Abstract The reasons for classifying causes of

death into aggregate groups are discussed and the

impact of mortality partitions on analyses of mortal-

ity is described. Special emphasis is given to a mor-

tality partition that distinguishes between intrinsic

causes of death that arise primarily from the failure of

biological processes that originate within an organ-

ism, and extrinsic causes of death that are primarily

imposed on the organism by outside forces. Examples

involving mortality data for mice, dogs, and humans

are used to illustrate how this mortality partition in-

fuses biological reasoning into mathematical models

used to analyze and predict senescent-determined

mortality, enhances the information content of the

mortality schedules generated from these models,

improves mortality comparisons between populations

within species separated by time or geographic

location, and provides a logical pathology endpoint

for making interspecies comparisons of mortality. By

bridging biology and the statistics of mortality, a

mortality partition based on intrinsic and extrinsic

causes of death provides both structure and direction

for research on senescent-determined mortality.

Keywords Biodemography Æ Comparative

mortality Æ Mortality partitions Æ Intrinsic mortality

Introduction

Since there are many ways for an organism to die,

researchers who study mortality often focus on sub-

sets of causes drawn from the pool of all possible

causes of death. For example, a radiation biologist

may be interested in deaths caused by cancer while a

cardiologist might focus on deaths caused by mal-

functions of the heart. Death caused by the failure of

a specific organ may be of more interest to some

researchers than the specific disease process that

caused the failure. An interest in the broad mortality

consequences of smoking or obesity might lead an

epidemiologist or demographer to consider cause of

B. A. Carnes (&)

Reynolds Department of Geriatric Medicine, University

of Oklahoma Health Sciences Center, Oklahoma City,

OK, USA

e-mail: Bruce-Carnes@ouhsc.edu

L. R. Holden

Sielken & Associates Consulting, Inc., Bryan, TX, USA

S. J. Olshansky

School of Public Health, University of Illinois at Chicago,

Chicago, IL, USA

T. M. Witten

Center for the Study of Biological Complexity, Virginia

Commonwealth University, Richmond, VA, USA

J. S. Siegel

J. Stuart Siegel Demographic Services, North Bethesda,

MD, USA

Biogerontology (2006) 7: 183–198

DOI 10.1007/s10522-006-9020-3

123

REVIEW ARTICLE

Mortality partitions and their relevance to researchon senescence

Bruce A. Carnes Æ Larry R. Holden ÆS. Jay Olshansky Æ Tarynn M. Witten ÆJacob S. Siegel

Received: 13 January 2006 / Accepted: 28 February 2006 / Published online: 27 May 2006

� Springer Science+Business Media, Inc. 2006

death only incidentally. In each of these cases, the

research interests of the investigator determine the

specific set of causes studied or whether such parti-

tioning of causes of death is even deemed necessary.

A focus on single diseases or individual organs,

however, is not as valuable when the aim of the re-

search is to analyze the mortality consequences of

senescence. Senescence produces a progressive deg-

radation of biological function over time at virtually

every level of biological organization. Death occurs

when that degradation exceeds the ability of the

organism to maintain its biological integrity. As such,

causes of death that are somehow linked to the

internal collapse of the biological system are a logical

point of focus for research on senescent-determined

mortality.

The need to partition total mortality into biologi-

cally relevant subcomponents has been recognized

and accepted as standard procedure in the scientific

literature for nearly 200 years (Carnes and Olshansky

1997). In a paper that gave birth to what is now called

‘competing risk theory,’ the British actuary Makeham

(1867) suggested that mathematical descriptions of

the ‘‘law of mortality’’ proposed by Gompertz (1825)

could be improved by partitioning causes of death

into: (1) a subset that he thought was responsible for

the age-dependent increases in mortality that char-

acterize the law, and (2) a subset ascribed to ‘‘acci-

dental circumstances’’ that do not depend on age. In

so doing, Makeham was the first scientist to provide

both the rationale and the methodology for the

development and use of mortality partitions.

A major difficulty with mortality partitioning,

however, is that knowledge about underlying mech-

anisms of senescence and disease has been and re-

mains incomplete. Makeham was aware of this

deficiency when he noted that advances in the

knowledge of disease causation would lead future

researchers to make improvements to his partitioning

of mortality (Benjamin 1959; Bodenheimer 1938;

Bourgeois-Pichat 1978; Clarke 1950; Deevey 1947;

de Finetti and Rossi 1982; Pearl 1921; Stearns et al.

1998).

A focus on causes of death related to senescence

does not mean that those considered unrelated to

senescence are unimportant or of no interest. To the

contrary, non-senescent related mortality (referred to

as extrinsic mortality) plays a central role in the

evolutionary theories of senescence (Kirkwood and

Holliday 1979). In addition, public health researchers

(Mackenbach et al. 1990) and clinical researchers

(McGinnis and Foege 1993) identify ‘avoidable

mortality’ and ‘actual causes’, respectively, as mod-

ifiable external factors that cause individuals to die

before attaining their life span potential. Despite their

different focus, the common theme that unites all of

these mortality partitions is a distinction made

between deaths that arise primarily from the failure of

biological processes that originate within an organism

(intrinsic mortality), and those that are primarily

imposed on the organism by outside forces (extrinsic

mortality)––(see Eakin and Witten 1995a; Carnes and

Olshansky 1997 for detailed discussions). The latter

group invariably leads to premature death.

