Frailty in Relation to the Accumulation of Deficits

Abstract

This review article summarizes how frailty can be considered in relation to deficit accumulation. Recalling that frailty is an age-associated, nonspecific vulnerability, we consider symptoms, signs, diseases, and disabilities as deficits, which are combined in a frailty index. An individual's frailty index score reflects the proportion of potential deficits present in that person, and indicates the likelihood that frailty is present. Although based on a simple count, the frailty index shows several interesting properties, including a characteristic rate of accumulation, a submaximal limit, and characteristic changes with age in its distribution. The frailty index, as a state variable, is able to quantitatively summarize vulnerability. Future studies include the application of network analyses and stochastic analytical techniques to the evaluation of the frailty index and the description of other state variables in relation to frailty.

Full text

Frailty in relation to the accumulation of deficits
Kenneth Rockwood
1,2
, Arnold Mitnitski
2
As accepted
The Journal of Gerontology – Medical Sciences
September 1, 2006
1
Division of Geriatric Medicine,
2
Department of Medicine, Dalhousie University,
Halifax, Nova Scotia, Canada
Address for correspondence: Kenneth Rockwood, Centre for Health Care of the Elderly,
1421-5955 Veterans’ Memorial Lane, Halifax, Nova Scotia, Canada, B3H 2E1.
Telephone: 902-473-8687. Fax: 902-473-1050. Kenneth.Rockwood@Dal.ca
Word count:
Total word count: 4309
Text word count: 2175
Running Head: Frailty and deficit accumulation
1

Abstract
This paper summarizes how frailty can be considered in relation to deficit accumulation.
Recalling that frailty is an age-associated, non-specific vulnerability, we consider
symptoms, signs, diseases and disabilities as deficits, which are combined in a frailty
index. An individual’s frailty index score reflects the proportion of potential deficits
present in that person, and indicates the likelihood that frailty is present. Although based
on a simple count, the frailty index shows several interesting properties, including a
characteristic rate of accumulation, a sub-maximal limit and characteristic changes with
age in its distribution. The frailty index, as a state variable, is able to quantitatively
summarize vulnerability. Future studies include the application of network analyses and
stochastic analytical techniques to the evaluation of the frailty index, and the description
of other state variables in relation to frailty.
Key words: frailty, index variables, stochastic process, ageing
2

Frailty is a non-specific state of increasing risk, which reflects multi-system
physiological change. It is highly age-associated. The physiological changes that underlie
frailty do not always achieve disease status, so that some people, usually very elderly, are
frail without having life-threatening illness. These statements about frailty are relatively
non-controversial. More controversial is how to operationalize frailty in clinical practice
and for research (1-6). We and others have done so by considering frailty in relation to
the accumulation of deficits (7-12).
Here, we review how studying deficit accumulation
can help elucidate frailty, its relation to aging, and its mechanisms. We focus on
mathematical and clinical aspects.
Background
The frailty index score is calculated as the proportion of potential deficits that are
present in a given individual, as elaborated below. The frailty index recognizes that
frailty is multi-factorial and dynamic (13, 14). We first tried to define frailty by
combining integrated items – and traditional foci of gerontologists – such as cognition,
mobility, continence and function (14). While this gave good construct (15)
and
predictive validity (14,16)
it left much variance unexplained, and did not consider relative
fitness. We aimed for a measure that could evaluate impairments in many systems,
accommodate change, was graded and was conceptually simple. By combining items in
a single index , we can consider frailty in absolute and relative terms, according to this
probabilistic consideration: the more things individuals have wrong with them, the higher
the likelihood that they will be frail. We now consider each part of that statement.
What should be counted as “things that individuals have wrong with them”? We
consider symptoms, signs, disabilities, diseases and laboratory measurements, which we
term deficits. The frailty index uses a range of deficits that are readily available in survey
or clinical data. [Examples are available: http://myweb.dal.ca/amitnits/STable.htm] A
standard Comprehensive Geriatric Assessment (CGA),(17) for example, records about 40
items, some of which are self-reported (e.g. ‘how would you rate your health’ ) others
ascertained by tests (e.g. Mini-Mental State Examination (18)) and still others by clinical
evaluation (e.g. congestive heart failure) or laboratory measurement (diabetes mellitus).
These can be combined by simply adding them – for example, a ‘1’ for each deficit that is
present, a ‘0’ when they are absent, and a fraction when they are present to a limited
extent (e.g. health as ‘good’=0, ‘fair’=0.5, ‘poor’=1) (19,,20). Obviously, there are many
ways to count, say, 10 deficits from a total of 40, but as illustrated below, the resulting
index score (10/40 = 0.25) has many characteristic features, even if the composition is not
the same between individuals. While it is understandable to be concerned about the
specific nature of the variables that might be included in the frailty index, our experience
suggests that, when some sufficiently large number (roughly, about 40) variables are
considered, the variables can be selected at random, and still yield comparable results of
the risks of adverse outcomes (21).
What we mean by “the higher the likelihood that they will be frail” is a greater
risk of adverse outcomes (e.g. death, institutionalization, health services use, further
deficit accumulation). Still, we note that frailty is neither necessary for death (even very
fit people can die unexpectedly, as in an accident) nor is it sufficient (even at the highest
level of the frailty index, the median survival time is more than one year). Moreover,
3

