American Journal of Epidemiology
Copyright O 1996 by The Johns Hopkins University School of Hygiene and Public Health
All rights reserved
Vol. 143, No. 8
Printed In USA.
Analysis of Change in Self-reported Physical Function among Older Persons
in Four Population Studies
Laurel A. Beckett,1 Dwight B. Brock,2 Jon H. Lemke,3 Carlos F. Mendes de Leon,4 Jack M. Guralnik,2
Gerda G. Fillenbaum,5 Laurence G. Branch,6 Terrie T. Wetle,7 and Denis A. Evans1
Change in self-reported physical function was examined using baseline and 5 years of follow-up data
between 1982 and 1991 from the four Established Populations for Epidemiologic Studies of the Elderly studies.
In East Boston, Massachusetts {n = 3,809), Iowa and Washington Counties, Iowa (n = 3,673), New Haven,
Connecticut (n = 2,812), and North Carolina (n = 4,163), noninstitutionalized persons aged 65 years and older
were asked a series of questions to assess their physical function: a modified Katz Activities of Daily Living
(ADL) scale, three items from the Rosow-Breslau Functional Health Scale, and questions on physical performance, adapted from Nagi, as well as information on demographic, social, and health characteristics.
Longitudinal statistical analyses (random effects and Markov transition models) were used to evaluate
improvement, stability, and deterioration in functional ability at both an individual and a population level over
multiple years of data. The average decline in physical function associated with age was found to be greater
than previous cross-sectional studies have suggested, and the rate of decline increased with increasing age.
Considerable individual variation was evident. Although many people experienced declines, a smaller but
substantial portion experienced recovery. Women reported a greater rate of decline in physical function and
were less likely to recover from disability. Am J Epidemiol 1996; 143:766-78.
activities of daily living; aging; longitudinal studies; population surveillance
Difficulty with physical function represented by inability to perform the usual activities of everyday life
is a serious problem among older persons. The magnitude of this problem is likely to become substantially
greater with continuing increases in longevity and in
the size of the oldest population age groups in the
United States and other developed countries. Several
previous community-based studies have provided
cross-sectional analyses of self-reported measures of
physical function (1-6). All indicate a strong association between age and disability, and some suggest
that women report more disability than do men. These
existing cross-sectional data have substantial limitations, however. Inferences from cross-sectional data
about the relation between age and disability may be
distorted by selective removal of disabled persons
from the population by death or institutionalization
and by possible birth cohort differences in occurrence
of disability. The extent to which reported differences
in disability between men and women are due to real
differences in disability as contrasted with sex-related
differences in reporting is not known.
Some previous studies of physical function have
examined older persons at more than one point in time.
Several have examined physical function at a single
point and have used it to predict other endpoints or
have related it to previously measured predictors (710). Others have measured physical function at two
time points from 2 to 25 years apart and have estimated transition probabilities or average change (1120). Analyses at two time points permit simple descriptions of change but do not allow modeling of the
individual variations in histories over time (21). For
that, at least three measurement points are needed.
Analyses of change in function over time based on
multiple, repeated observations can provide more informative answers about physical function in older
persons; however, there have been few large longitudinal studies in defined populations. In one such study,
Received for publication May 12,1994, and in final form January
31, 1996.
Abbreviation: ADL, activities of daily living.
1
Rush Institute on Aging, Rush University and Rush Presbyterian
St. Luke's Medical Center, Chicago, IL
2
Epidemiology, Demography and Biometry Program, National
Institute on Aging, Bethesda, MD.
3
Department of Preventive Medicine and Environmental Health,
University of Iowa, Iowa City, IA.
4
Department of Epidemiology and Public Health, Yale University
School of Medicine, New Haven, CT.
3
Center for the Study of Aging and Human Development, Duke
University Medical Center, Durham, NC.
9
Abt Associates, Cambridge, MA, and Boston University School
of Medicine, Boston, MA.
7
Braceland Center for Mental Health and Aging, Institute of
Living and Department of Community Medicine and Health Care,
University of Connecticut School of Medicine, Hartford, CT.