In this paper we provide examples from human,

dog, and mouse mortality in order to illustrate how

the intrinsic/extrinsic mortality partition can provide

an informative structure and direction for analyses of

senescent-determined mortality. Biodemographic

concepts as well as methods of analysis and their

interpretation will be explored.

Intrinsic-Extrinsic mortality partitioning

In the terminology of Shryock et al. (1975), endoge-

nous [intrinsic] mortality is described as having a

‘‘biological character’’ such as that arising from ‘‘the

genetic makeup of the individual,’’ and as being

‘‘resistant to scientific progress.’’ It was defined to

include the ‘‘degenerative diseases of later life (e.g.,

heart disease, cancer, diabetes) and certain diseases

peculiar to early infancy.’’ In contrast, exogenous

[extrinsic] mortality results from causes that are

‘‘relatively preventable and treatable’’ and includes

‘‘mortality mainly from infections and accidents.’’

Like Makeham (1867, p. 335), Shryock et al. (1975,

p. 405) warned that their classification was not perfect

and the specifics of its composition would depend on

the prevailing state of biomedical knowledge about

disease processes.

Some researchers, including Makeham (1867,

p. 333), have suggested that age-independence is the

criterion to use when distinguishing extrinsic mor-

tality from intrinsic mortality. We disagree. It is

difficult to envision a cause of death for humans or

any other species, either intrinsic or extrinsic, that

does not exhibit age-dependence. Vulnerability to

184 Biogerontology (2006) 7: 183–198

123

‘‘all’’ mortality risks varies by age, with children and

the elderly being especially likely to succumb to

external risks (e.g., infectious disease, predation,

starvation) that we define as extrinsic. The presence

or absence of age dependence is not the criterion that

we use to distinguish between intrinsic and extrinsic

causes of death. Instead, our distinction is based on

whether the primary cause of death does or does not

originate from within the organism.

Conceptually, intrinsic causes of death are those

that remain after the total elimination of extrinsic

causes of death. Consider a hypothetical experiment

in which animals are maintained in an optimal envi-

ronment where they are completely protected from

infectious diseases, aggression, fatal accidents, etc. In

this admittedly unrealistic (but nevertheless imagin-

able) scenario, all deaths arising from external forces

have been eliminated. Every animal in this hypo-

thetical population would theoretically achieve their

life span potential and succumb to an intrinsic cause

of death (Carnes et al. 2005). The mortality signature

(schedule of age-specific death rates) constructed for

this population is what we refer to as an intrinsic

mortality signature.

Optimum conditions are impossible to know and

impossible to achieve, but they can be approached.

Thus, investigators conducting controlled studies

involving laboratory animals attempt to provide the

optimal conditions of our hypothetical experiment,

but they can never do so with perfection. However, if

extrinsic causes of death can be identified, then it is

possible to filter them out mathematically in order to

arrive at an approximation of the intrinsic mortality

signature. That process is straightforward. If an ani-

mal dies at age T from an intrinsic cause, then the

intrinsic age of death is simply equal to T. However,

for an animal dying from an extrinsic cause at age t, all

we know is that the intrinsic age at death T is greater

than t. That is, only the lower bound for death times is

known for extrinsic deaths. Except under extreme

circumstances, such as analyses involving sparse data,

this so-called ‘‘right censoring’’ presents little prob-

lem for estimating the intrinsic mortality signature.

Mortality partition applied to humans

Deaths for all causes combined are commonly used in

the analysis and comparison of human mortality.

However, our interest in the biodemography of

senescence (Carnes and Olshansky 1993) led us to

conclude that all-cause mortality is a heterogeneous

mixture of mortality dynamics that we labeled

extrinsic and intrinsic mortality (Carnes and

Olshansky 1997). Extrinsic deaths account for the

majority of human mortality early in life, while those

caused by senescence progressively dominate the

intrinsic mortality schedule of both sexes from the

fifth decade onward (Fig. 1).

Our mortality partitioning for humans was based

on public-use demographic data obtained from the

National Center for Health Statistics (NCHS). These

data were tabulated for the underlying cause-of-death

listed on death certificates in the form of standardized

medical codes listed in the 6th, 9th and 10th Revi-

sions of the International Classification of Diseases

(ICD) published by the World Health Organization

(WHO). Coding differences between the revisions are

unlikely to affect our partitions because extrinsic and

intrinsic causes of death were broadly defined.

Finally, intrinsic causes of death were operationally

defined as the ICD codes remaining after those listed

in Table 1 were judged (after ongoing input from

knowledgeable colleagues, pathologists, physicians

and the author’s review of the literature) to be

extrinsic causes of death.