while death is individual, the mortality rate is a group statistic, so our inquiries are
necessarily probabilistic. Further, we are not concerned about mortality prediction per se
– instead, mortality prediction has served as a means of validating the concept. Were our
focus mortality prediction, we would have given heavy weight to chronological age, or
diseases of known lethality, such as late-life cancer (22). Rather, we view frailty such
that chronological age can be understood as a contextual factor – for example, as
providing an expected value for deficit accumulation. Our model suggests that the effect
of chronological age on adverse outcomes can be negligible when deficits are taken into
account (20, 21, 23, 24).
Still, apparent intuitiveness would be no advantage if it gave unintelligible or
trivial results. But the self-evident statement that people with more things wrong are
more likely to suffer an adverse is quantifiable with the frailty index, and manipulating
the resulting data gives rise to insights (including hints of mechanisms) that are not self-
evident. Before considering these mathematical aspects, we first summarize some
essential features. On average, deficits accrue at a characteristic rate. In elderly people
from four developed countries, the mean rate of deficit accumulation across ages was
close to 0.03 (observed range 0.02-0.04) per year on a log scale (Figure 1) (24).
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
Frailty Index
0.1
0.2
0.3
0.5
1.0
0.05
Age (years)
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
Frailty Index
0.1
0.2
0.3
0.5
1.0
0.05
Age (years)
65 70 75 80 85 90 95
ALSA (pb)
CSHA-comm(pb)
CSHA-clin(pb)
NHANES (pb)
NPHS (pb)
SOPS (pb)
Breast cancer
CSHA-inst
MyocInfarct
US-LTHS
H70-75 (pb)
0.1
0.2
0.3
0.5
1.0
0.05
0.1
0.2
0.3
0.5
1.0
0.05
0.1
0.2
0.3
0.5
1.0
0.05
Figure 1. (From Mitnitski et al., 2005 J Am Geriatr Soc) Relationship between the frailty index and
chronological age for 7 population-based,(pb) community-dwelling samples,(n=33,581) denoted as (pb)
(ALSA (pb) -Australian Longitudinal Study of Aging; CSHA-screen (pb) Canadian Study of Health and
Aging screening sample; CSHA-exam (pb) clinical examination sample; H-70 (pb), Gothenburg study,
Sweden; NPHS – National Population Health Survey (pb) Canada; NHANES (pb) National Health and
Nutrition Examination Survey, United States; SOPS (pb) Sydney Old Persons Study, Australia), and; 2,573
people from 2 institutional (CSHA-inst CSHA wave 1 institutionalized sample; US-LYHS-inst National
Long Term Care Survey, USA) and 2 clinical studies (Breast cancer -cohort of metastatic breast cancer
survivors, Canada; MyocInfarct -Improving Cardiovascular Outcomes of Nova Scotians (ICONS),
Canada). The lines show the regression of mean frailty index with age. For community-dwelling people,
4

