0.016 | 0.143 | 0.112 | 0.024 | 0.117
1890–1950 | 0.374 | 0.118 | 0.344 | 0.351 | 0.108 | 0.339
1950–2010 | 0.197 | 0.126 | 0.174 | 0.159 | 0.144 | 0.141

Note: ELS is derived from intrinsic and extrinsic survival functions calculated with Eqs. (1) and (2) after fitting HMD with a six-parameter vitality model.

Intrinsic ELS—a measure of longevity acted on by physiological factors, such as genetics and long-term cumulative health behaviors—grew slowly up through 1950 until a second phase of longevity evolution began, presumably driven by lifesaving technologies and improvements in cumulative health behaviors. Table 2 shows that the increase in life expectancy slowed during this post-1950 period. In addition, especially for males, the pace of change for the two mortality processes converged as the gains from controlling extrinsic death with various public health and medical advancements began to level off. Although intrinsic survival increased during all three periods, the most recent data suggest that the intrinsic ELS is stabilizing for both sexes but especially for females.

### Divergent Populations

Although most populations realized consistent gains in overall survival, several eastern European countries deviated from this trend in recent decades, especially for males. The recent factors affecting longevity in these countries have been documented (Lopez et al. 2006; Salomon and Murray 2002). Researchers attribute a substantial portion of the excess adult mortality in this region to several causes—including diseases of the cardiovascular, circulatory, and respiratory systems, as well as injuries and accidents (Guo 1993; McKee and Shkolnikov 2001; Notzon et al. 1998)—brought on by a host of behavioral and environmental challenges, such as alcohol consumption and smoking (Bobak and Marmot 1996; McKee and Shkolnikov 2001), stress related to precipitous economic fluctuations (Shkolnikov et al. 1998), and inadequate health care and social support (Andreev et al. 2003).

Figure 3 plots the intrinsic and extrinsic ELS for males over time, with eastern and central European countries highlighted. Extrinsic ELS is shown with diamond plotting symbols. In the last third of the twentieth century (1970–2000), the extrinsic ELS exhibited a complex and shared pattern of variation in several eastern European countries. Figure 4 plots the change for each five-year period in extrinsic and intrinsic ELS, as well as the change in observed life expectancy at birth for six eastern European countries (Belarus, Estonia, Latvia, Lithuania, Russia, and Ukraine). This figure illustrates that the variation, containing overall declines and short-term increases in ELSe, followed the same pattern in the six countries. ELSe first declined during each five-year period from the 1970s through the early 1980s. It then increased in the 1985 period and sharply declined in the 1990 period along with observed life expectancy at birth, coinciding with the dissolution of the Soviet Union. Since the early 1990s, most of the six countries have experienced rebounds in extrinsic ELS and life expectancy at birth. In contrast, ELSi in the six countries did not exhibit a similar coherence. Notably, the changes in ELSe closely tracked observed life expectancy at birth because overall survival in childhood and most of adulthood before old age is governed by extrinsic survival, which is sensitive to many of the primary causes of excess adult mortality in eastern European countries.
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Fig. 3

Male intrinsic (circular plotting symbols) and extrinsic (diamond plotting symbols) ELS from HMD 1850–2005, with central and eastern European countries highlighted. ELSi and ELSe are the life expectancies at birth derived from life tables calculated with intrinsic and extrinsic survival curves, respectively. Vitality parameters are estimated for the six-parameter model

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Fig. 4

Five-year changes in male ELSi and ELSe and observed male life expectancy at birth for six countries. ELSi and ELSe are the life expectancies at birth derived from life tables calculated with extrinsic and intrinsic survival curves, respectively. Vitality parameters are estimated for a six-parameter model