Within a calendar year

The age trajectories of all-cause mortality and its

extrinsic and intrinsic partitions are plotted for Uni-

ted States females (Fig. 2A) and males (Fig. 2B) in

1996 (NCHS 1998, 1999). Although the mortality

trajectories of extrinsic and intrinsic causes of death

are similar (within sex) during the first decade of life,

they begin to separate around the age of sexual

maturity (13–15 years). By age 20, it is apparent that

the hump in the all-cause mortality curve of either

sex is caused by an increase in mortality from

extrinsic causes. By the effective end of the repro-

ductive period (40–50 years), mortality from intrin-

sic causes surpasses that attributable to extrinsic

causes (i.e., a cross-over occurs, Hirsch et al. 2000).

In the post-reproductive period of the life span, the

extrinsic and intrinsic components of all-cause mor-

tality continue to diverge. By age 60, the trajectories

of intrinsic and all-cause mortality are nearly

Biogerontology (2006) 7: 183–198 185

123

indistinguishable. Our mortality partition added

value to this analysis by revealing that all-cause

mortality is a complex mixture of extrinsic and

intrinsic mortality dynamics that varies within and

across age segments of the human life course.

Heterogeneous mixtures of mortality trajectories

can affect quantitative methods of analysis and their

interpretation. For example, the approximate linearity

of death rates as a function of age on a semi-loga-

rithmic plot (as seen in Fig. 2) provides a visual

Fig. 1 The proportion of

age-specific deaths rates

(ages 15 and older)

attributable to intrinsic

causes for males and

females (US 1996)

Table 1 List of ICD codes

(based on the 9th revision)

used to identify extrinsic

causes of death for humans

ICD code Cause of death

E800–E999 Injuries and poisoning

001–139 Infectious and parasitic diseases

162 Lung cancer

180 Cervical cancer

260–269 Nutritional deficiences

278 Obesity, adiposity, hyperalimentation

280–281 Iron and other deficiency anemias

283.1–283.2 Acquired hemolytic anemias

291 Alcoholic psychosis

303 Alcohol dependence syndrome

304 Drug dependence

320–322 Meningitis

390–398 Rheumatic fever and rheumatic heart disease

460–519 Diseases of the respiratory system

571.0–571.3 Chronic liver diseases and cirrhosis, alchohol-related deaths

571.4–571.7 Chronic hepatitis and biliary cirrhosis

590 Infections of the kidney

595 Cystitis

597 Urethritis, not sexually transmitted

598 Urethral stricture

599 Other disorders of the urethra and the urinary tract

601 Inflammatory diseases of the female genitourinary system

630–676 Complications of pregnancy, childbirth, and the puerperium

725 Polymyalgia rheumatica

730 Osteomyelitis, periostitis, and other infections involving bone

186 Biogerontology (2006) 7: 183–198

123

diagnostic for the appropriateness of the Gompertz

model of mortality change with age (Elandt-Johnson

and Johnson 1980). As such, the nonlinear behavior

of all-cause mortality prior to age 40 would suggest

that the Gompertz model is an inappropriate one for

this age range. Similarly, the deceleration in the rise

(non-linearity) of all-cause death rates observed at

advanced ages for humans has led scientists

(including Gompertz) to conclude that the Gompertz

model is also inappropriate for these ages (Gompertz

1825; Carey et al. 1992; Fukui et al. 1993). In con-

trast, an examination of the intrinsic mortality sig-

natures yields a much different interpretation (Fig. 2).

Intrinsic mortality between ages 15 and 90 conforms

remarkably well to Gompertzian mortality dynamics.

Within calendar year, between subgroups

Human populations are never homogeneous. Instead,

they are a heterogeneous mixture of relatively

homogeneous subgroups (Carnes and Olshansky

2001). As such, no mortality trajectory estimated for

an entire human population can capture the variation

that we believe is present among subgroups within

that population. In order to illustrate this variation,

Age (years)

0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

1

All CauseExtrinsicIntrinsic

U.S. Females (1996)Mortality Partitions

B

A

Age (years)

0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

1

All CauseExtrinsicIntrinsic

U.S. Males (1996)Mortality Partitions

Fig. 2 Age-specific death

rates (US 1996) for all-

cause mortality and its

intrinsic and extrinsic

subgroups for females Aand males B

Biogerontology (2006) 7: 183–198 187

123

differences in mortality trajectories were examined

for three racial groups (white, black, and other) of

females (Fig. 3) and males (Fig. 4) from the same

NCHS data (1996 U.S. population) used previously.

As anticipated, these figures reveal information that

pooling obscured in the previous figures. We now see

that both extrinsic and intrinsic mortality is generally

higher for blacks than whites and that the ‘other’

group has the lowest mortality. To give these differ-

ences a sense of magnitude, age-specific mortality

rates for blacks are over twice those of the ‘other’

group. Extrinsic mortality for blacks and whites

converge around age 60 for females (Fig. 3A), but the

convergence does not occur until beyond 80 for males

(Fig. 4A). Eventually, a mortality crossover occurs

between blacks and whites of each sex. Although the

intrinsic mortality trajectories for each sex (Figs. 3B,

4B) retain their approximate Gompertzian form be-

yond the age of sexual maturity, the bending of the

trajectory (deceleration of the increase in age-specific

death rates) becomes more apparent when the data

are stratified by racial subgroups. The bending of the

intrinsic mortality trajectory is also more apparent for

blacks than for either whites or those listed in the

Age (years)

0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

WhiteBlackOther

U.S. Females (1996)Extrinsic Mortality

B

A

Age (years)

0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

1

White BlackOther

U.S. Females (1996)Intrinsic Mortality

Fig. 3 Age-specific death

rates (US 1996) for

extrinsic mortality A and

intrinsic mortality B for

females separated by race

into black, white and all

others (Smoothing lines are

shown to improve

visualization)

188 Biogerontology (2006) 7: 183–198

123

‘other’ category. As before, our mortality partition

added value to this analysis by revealing subgroup

differences imbedded within an overall pattern of

mortality similarity.