the line parameters are: slope=0.029 (95% confidence interval=0.0267, 0.0301) and intercept = -4.012 (-
3.872, -4.142).
Note that the samples differed not just by country, but were collected up to 20
years apart and employed different variables (e.g. self-report, clinically assessed,
laboratory measures). Moreover, the frailty indices used different numbers of variables
(from <30-70). The only restrictions on variables we used were that they reflected
deficits (cf. attributes - e.g. such as eye colour) accumulated across ages, and had < 5%
missing values. While a recent Chinese estimate put the rate of deficit lower (at about
1.4%) (8) this appears to reflect a survivor effect after age 87. By contrast, the frailty
index has otherwise correlated very highly (typically >0.96) with age (12,24,25). In
addition, women accumulate more deficits than men, even though, for any given level of
deficits, men have the higher mortality rates
(8-12, 24). In contrast to community
dwelling people, in the institutional and clinical cohorts, the frailty index was high at all
ages, and thus showed no relationship to age, consistent with high levels of frailty in
those settings (24).
Mathematical explorations in relation to mechanisms
The frailty index approach has a certain similarity with other quantitative
approaches. Vaupel et al., proposed that a largely undefined ‘frailty’ could account for
heterogeneity in health status to explain mortality outcomes (26). The origin of this frailty
was hypothesized to come from genetic differences and this was addressed in a
mathematical model incorporating pleiotropy of several genes (27).
Our approach of quantifying deficit accumulation yields some understanding of
the vulnerability of both individuals and groups. For example the distribution of the
index shows both characteristic changes with age (28) and a limit that does not depend on
age (29). Here, however, we focus on two findings that hint at biological mechanisms:
changes in the heterogeneity of health with age, and transitions between health states.
The average rate of deficit accumulation increases monotonically with age, as does the
standard deviation, underlying the generally accepted contention that, with age, health
status becomes more variable. Importantly, however only absolute heterogeneity in
health status (e.g. as measured by the variance) increases with age. Relative
heterogeneity decreases with age, as illustrated by the coefficient of variation, which is
the ratio of the standard deviation to the mean. We have found that the coefficient of
variation of the frailty index consistently decreases with age (Figure 2) (28, 30).
The decrease with age in the coefficient of variation has theoretical implications.
Ashby’s theory of 'requisite variety' (31,32) suggests that if the number of insults faced
by an organism overwhelms the number of responses that it can mount, the system will
fail. Therefore it is reasonable to expect that, as systems age, they lose variety in their
response repertoires, here captured, at the group level, by the coefficient of variation.
Further, a simple stochastic process of deficit accumulation yields a power-law
relationship between the mean frailty index m and its coefficient of variation, v ~ m
-1/2
(30). The same exponent ½ has also been found in the relationship between the average
flux in complex networks, and its fluctuations as measured by its standard deviation (33).
Consistent with the exponent representing influences external to the network, we interpret
this to mean that large environmental effects - for example cohort effects - become less
important closer to the end of life, where more proximate effects dominate. In
5