Reprint requests to Laurel A. Beckett, Rush Institute on Aging,
1645 W. Jackson Blvd., Chicago, IL 60612.
766
Physical Function in Older Persons
growth curve analyses were used to describe individual trajectories and their correlates using 6 years of
observations over a decade for participants initially
aged 58 to 63. The average trajectories were found to
be nonlinear and to differ by race, sex, income, and
educational level (22, 23). In this report, we examine
the relation of age and sex to individual change in
function over a 5-year period, using annual selfreported measures of physical function from four large
coordinated community studies of persons age 65 and
older. Both the average trajectory of functional level
and the patterns of becoming disabled and recovering
from disability are described.
METHODS
Study population
The data for this report were gathered between 1982
and 1991 from the National Institute on Aging Established Populations for Epidemiologic Studies of the
Elderly. These studies are described briefly here and in
detail elsewhere (3). The following four communities
were studied: East Boston, Massachusetts; two counties in Iowa; New Haven, Connecticut; and five counties in North Carolina. In East Boston and the two
counties in Iowa, the entire populations of community
residents aged 65 years and older were invited to
participate; in New Haven and the five North Carolina
counties, complex sampling designs were used to
identify representative samples of community residents 65 and older. Information on health status was
collected at annual interviews; the interviews were in
the home at baseline and follow-up year 3 and by
telephone in the other years. We analyzed information
from the first six interviews (first five for North Carolina) and ascertained vital status for respondents at
each follow-up. The participation rate at baseline in
the evaluation of physical function ranged from 80 to
85 percent (table 1).
Data were obtained from proxies only when it
would otherwise have been missing. Proxies provided
information only on matters that could be observed.
Their reports appeared to be reliable: the study participant's functional status as reported by a proxy was
consistent with the reason given for requiring a proxy.
The prevalence of disability for proxy and nonproxy
responses is shown in table 2. Subjects who were "too
ill" tended to have proxy reports of disability, whereas
subjects who were "too busy" tended to have proxy
reports without any disability (24). Responses from
proxies were therefore included in the analysis to
minimize missing data and to reduce bias. The proportion of proxy respondents varied somewhat by site
(greatest in Iowa) but in general was small. The greatest for any site in any year was 8.7 percent.
Am J Epidemiol
Vol. 143, No. 8, 1996
767
TABLE 1. Sample size and participation by center and year
of data collection for study of change In physical function in
four communities based on 1982-1991 data, Established
Populations for Epidemiologic Studies of the Elderly
Center
Data
collection
Baseline
Targeted population
Respondents (%)
Follow-up year 1
No. of survivors
Respondents (%)
Follow-up year 2
No. of survivors
Respondents (%)
Follow-up year 3
No. of survivors
Respondents (%)
Follow-up year 4
No. of survivors
Respondents (%)
Follow-up year 5
No. of survivors
Respondents (%)
1
Iowa
East
Boston,
MA
New
Haven,
CT
North
Carolina
4,601
79.7
4,485
84.8
3,337
83.4
5,223
79.7
3,540
98.5
3,583
95.0
3,809
96.2
3,972
98.4
3,394
98.1
3,434
95.0
3,583
96.5
3,768
98.3
3,232
96.6
3,244
92.1
3,434
93.3
3,517
94.9
3,089
96.7
3,072
86.7
2,160
97.3
3,288
98.1
2,908
96.0
2,864
2,001
96.1
NA*
NA
88.3
NA, not available.
TABLE 2. Percentage of persons with any disability at
baseline by proxy status and center based on 1982-1991
data, Established Populations for Epidemiologic Studies of
the Elderly
Physical function
scale
proxy status
Katz
Self
Proxy
Rosow-Breslau
Self
Proxy
Nagrt
Self
Subjects (%)
Iowa
East
Boston,
MA
New
Haven,
CT»
North
Carolina*
4.8
1.9
11.5
60.8
14.7
59.2
11.3
11.3
32.4
4.2
40.0
80.2
47.6
83.1
44.2
87.2
23.6
38.7
35.9
NAt
* Adjusted for complex sampling design.
t Proxy responses were not reported for the Nagl items.
t NA, not available.