Lastly, median and interquartile range (IQR) for

survival ages were calculated to gauge the variation

of intrinsic mortality signatures within human data

(Fig. 5). These data show that male-female differ-

ences in intrinsic mortality have more to do with a

shift in the median age-at-death than the relative

distribution of deaths around that median. The

medians for males are about 5 years less than those

for females regardless of the racial group; and

regardless of gender blacks have shorter median life-

spans (for intrinsic deaths) than whites. Whites, in

turn, have lower medians than the ‘other’ group. Also

note the variation in age-at-death by race. Although

the middle 50% of intrinsic deaths occur within a 16-

year interval for whites, the nearly 20-year interval

for blacks is less ‘compressed’. The distribution of

deaths for the ‘other’ racial group is intermediate

between blacks and whites.

Age (years)0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

1

WhiteBlackOther

U.S. Males (1996)Extrinsic Mortality

B

A

Age (years)

0 20 40 60 80 100

Age

-Spe

cifi

c D

eath

Rat

es (

deat

hs p

er 1

00,0

00)

0.00001

0.0001

0.001

0.01

0.1

1

WhiteBlackOther

U.S. Males (1996)Intrinsic Mortality

Fig. 4 Age-specific death

rates (US 1996) for

extrinsic mortality A and

intrinsic mortality B for

males separated by race into

black, white and all others

(Smoothing lines are shown

to improve visualization)

Biogerontology (2006) 7: 183–198 189

123

Between calendar years

Next, we compared US death rates (classified by age,

sex, and cause of death) for 1950 and 2000 (NOVS

1954, NCHS 2002) to see if humans exhibit changes

in partitioned death rates over broad time periods.

During this 50-year period, age-related death rates for

all-cause mortality declined by about 40% for ages 15

and older. The temporal dynamics of the extrinsic and

intrinsic mortality trajectories (10-year age intervals,

sexes combined) for both years were consistent with

the more detailed (1-year age intervals) data pre-

sented for 1996 (Figs. 1–3). In both cases, intrinsic

mortality dominates at older ages (age > 40) while

extrinsic mortality dominates at younger ages, and

the two categories of death have dissimilar mortality

trajectories.

It is only when the extrinsic (Fig. 6A) and intrinsic

(Fig. 6B) mortality trajectories for 1950 and 2000

were superimposed that the temporal differences be-

tween them became evident. The changes in extrinsic

mortality (sexes combined) between 1950 and 2000

were strongly age dependent. Extrinsic death rates

decreased by about 30% over this 50-year period at

ages between 15 and 55, they remained essentially

unchanged in the 55–65 age interval, and they in-

creased by about 30% for people over age 65. In con-

trast, age-specific death rates for intrinsic causes (sexes

combined) decreased uniformly by approximately

50% over this period. Thus, for persons aged 15 years

and older, the changes in extrinsic mortality over this

period were smaller in magnitude and different in

pattern than was the case for intrinsic mortality.

The nearly uniform 50% drop in intrinsic mortality

between 1950 and 2000 was too substantial to be an

artifact. Coding differences between the Sixth (1950

data) and Tenth (2000 data) Revision of the ICD List

are not large enough to explain a change of this

magnitude. It is also unlikely that the biological

nature of the population changed appreciably over

this time period. Instead, the most plausible expla-

nation for this change in the age pattern of intrinsic

mortality is that humans have benefited from an

expansion of life-extending medical interventions

that affect the risk of death from intrinsic disease

processes.

Interventions that delay intrinsic deaths by man-

aging their symptoms (e.g., chemotherapies for can-

cer) or altering their underlying pathogenesis (e.g.,

cardiotonic therapies for congestive heart failure)

manufacture survival time that extends the lives of

individuals and lowers the death rates of populations

(Olshansky et al. 1998). In this case, the ability of

humans to lower death rates for intrinsic disease

processes appears to have exceeded the influence of

factors that can raise them (e.g., pollution, poor life

style choices). Clearly, intrinsic mortality signatures

for human populations depart from the original

thought experiment used to develop the concept;

namely, a mortality schedule calculated for individ-

uals living under optimum conditions where external

perturbations affecting mortality, whether beneficial

or detrimental, do not exist. Despite this added

complexity, the analyses of human data revealed that

useful insights into patterns of human mortality could

be gained from examining the mortality trajectories

of the intrinsic and extrinsic components of all-cause

mortality.