This age difference in the influence of extrinsic and intrinsic processes on observed mortality is illustrated in Fig. 5, which contrasts the historical pattern in extrinsic and intrinsic survival for males in Ukraine and Japan. For both countries, the intrinsic survival probability was 1.0 until about age 70; thereafter, intrinsic survival improved progressively for each five-year period. In contrast, the period patterns of extrinsic survival differ considerably for the two countries. For Japan, extrinsic survival progressively increased from 1950 to 2005, with most of the gain being driven by decreasing childhood mortality for each five-year increment. For Ukraine, extrinsic survival progressively worsened from 1960 to 2005 as a result of increased extrinsic adult mortality rather than childhood mortality, which improved over time. The primary difference between the age patterns of mortality for males in eastern European countries and the other countries in the HMD is elevated adult mortality, especially during the two decades preceding the collapse up of the Soviet Union (Bobak and Marmot 1996; McKee and Shkolnikov 2001); these patterns are consistent with our finding of losses in ELSe for these countries during the same period.
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Fig. 5

Fitted extrinsic (solid lines) and intrinsic (dashed lines) survival curves for males in Ukraine (1960–2010) and Japan (1950–2010). Both intrinsic and extrinsic curves are calculated with the six-parameter model

Some of the aforementioned former Soviet countries, along with a few central European countries, display relatively high intrinsic ELS in some recent periods, although the gap in intrinsic ELS between these countries and the rest of the HMD is not as large as for extrinsic ELS. This elevated ELSi is driven by a downward trend in the intrinsic parameter r, which controls the rate of vitality loss, coupled with either a downward or a flat trend in s, which controls the variability in the rate of vitality loss. Under these conditions, the break of the intrinsic survival curve (i.e., \( {l}_x^i<1 \)) begins at a later age, and the intrinsic survival curves become more rectangular (i.e., the distribution of the age at intrinsic death is narrower). With this rectangularization, intrinsic mortality is not influential until older ages. At younger ages, the relatively severe extrinsic mortality in many of these countries dominates the survival patterns. In this case, the high ELSi is driven by the continuing decrease in the rate of vitality loss, which we view as a measure of the rate of aging. For example, Poland saw a decreasing trend in both intrinsic parameters, thus increasing the age at which intrinsic mortality begins to influence the overall survival curve.

In contrast to the high and stable ELSi pattern in most countries, others exhibit rapid changes in ELSi, shifting sometimes by up to four years in a five-year period (Fig. 4). In these populations, the rate of vitality loss (r) declines over time, while the variability in the rate (s) increases. This parameterization results in young intrinsic deaths (~50–60), dragging down the ELSi because it is a synthetic period measure reflecting the weighted contributions from all the cohorts that make up the period. Thus, the increased variability from one period to the next is brought on by newer aging cohorts, with some members of those cohorts likely engaging in harmful cumulative health behaviors throughout life and dying relatively early. Of these cumulative health behaviors, smoking is arguably the most influential at a population level. Li and Anderson (2013) showed that a substantial increase in s from roughly 1950 to 1980 for Swedish males coincided with the timing of cohort smoking behavior. In essence, heterogeneity in living conditions and cumulative health behaviors influence the overall pattern of intrinsic survival in cohort-specific ways when fitting period data and can result in substantial change in intrinsic life expectancy over intervals of a few years.

## Discussion

Researchers concerned with mortality and longevity generally have not distinguished intrinsic and extrinsic processes because most models do not distinguish between them. We argue in this article and elsewhere (Li and Anderson 2013, 2015) that casting overall survival as a two-process framework provides a more mechanistic understanding of historical mortality and health transitions than can be obtained by considering mortality as a single process.

We fit a version of a two-process vitality model to 743 cumulative survival curves (for each sex) from the Human Mortality Database. The model blends point-of-view and force-of-mortality models to yield insights into how the processes change independently with age and time. The model characterizes two extrinsic processes that separately dominate childhood and middle age, and one intrinsic process that dominates in old age. The model’s tractable six parameters have intuitive links to age- and environment-related processes of mortality. This partition allows us to define independent measures of intrinsic and extrinsic survival whose product is overall cumulative survival or the lx column of the life table. From the cumulative survival curve for each country-period, we derive intrinsic and extrinsic survival curves and track the life expectancy at birth for each process, which we refer to as intrinsic and extrinsic ELS. The historical patterns of intrinsic and extrinsic ELS provide a quantitative description of the epidemiologic transition over the last century and a half.