6
consequence, at extreme old age, people become more susceptible to smaller
perturbations. That the coefficient of variation itself can be summarized in network
analyses is of considerable interest, and is motivating further inquiries by our group.
Figure 2. (From Rockwood et al., 2004 Mech Ageing Dev) Changes with age in the frailty index. Panel A.
Change in the shape of the distribution, both sexes. Panel B. Change in the coefficient of variation
separately in men (triangles) and women (circles).
Aging involves many interacting processes, in which stochastic components play a key
role – even in genetically identical twins raised in a constant environment (34). With
aging, damage accumulates in cells and tissues, whether by random (35) or genetic (36)
mechanisms, involving sub-cellular and organ-specific pathways (37). Each results in
declines in functional capacity (38-39) and redundancy exhaustion (40). Our modeling
(23) reveals stochastic mechanisms and opens the prospect of using powerful analytical
techniques derived from the theory of stochastic processes (41). A modified Poisson
model with two nontrivial parameters gives a unified description of transitions to worse
health states, health improvements and mortality. The probability of transitions between n
(at baseline) and k deficits can be expressed as following:
),1)(exp(
!
ndn
k
n
nk
P
k
P −−=
ρ
ρ
where P
nd
is the probability to die during time between two consecutive assessment,
ρ
n
=
ρ
0
+b
1
n and P
nd
= P
0d
exp(b
2
n),
ρ
0
and P
0d
are the baseline characteristics. The two
parameters b
1
and b
2
describe respectively, given the current number of deficits, the
increments of their expected change, and in the risk of death (23). The very high model
fit (R=0.99) (Figure 3) with so few parameters has encouraged additional inquiries. The
simple stochastic multistage model shows not only deficits accumulation but also its flip
side. It shows that improvement is also possible and not so rare (roughly third of the
sample showed some degree of improvement in 5 years). Still the likelihood of death
increases exponentially with the number of deficits and therefore, in the long run, the
negatives outweigh the positives.
20 30 40 50 60 70 80 90
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
80-85
71-75
61-65
-60
46-50
56
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
71-75
61-65
-60
46-50
A
B
56
70
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Frailty Index
tionDensity Distribu
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
71-75
61-65
-60
46-50
56
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
-
-
-
-
Age (years)
Coefficient of variation
A
B
20 30 40 50 60 70 80 90
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
80-85
71-75
61-65
-60
46-50
56
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
71-75
61-65
-60
46-50
A
B
56
70
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Frailty Index
tionDensity Distribu
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
71-75
61-65
-60
46-50
56
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
76-80
-
-
-
-
-
Age (years)
Coefficient of variation
A
B

Number of deficits, k
The transition probabilities
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10 15
0.2
0.4
0.6
0.8
n=0 n=1 n=2 n=3
n=4 n=5 n=6 n=7
n=8 n=9 n=10 mortality
Number of deficits, k
The transition probabilities
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10
0
0.1
0.2
0.3
0 5 10 15
0.2
0.4
0.6
0.8
n=0 n=1 n=2 n=3
n=4 n=5 n=6 n=7
n=8 n=9 n=10 mortality
Figure 3. (From Mitnitski et al., 2006, Mach Ageing Dev) The probability of transition from n to k deficits,
and to death (right lower corner) in relation to the starting n deficits. Circles represent observational data of
transitions from CSHA-1 to CSHA-2 (filled circles), and from CSHA-2 to CSHA-3 (empty circles).
Estimates are presented for the model that combines transitions from CSHA-1 to CSHA-2, and from
CSHA-2 to CSHA-3.
Clinical utility of frailty index measures
Few clinicians would doubt that the more things that people have wrong with
them, the frailer they will be, but few too would embrace a 70-item scale. For now, we
have itemized the elements of a standard CGA to produce an ‘FI-CGA’ (20,21). The FI-
CGA has the usual properties of other versions – i.e. it is highly correlated with age,
shows a gamma distribution, is higher in women, and correlates with several adverse
outcomes, including institutionalization and health care use (Figure 4). If further coross-
validated, an FI-CGA could aid clinical decision-making by indicating the degree of
frailty, and thus the likelihood of an adverse outcome.
The FI-CGA, like other versions of the frailty index (including the widely used 5-
item phenotype definition (42)) largely weights items equally. It might seem obvious to
apply differential weights to the variables, so that cancer, for example, would be
weighted more heavily than skin disease. While in individual samples the performance
of the index (e.g. in predicting death) can be improved by weighting (43), in general,
weighting limits generalizability. For now, generalizability appears to have the greatest
value, and therefore we have pursued studies without weighting. Still, studies that might
aid clinical decision-making (for example, by demonstrating how closely an individual
7