Measures of physical function
Three years of questions were used to assess selfreported physical function at each annual interview.
The modified Katz Activities of Daily Living (ADL)
scale (25) addressed the self-reported ability to perform without help six basic activities (bathing, dressing, walking across a room, transferring from a bed to
a chair, eating, and toileting). The questions from the
modified Rosow-Breslau Functional Health Scale (26)
assessed three gross mobility items (walking half a
mile, climbing stairs, and doing heavy work around
768
Beckett et al.
the house). The Nagi items (1) concerned level of
difficulty performing four physical activities (bending,
stooping or crouching, pushing or pulling an object
like a chair, and reaching above the shoulders). A
person who reported being able to do an activity with
little or no difficulty was considered to have no disability for that item. No proxy reports were obtained
for the Nagi items. At the North Carolina site, information was obtained from all sample members for
only three of the Nagi items, so the Nagi scale was not
analyzed for that site.
These three measures were chosen to assess ability
to perform a wide range of common activities of older
persons. In general, the Katz ADL scale concerns the
most basic personal self-maintenance tasks whereas
the Rosow-Breslau and Nagi items require greater
physical activity. All have been extensively used in
previous investigations, including studies of large populations. Short-term variability (reliability) of the three
measures has been directly assessed in one of the
populations of the Established Populations for Epidemiologic Studies of the Elderly (27), and the measures
appear sufficiently stable for use in longitudinal analyses such as ours. Inability to perform these activities
falls within the concept of disability outlined in the
World Health Organization International Classification of Impairments, Disabilities and Handicaps (28),
the terminology of which is used here.
For each set of questions, a score corresponding to
the number of items without disability was calculated.
Thus, higher scores (a maximum of 6 for the Katz, 3
for the Rosow-Breslau, and 4 for the Nagi) indicated
better physical function, and a score of 0 indicated
disability on all items in a particular scale. In addition,
for some analyses each scale was dichotomized according to whether there was disabihty in one or more
items (score = 1) or no disability (score = 0). If there
was a missing response on any item, that set of questions was treated as missing.
Statistical methods
The study design, with up to six annual measurements on participants, enabled us to characterize the
changes in physical function over time in much more
detail than in previous research. Although crosssectional analysis and longitudinal studies suggest that
physical function tends to decline with increasing age,
it was also evident that the rate of decline might be
quite variable across individuals and that some would
improve over time. In this report, we used two different statistical methods to characterize individual differences in rate of change in functioning over time.
The first characterization emphasized the average
change over time, typically a gradual decline. This was
accomplished by using a random effects model, which
focused on the individual time paths for each scale of
functioning and estimated the average effect of the
covariates (sex, age) on those paths. The second characterization addressed the possibility that the average
pattern of change over time reflected transitions into
and out of disability. Markov models were used to
analyze such transitions between disabled and nondisabled states at successive interviews and the effects of
age and sex on the likelihood of transition. These two
approaches were complementary rather than conflicting.
The random effects models (29) that were used
represented the observed score Y^ for individual i at
study year tj by a linear model of the form as follows:
cto + ax age, + a2 age? + a 3 male, + a 4 died,
+ Oo + fr age, + & male, + /33 died,)/,
+ A, + B,tj + e,j.