Increases in life expectancy at birth prior to 1950 can largely be attributed to improvements in extrinsic mortality because intrinsic ELS changed very little during this time. These increases in longevity are primarily associated with reductions in childhood mortality as lethal, acute infectious diseases were brought under control. Post-1950, a second phase of longevity evolution began, ostensibly brought on by advances in technologies that reduced old-age death and by improvements in cumulative health behaviors. In the two-process framework, the rectangularization of the survival curve over the twentieth century (Yashin et al. 2002) is explained largely by decreasing extrinsic mortality (Li and Anderson 2015), which nearly doubled extrinsic ELS (from 40 to 75 years) between 1800 and 1950 (Fig. 2). Intrinsic ELS contributed little to increasing life expectancy at birth during this interval. However, since the mid-twentieth century, changes in intrinsic ELS have become more important, increasing from 80 years to over 90 years during this time.

The varying dominance of extrinsic and intrinsic mortality processes has implications for public health policy. Actions that reduce environmental challenges, such as acute childhood illness and auto accidents, or that increase lifesaving technology should be reflected in increases in extrinsic ELS. In contrast, actions to reduce chronic stress associated with nutrition and aging should be reflected in increases in intrinsic ELS. Thus, the relative impacts of policies that address these different categories should be quantifiable through partitioning period survival data into intrinsic and extrinsic parts. The historical patterns for these measures also provide some information on the potential sensitivity of these processes to policy and societal changes. In general, intrinsic ELS steadily increased over the last half-century in the countries we analyzed. However, extrinsic ELS revealed a divergence, decreasing in eastern European countries but rising in the others (Fig. 3). For example, since 1950, male extrinsic survival curves for Japan steadily improved but those for Ukraine steadily worsened with increasing extrinsic mortality among adults (Fig. 5). Furthermore, the model attributes rapid changes in life expectancy at birth across years to changes in the degree of heterogeneity of health behaviors within a population.

We suggest that forecasts of life expectancy for individual countries can and should be based on the temporal trends in the specific ELS components, which are characterized by the temporal trends in the model parameters. The identification of processes driving model parameters and, by extension, ELSi and ELSe has been mostly qualitative and inferential; for example, in Sweden, a correspondence of smoking to the temporal increase in heterogeneity factor s (Li and Anderson 2013) links smoking to the decline in intrinsic ELS between 1955 and 1980. We suggest that an understanding of historical patterns and projection of future trends requires that researchers consider expected life span in terms of changes in external challenges and internal aging. Indeed, researchers are investigating how genetic and nongenetic changes contribute to aging (Ukraintseva et al. 2016; Yashin et al. 2016), and research is underway to quantify the linkages among health behavior, environmental conditions, and longevity (Crimmins et al. 2010). We suggest that the partition of intrinsic and extrinsic mortalities provides a simple and powerful framework for merging these endeavors.

Footnotes
1

Defining independent intrinsic and extrinsic processes achieves a closed-form solution of total mortality that can be fit to data to yield parameter estimates (Li and Anderson 2013). We are currently exploring a version of the model with greater interaction between these processes.

2

See the online version of this article to view all figures in color.

3

Li and Anderson (2013) showed that extrinsic challenges to stochastic vitality trajectories preferentially eliminate lower vitality paths, reshaping the distribution of vitality at each age. Because the effect of this reshaping cannot be captured in a closed-form solution that could be fit to data and yield parameter estimates, Li and Anderson expressed the extrinsic mortality process as challenges to the mean rate of loss of vitality—a deterministic function. This modified version of the two-process model with independent intrinsic and extrinsic parts is the model form used in this article.

4

Fitting the closed-form solution of the model to data can result in slightly biased parameter estimates, with r and β slightly low, and s and λ slightly high. Li and Anderson (2013:350) provided bias correction formulas for the four adult parameters based on simulation with a numerical model with greater parameter interaction. However, we avoid direct parameter interpretation here in favor of the summary metric ELS, which is unaffected by the parameter bias.

## Acknowledgments

This work was supported by Grant No. 1R21AG046760-01 from the National Institute on Aging.

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