In the next section, we will examine whether the

variable intrinsic mortality signatures of humans bear

any resemblance to the more stable ones expected for

laboratory mice and dogs that were reared in the

controlled environments of the laboratory without the

confounding influence of life-extending interventions.

Interspecies comparison of intrinsic mortality

patterns

As long as intrinsic diseases are influenced to some

degree by genetic factors, then natural selection will

affect their frequency in a population and their age of

US, 1996

Median Age at Death (Years)

70 75 80 85 90 95

Inte

rqua

rtile

Ran

ge, I

QR

(Y

ears

)

10

15

20

25

MaleFemale

BLACK

OTHER

WHITE

Fig. 5 A plot showing differences between racial groups

(black, white and all other; US 1996) and sexes as measured by

the interquartile range and the median age at death (for

intrinsic causes)

190 Biogerontology (2006) 7: 183–198

123

expression (Medawar 1952). For iteroparous species,

the magnitude of this selection effect is greatest dur-

ing the pre-reproductive period, and then diminishes

progressively as the cumulative reproductive output

of a population is achieved. The universality of this

temporal pattern of selection pressure suggests that

the intrinsic mortality signatures that result from it

may be similar for different species when expressed

on an appropriate relative time scale (Carnes et al.

1996). Although species die from many of the same

intrinsic causes, they also die from species-specific

intrinsic causes. However, the interspecies conver-

gence of intrinsic mortality patterns only requires that

intrinsic causes in the collective respond to selection

pressure in the same way.

An alternative portrayal (hazard function, survi-

vorship curve) of intrinsic mortality is provided for the

1996 US human data for females used earlier (Fig. 7).

Mortality rates reach their minimum at the ages of

sexual maturity (12–15 years), climb gradually during

A U.S. Extrinsic Mortality

Age at Death (years)(Rates plotted at midpoints of intervals)

10 20 30 40 50 60 70 80 90 100

Age

-Spe

cifi

c D

eath

Rat

es (

Dea

ths

per

100,

000)

10

100

1000

10000

1950

2000

Source: National Center for Health Statistics

Age at Death (years)(Rates plotted at midpoints of intervals)

10 20 30 40 50 60 70 80 90 100

Age

-Spe

cifi

c D

eath

Rat

es (

Dea

ths

per

100,

000)

10

100

1000

10000

100000

1950

2000

Source: National Center for Health Statistics

B U.S. Intrinsic Mortality

Fig. 6 A comparison of

age-specific death rates

(ages 15 and older, plotted

at midpoints of intervals,

both sexes combined, US)

for extrinsic A and intrinsic

B mortality between 1950

and 2000

Biogerontology (2006) 7: 183–198 191

123

the reproductive period, and then begin a progressive

increase that becomes dramatic by age 80––a mor-

tality pattern mirrored by the temporal behavior of the

cumulative survivorship curve. If dogs and laboratory

mice were now added to this plot, the vast differences

in their average life span––approximately 2.5 years

for mice, 12 years for beagles and 85 years for human

females––would visually dominate the interspecies

comparison of mortality. However, a visual stretching

(i.e., scaling) of the time axes to remove life span

effects reveals intrinsic mortality patterns that share

far more similarities than differences (Fig. 8, Carnes

et al. 1996, Eakin and Witten 1995b).

The human data portrayed in Fig. 2 illustrates the

theoretically appealing and mathematically tractable

behavior of intrinsic mortality compared to either

extrinsic or all-cause mortality. The discussion of

Fig. 8 suggested a visual (proportional) scaling of the

age axis would reveal similarities among the intrinsic

mortality profiles of taxonomically diverse species

that are normally hidden in the absence of scaling.

We now consider the possibility that, for each species

or strain s, there are factors, ks, that give similar

mortality profiles when time, t, is re-expressed as t/ks.

Theoretical considerations also suggest that this

scaling factor, ks, is positively correlated with each

species’ effective end of reproduction (EER) (Carnes

et al. 2003a).

This logic raises two important questions. First,

how do we find the time-scaling factors ks? Second,

how do we then compare mortality patterns that have

been scaled (normalized, aligned)? Although several

viable scaling options exist, the simplest approach is

to use some general life-scale characteristic, such as

the median age at death or other percentile, obtained

from the species’ survival curve (Carnes et al. 1996).

A more sophisticated procedure would be to find ks as

the set of values that optimize some criterion of

similarity among survival curves. Provided the data

were available, it is even feasible to use a life-scale

characteristic that is not derived from time-to-death

Human(Female, US, 1996)

Age (Years)

Pro

bab

ility

0.00 20 40 60 80 100 120

0.2

0.4

0.6

0.8

1.0Mortality RateS(t)

Reproductive Period

Fig. 7 Plot showing the relationship between cumulative

survivorship and mortality rate curves for females (US, 1996)

Fig. 8 Cumulative

survivorship curves for

mice (B6CF1), dogs

(beagle) and humans with

death times normalized to a

common median age of

intrinsic death (Source:

Carnes et al. 1996)

192 Biogerontology (2006) 7: 183–198

123

data, such as EER or resting metabolic rate (Brown

and West 2000; Eakin and Witten 1995a).

We do not intend to obtain values for ks directly.