The first line on the right side of the equation specifies
that the mean baseline score is a linear function of an
indicator for male sex and an indicator for whether the
person died before the end of the study as well as a
quadratic function of age (in years exceeding 65). The
coefficients a provide tests of the differences at baseline between people of different ages, between males
and females, and between survivors and those who
died during the study. The second line specifies the
mean change per year during the study as a linear
function of male sex, whether the person died, and age
in years exceeding 65. The /3 coefficients provide tests
of whether rates of decline in function differ between
males and females, younger and older subjects, and
those who survive compared with those who die. Note
that allowing change per year to be a linear function of
the continuous variable age leads, by differential equations, to a quadratic function for score at a given year
of age; thus, the first two parts of the model are
consistent. The third line of the equation specifies
random components to account for deviations from the
mean scores predicted by the model. Individuals might
have person-specific, normally distributed random deviations At and 5, from the baseline score and change
per year predicted by the model. Thus, the expected
physical function for an individual might start higher
or lower than the overall average and decline faster or
slower. Finally, the values observed at each successive
interview were assumed to deviate from each person's
own true time path by errors ei}, which were independent and normally distributed with a common variance.
Am J Epidemiol
Vol. 143, No. 8, 1996
Physical Function in Older Persons
The parameters a, /3, and the variances of the Ait B,,
and e(j and their standard errors were estimated using
the BMDP 5V program (30). We included persons for
whom any year(s) of follow-up interviews were missing. Model validation included fitting alternative models (interactions, other covariance structures besides
random effects), use of Akaike's criterion to test
whether more elaborate models provided a better fit to
the data, and comparison of variance estimates with
independent estimates of short-term variability for
these scales.
We used the second class of models to analyze the
transitions between states of disability (inability to
perform one or more items in the scale) and no disability in successive years. The Markov model (31)
assumed that the probability of transition from no
disability to disability by the next interview was a
logistic regression function of the covariates; in other
words, a one-unit increase in the covariate would lead
to a constant change in the log odds (natural logarithm
of odds) of a transition. A separate logistic model was
used for transitions from disability to a nondisability
state. Each logistic regression model was quadratic in
age with an indicator for male sex. Maximum likelihood parameter estimates were obtained using a Fortran program implementing the Muenz-Rubinstein algorithm and verified against SAS Proc Catmod for
cases with no missing data (32). This algorithm permitted inclusion of persons with some missing interviews in the analyses. Model validation included fitting alternative models with interactions and residual
analysis (33).
To permit maximum likelihood estimation with the
EM-algorithm for both the random effects and Markov
models, we assumed that the missing data mechanisms
were ignorable and "missing at random." Thus, we
assumed that any missing value was a function only of
observed values, including the covariates and values at
other interviews, and did not contain any additional
information. Because complex sample designs were
used at two of the sites (New Haven and North Carolina), all estimates of proportions and percentages
from these sites were adjusted for the sample design
using SUDAAN (34). In both the random effects models and Markov models, indicator variables for stratum
were included that reflected the sampling design. For
the New Haven data, the indicator variables noted
whether the housing stratum was age and income
restricted (public housing) or age restricted (private
housing), with community housing as the referent. For
the North Carolina data, an indicator was added for
African-American race, with all other races as a combined referent. In addition, logistic regression models
adjusted for sample design were fitted to the 1-year
Am J Epidemiol
Vol. 143, No. 8, 1996
769
transitions to assess the effect of the sample design on
parameter estimates and statistical inferences.
RESULTS
Self-reported disability at baseline
In cross-sectional baseline data, the prevalence of
self-reported disability in any activity was highest for
the Rosow-Breslau scale and lowest for the Katz scale
(table 3). The proportion of subjects reporting disability at baseline increased with age for each of the three
scales and at each of the four sites. The proportion
disabled was generally higher among women than
among men within each 5-year age group. These differences were smallest at the Iowa site and in the
youngest age groups. These results were consistent
with earlier reports from cross-sectional studies of
substantial increases in disability with age and of
greater prevalence of disability in women. The proportions reporting disability were consistently smaller
in the Iowa subjects than at other sites, especially in
the younger age groups.
The cross-sectional decrease in self-reported physical function with age may reflect declines with age,
birth cohort effects, or some combination of these. The
availability of up to 5 years of follow-up data with
minimal loss to follow-up in these studies permitted
simultaneous comparison of the cross-sectional
changes with longitudinal changes in the same cohorts. The longitudinal data also allowed estimation of
the degree to which the higher rates of disability
reported by women at a fixed time point resulted from
a more rapid decrease in functioning. The possibility
of a more rapid decline in the years immediately
preceding death was also explored. Finally, the degree
to which the decrease in self-reported function resulted
from transitions into and out of disability rather than a
steady decline was assessed.