has approached the theoretical limit of frailty) will require scrupulous attention to
whether the price paid in precision is too high for the rewards in generalizability.
Alternately, other groups might cross-validate an un-weighted frailty index, but use
weighting for local use. Whether there are demonstrable levels or severity classes also
need careful investigation (16,44).
0 10 20 30 40 50 60 70
-
0 10 20 30 40 50 60 70
Probability of institutionalization
CFS=1-3
CFS=4
CFS=5
CFS=6-7
0 10 20 30 40 50 60 70
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-
0 10 20 30 40 50 60 70
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of survival
CFS=1-3
CFS=4
CFS=5
CFS=6-7
Time (month)
AB
0 10 20 30 40 50 60 70
-
0 10 20 30 40 50 60 70
Probability of institutionalization
CFS=1-3
CFS=4
CFS=5
CFS=6-7
0 10 20 30 40 50 60 70
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-
0 10 20 30 40 50 60 70
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of survival
CFS=1-3
CFS=4
CFS=5
CFS=6-7
Time (month)
AB
Figure 4. (From Rockwood et al., 2005, CMAJ) Panel A. Kaplan-Meier medium-term survival curves
(adjusted for age and sex) for subjects with different values of the CSHA Clinical Frailty Scale (CFS). The
number of people at the start of each group: n=952 for CFS=1-3; n=349 for CFS=4; n=305 for CFS=5;
n=691 for CFS=6-7. Panel B. Kaplan-Meier medium-term institutionalization curves for subjects (adjusted
for age and sex) with different values of the Clinical Global Frailty Scale. The number of people at the start
of each group: n=828 for CFS=1-3; n=256 for CFS=4; n=136 for CFS=5; n=66 for CFS=6-7.
Future directions
In addition to studies that further explore the frailty index’s mathematical
properties, evaluate the limit to frailty, locally cross-validate weighted and un-weighted
clinical versions, and investigate grades, we see other uses of the frailty index approach.
We are keen that insights on frailty can translate into pragmatic techniques for
geriatricians (45). Clearly, the frailty index does not define a syndrome, which is a
collection of specific symptoms and signs. Instead, the frailty index can be considered as
a state variable, in that it characterize the whole health of individuals and validly
classifies risk across a wide range of people (7,46). This does not contradict the idea of a
syndrome; indeed it should be the case that people classified as frail syndromically will
have higher frailty index values than those who do not.
If the frailty index can be considered as state variable, perhaps there are others. In
our view, attention and concentration, function and mobility and balance each seem to be
logical candidates, as they are evolutionarily high order, and integrate many pathways.
Mobility and balance especially seems to have merit in the acute care setting, where they
fluctuate with changes in an individual’s overall state of health, can readily be tracked,
have plain language descriptors, and are susceptible to quantification (47). Perhaps the
8

most ambitious application of the frailty index is as a means of summarizing the
commonly invoked concept – but less commonly quantified – notion of “biological age”
(7,8,12,48-50,). Such studies might best be situated within the idea of biomarkers, and
could thereby benefit from the considerable experience of those inquiries (51-53). For
now, the evaluation of deficit accumulation index points out how we can embrace the
complexity of frailty.
9

Conflict of interest
We declare no conflict of interest.
Acknowledgments
Kenneth Rockwood receives career support from the Canadian Institutes of Health
Research (CIHR) through an Investigator Award, and from the Dalhousie Medical
Research Foundation as the Kathryn Allen Weldon Professor of Alzheimer Research.
Some of the analyses included in this review were conducted with CIHR support through
grants MOP-62823 (PI:KR) and MOP-64169 (PI:AM). The authors assert no proprietary
interest in this work.
10

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