Instead, our goal is to reveal and quantify interspecies

differences between age patterns of mortality that

cannot be removed by proportional methods of scal-

ing. For example, statistics that measure relative

differences between mortality or survivorship pat-

terns at different ages (e.g., the ratio of mortality rates

or survivorship percentiles) are unaffected by any

proportional scaling of time. Similarly, measures of

relative variation like the coefficient of variation

(CV) are also unaffected by scaling. As such, these

statistics describe the mortality pattern without actu-

ally performing the time scaling directly.

We have chosen to employ a simple empirical

distribution analog of the CV, the relative inter-

quartile range (%IQR), as our measure of variation.

This statistic derived for intrinsic causes is computed

as the difference between the 75th and 25th percen-

tiles of the survivorship distribution (i.e., the IQR)

expressed as a percent of the median. The %IQR is

particularly advantageous for time-to-event data that

is censored, like that produced by mortality parti-

tions, because the three quartiles used in its calcula-

tion are almost always well defined. Deaths that

cluster around the median produce: (1) smaller %IQR

values, (2) ‘rectangular’ or ‘compressed’ survivorship

curves (Eakin and Witten 1995a), and (3) death rate

or hazard curves characterized by low initial mor-

tality followed by a sharp rise later in life (Fig. 9A).

Conversely, larger %IQRs are associated with mor-

tality that increases gradually with age (Fig. 9B).

%IQR was calculated (from the age of sexual

maturity onward) for 23 strains of laboratory mice

(inbreds, hybrids, outcross and marker stock from

experiments conducted at Argonne National Labora-

tory; Grahn 1994; Grahn et al. 1995), six different

beagle colonies from six different laboratories (data

derived from the National Radiobiological Archive

maintained by the Department of Energy; Thomson

1989), the control population from an intensively

scrutinized epidemiological study of human females

(radium dial painters; Mullner 1999), and other human

data (by gender and racial group) for the United States

in 1996. The results are presented graphically for fe-

males (Fig. 10A) and males (Fig. 10B) separately.

The data for laboratory animals and the human epi-

demiological study (radium dial painter controls) were

based on individual death times. As such, %IQR is

subject to sampling error depending on the cohort si-

zes and the degree of censoring by extrinsic deaths.

Uncertainty in these estimates is described by 95%

confidence limits derived from the percentile boot-

strap method (Efron and Tibshirani 1993) with 1000

bootstrap replicates. Except for the dial painter con-

trols, the %IQR estimates for humans came from life

tables in 1-year age intervals (NCHS 1999) partitioned

into three broad racial groups: white, black, and

‘other’. No information on the uncertainty of these

values was available, thus no confidence intervals are

provided. However, in order to aid visual comparison

with animal values, a dashed horizontal line was put

on the graphs to delineate the range of values derived

from the NCHS data for humans.

As a whole, the %IQR values seem clustered in the

vicinity of 20–30%. Mortality that is completely

age-independent (i.e., conforms to an exponential

distribution) would have a %IQR equal to 158.5%.

Thus, %IQR values that are one-fifth to one-eighth

smaller than this value suggest that intrinsic mortality

for all three species is strongly age-dependent. %IQR

values appear to reach a minimum around 16–20%.

While this taxonomically diverse group is not nec-

essarily representative of all mammals, this ‘bot-

toming-out’ effect suggests that there may be a limit

on how compressed intrinsic deaths can be around

their median. Further, while some of this presumed

limit to compression can be attributed to the genetic

heterogeneity produced by sexual reproduction, it is

notable that genetically identical mouse strains are

exhibiting a similar compression. To put this com-

pression in context, a %IQR = 20 implies that half of

the intrinsic deaths (beyond sexual maturity) will

occur within –10% of the median age at death.

The three human racial groups in the 1996 data are

all near this 20% lower limit for %IQR. Interestingly,

this apparent lower limit to mortality compression

also applies to the control population of female dial

painters, a cohort whose lives straddled the boundary

between the 19th and 20th century. The remarkable

similarity between these two populations is interest-

ing because the more recent population has benefited

from interventions for intrinsic diseases that were not

available to the women in the dial painter study. One

possible explanation for this unanticipated similarity

is the ‘healthy worker effect’ that often arises in

epidemiological studies where the control group is

Biogerontology (2006) 7: 183–198 193

123

healthier than an otherwise comparable group drawn

from the general population. Although definitive

conclusions cannot be drawn from such a limited

sample of human variation, these results provide an

initial prediction that a typical intrinsic mortality

signature for humans who survive beyond the age of

sexual maturity will be characterized by a %IQR in

the range of 19–23%.

The median %IQR levels for the six beagle

populations of either sex are nearly identical to

those of the human racial groups. Although the

variation among dog populations is slightly greater

than that among human groups, the greater sampling

error in the dog data may account for much of the

observed inter-population variation. The one excep-

tion is the female population from the Colorado

Smaller IQRAge

Su

rvio

rsh

ip:

S(t

)

0.0

0.2

0.4

0.6

0.8

1.0

Mortality(Hazard)

Rate

Median

T25T75

S(t)

Larger IQR

Age

Su

rviv

ors

hip

: S

(t)

0.0

0.2

0.4

0.6

0.8

1.0

Mortality(Hazard)

Rate

Median

T25T75

S(t)

A

B

Fig. 9 Plots demonstrating

the survivorship and

mortality characteristics of

hypothetical populations

having either a smaller A or

larger B IQR (T25 and T75

are the 25th and 75th

percentiles of age)

194 Biogerontology (2006) 7: 183–198

123

State University (CSU) colony which has a %IQR

of around 40%, nearly twice that of the other pop-

ulations and 1.5 times greater than the males from

the same colony. No obvious problems in the data

could be detected. Beagles have served as surrogates

for humans in a variety of experimental studies, and

these results suggest that they would also be a good

model for the prediction of intrinsic mortality

patterns in humans.

There is considerable variation in %IQR among the

23 mouse strains. The median %IQR for female mice

(24%) is very similar to that for beagles and humans,

FEMALES

Strains or Subpopulations

A/H

eA

/JB

ALB

/cC

3Hf

C57

BL

C57

L

BaB Bab C E K N Q S Z

B6C

F1

LAF

1

B6B

C1

B6C

F2

B6C

F3

MW

A PR

uby

AN

LC

SU

Dav

isIT

RI

PN

LU

tah

Dia

l96

W96

B96

O

Rel

ativ

e IQ

R, %

0

20

40

60

80

100

HUMAN

BEAGLE

MOUSE STRAINS

CommercialInbred

Hybrid

Outcross

MarkerStock

Non-CommercialInbred

MALES

Strains or Subpopulations

A/H

eA

/JB

ALB

/cC

3Hf

C57

BL

C57

L

BaB Bab C E K N Q S Z

B6C

F1

LAF

1

B6B

C1

B6C

F2

B6C

F3

MW

A PR

uby

AN

LC

SU

Dav

isIT

RI

PN

LU

tah

96W

96B

96O

Rel

ativ

e IQ

R, %

0

20

40

60

80

100

HUMANBEAGLE

MOUSE STRAINS

CommercialInbred Hybrid

Outcross

MarkerStock

Non-CommercialInbred

A

B

Fig. 10 Relative interquartile range values based on intrinsic

mortality for 23 strains of laboratory mice, 6 colonies of

beagles, 3 racial groups of humans (US 1996) plotted

separately for females A and males B. Note, the female plot

also contains relative IQR results for the control population

used in the epidemiological study of radium dial painters at the

beginning of the 20th century

Biogerontology (2006) 7: 183–198 195

123

but the value for their male counterparts (31%) is

higher. There were 18 strains (13 female, 5 male) out

of the 46 possible strain/sex combinations with %IQR

values within the range observed for humans and

beagles, and only five instances (two female, three

male) where the confidence intervals for mice failed to

fall within this range. The size of the confidence

intervals suggests that most of the apparent variation

observed for the mice could be due to sampling error.

Finally, the significant positive association between

%IQR and the length of its confidence interval

(r = 0.55, P < 0.0001) is expected since larger

%IQR indicates greater variation in death times that,

in turn, translates into greater uncertainty for the sta-

tistic used to measure the variation.

On balance, a strong age-dependence for intrinsic

mortality characterized by a relative IQR near 20%

is shared by humans, beagles and a considerable

number of mouse strains. A few beagle populations

and several mouse strains have higher %IQR levels,

but they still fall within the range of 30–40%. It

would be interesting to know whether these rela-

tively less compressed mortality patterns provide

information about the true variation of intrinsic

mortality profiles or whether they are merely

experimental anomalies. If the former is true, this

could provide insight into the variation expected of

analogous human populations.

Discussion

Mortality partitions have been the focus of this paper.

There are a nearly unlimited number of ways to

partition mortality. We have chosen to partition total

mortality into intrinsic and extrinsic causes of death

using historically accepted concepts with roots that

can be traced to the origins of numerical efforts to

study the age-determined loss of what scientists many

years ago called ‘‘vital force’’ (Olshansky and Carnes

1997). A perfect classification of causes into extrinsic

and intrinsic categories is not attainable. However,

instead of focusing on the imperfection of the parti-

tion, the important issue is whether analyses using an

imperfect partition provide more useful insights into

senescent-determined mortality than analyses based

on total mortality that ignore cause of death (Carey

2003; Carnes 2004). In this context, uncertainties

become a statement of present knowledge and a

source of future improvement rather than a reason for

rejecting all mortality partitions.

In this paper, we discussed the theoretical rationale

and illustrated the quantitative value of partitioning

all-cause mortality into intrinsic and extrinsic com-

ponents. Our goal for this partition was to achieve a

better approximation of the mortality consequences

of causes of death that arise from the progressive

inability of organisms to maintain their biological

integrity. Although our focus was on intrinsic mor-

tality, we are not implying that extrinsic causes of

death are unimportant. In fact, we called attention to

the central role that extrinsic mortality (e.g., preda-

tion, infectious disease) has played in molding the

biology of species, especially aspects that affect rates

of development and life span determination. On a

much shorter time scale, the mortality and morbidity

consequences of extrinsic causes of death are also of

great interest to epidemiologists, actuaries, and

demographers.

Focusing on the intrinsic component of our mor-

tality partition enabled us to demonstrate that death

rates for intrinsic mortality declined by a nearly

uniform 50% across all ages between 1950 and 2000

in a heterogeneous human population. Intrinsic dis-

eases were not cured during this time interval, nor

could the basic biology of the population have

changed over such a brief period of time. Although

successful medical interventions and better lifestyle

choices could account for these desirable changes to

the intrinsic mortality signature, the key question is

whether the changes are permanent or ephemeral.

Medical interventions that delay death by suppressing

symptoms do not necessarily affect the actual rate of

progression of the underlying disease. Similarly, the

avoidance of deleterious behaviors that elevate

intrinsic mortality risks is not the same as lowering

the intrinsic risks that would apply in their absence.

Although interventions like these that do not affect

the underlying causes of intrinsic disease can appear

to alter the mortality signature, it would revert back

to its fundamental form (the one existing under ideal

conditions and without interventions) in their ab-

sence. Conversely, interventions that alter the

underlying pathogenesis of intrinsic disease processes

could transform the fundamental intrinsic mortality

signature into a new form by providing a degree of

control over the previously immutable determinants

of health and longevity.

196 Biogerontology (2006) 7: 183–198

123

Another implication of this perspective is that

intrinsic diseases are manifestations of senescence,

not its cause (Hayflick 2000). In order to modify the

fundamental intrinsic mortality signature of humans,

the internal (i.e. physical and genetic) senescent

processes themselves must be altered. However, as of

now, no one knows how to stop or reverse the process

of senescence, and experts disagree over whether it

can be slowed (Olshansky et al. 2002). Further, even

the interventions proposed by those who think

senescence can be slowed (e.g., caloric restriction

mimetics) are not yet available. Once again, this logic

suggests that the observed intrinsic signature would

revert to its original form in the absence of inter-

ventions. The improbability of this scenario is why

scaling, mortality comparisons and interspecies pre-

dictions of mortality is a subject worthy of scientific

pursuit. If measures of shape for intrinsic mortality

are similar among species, as illustrated in this paper,

then scaled intrinsic signatures for appropriately se-

lected laboratory animals may provide an estimate for

the fundamental intrinsic signature of humans. The

difference between the observed intrinsic signature

for humans and the more unperturbed signature

estimated from the animal data provides an estimate

of the survival time that has been manufactured for

humans as well as a useful unit of mortality for

exploring the life-saving potential of future inter-

ventions.

Our analyses also revealed differences in intrinsic

mortality that exist by gender and between subgroups

within humans as well as differences that remain

between species after adjusting for differences in life

span (Fig. 10). Differences between genders illustrate

the well-known loss of detail (confounding) that can

occur when data are aggregated over what epidemi-

ologists call effect modifiers (Kleinbaum et al. 1982;

Kier and Witten 2005). Reproductive biology drives

evolutionary theories of senescence and gender dif-

ferences in that biology suggests that each sex should

have its own intrinsic mortality signature.

The variation in %IQR for mice (strains of Mus

musculus) and beagles almost certainly reveals

(within a context of sampling error) information on

the genetic plasticity of those species, and the

uncertainties of their intrinsic mortality signatures.

The human data, however, are simply too aggregated

to speculate on the meaning or significance of the

observed variation. Thus, it appears that while an

aggregate intrinsic mortality signature may have

appealing mathematical properties, it is likely to

sacrifice information on uncertainties (variation) that

could be important in predicting mortality across

species.

Ever since Gompertz, scientists have speculated

that common age patterns of death could be observed

and used to inform both the actuarial and biological

sciences about the mortality of senescence. By

merging the theoretical predictions about the timing

of death from evolutionary biology; the empirical

observations of death from demographers and actu-

aries; and the pathobiology of cause of death from the

pathologists, we have attempted to refine our under-

standing of what many scientists have observed for

centuries––namely, that similarities exist among

patterns of intrinsic deaths (largely senescent-deter-

mined) across many forms of life. It is this similarity

that brings predictability (Carnes et al. 1998, 2003b).

We suggest that a biologically motivated partitioning

of mortality into extrinsic and intrinsic causes of

death provides not only a conceptual framework, but

also a biological rationale and methodology for

making quantitative comparisons of mortality

between populations separated by time, location, or

species taxonomy. As such, intrinsic mortality

provides a needed conceptual bridge between biology

and the statistics of mortality.

Acknowledgments We would like to express our apprecia-

tion to Dr. Fletcher Hahn from the Lovelace Respiratory

Research Institute for providing the Institute’s data on dogs and

his advice on pathology issues. We would also like to thank

Dr. Douglas Grahn for his insights on the animal studies.

Funding for Dr. Carnes was provided by the National Aero-

nautics and Space Administration (NAG9-1518) and the

National Institute on Aging (NIA, 7 K02 AG000979-06). Drs.

Olshansky and Witten were funded by the National Institute on

Aging (K02 AG00785-05) and (R01 AG11079 and the Nathan

and Ethel Shock Memorial Aging Foundation) respectively.

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