Mean change in number of disabilities per year of
age
The random effects models (displayed equation)
provided estimates of the mean change in number of
disabilities per year after baseline (tables 4-6). Women
65 years old at baseline who survived the entire study
period were used as the comparison group; the effects
of each additional year older at baseline, male sex, and
death before the end of the study period were estimated separately. The a coefficients in the tables
summarize the predicted baseline scores, and the /3
coefficients summarize the predicted change per year
of study. The coefficient for the mean change per year
for women 65 years old at baseline who survived the
770
Beckett et al.
TABLE 3. Baseline disability In self-reported physical function based on 1982-1991 data, Established Populations for
Epidemlologic Studies of the Elderly
Persons with disability (%)
Age
Katz scale
QTOiip
(years)
65-69
Men
Women
70-74
Men
Women
75-79
Men
Women
80-84
Men
Women
85-89
Men
Women
Iowa
East
Boston,
MA
Rosow-Breslau scale
New
Haven,
CT«
North
Carolina*
Nag! scale
Iowa
East
Boston,
MA
New
Haven,
CT«
North
Carolina'
Iowa
East
Boston,
MA
New
Haven,
CT»
2
2
9
8
6
10
8
7
24
19
29
37
23
32
30
37
12
19
17
33
23
40
5
3
10
12
10
7
10
10
29
29
33
49
30
36
33
45
16
27
22
38
31
41
7
7
16
19
14
15
14
15
42
43
48
63
41
51
39
56
22
34
22
52
27
53
10
13
14
37
17
19
21
23
48
66
58
75
41
63
58
73
31
44
33
60
30
49
13
14
33
50
22
35
24
40
71
78
75
92
51
77
61
82
30
56
45
75
32
65
40
46
47
37
37
54
57
79
87
89
94
75
87
79
96
19
42
67
44
75
50
70
6
7
13
18
11
14
12
14
36
41
41
54
33
46
40
50
19
32
23
44
28
46
£90
Men
Women
Total
Men
Women
1
Adjusted for complex sample design.
TABLE 4. Longitudinal change in Katz scale: results of random effects models based on 1982-1991
data, Established Populations for Epidemlologic Studies of the Elderly
Center
Parameter
Iowa
East
Boston,
MA
New
Haven,
CT*
North
Carollnaf
Estimated mean baseline score (a coefficients)
Women survivors, age 65 years (a,,)
Effect on baseline score
Age past 65 years (a,)
Age past 65 years (a,)
Male sex (a,)
Nonsurvtvor (aj
5.85*
0.017*
-0.00144*
0.036
-0.184*
5.71*
5.71*
5.87*
0.021*
-0.0022*
0.154*
-0.436*
0.023*
-0.0016*
0.055
-0.212*
0.001
-0.0004*
0.082*
-0.131*
Estimated mean change per year (p coefficients)
Women survivors, age 65 years (p,,)
Effect on change per year
Age past 65 years (p,)
Male sex (P2)
Nonsurvivor (B,)
-0.072*
-0.055*
-0.088*
-0.319*
-0.0137*
0.0054
-0.259*
-0.0102*
0.0275*
-0.164*
-0.0134*
0.0559*
-0.239*
-0.0147*
0.0275
-0.590*
* Adjusted for housing stratum.
t Adjusted for African-American stratum.
* Significant at a = 0.05.
entire study period (/30) indicated that they experienced a significant decline in functional status for all
three scales and for all four sites. The rate of decline
increased significantly with increasing age at baseline
(/3j, consistent with the significant quadratic crosssectional effect, ct^). Because the rate of decline
changed with age, the overall decline in physical function with increasing age could not be summarized by
Am J Epidemiol
Vol. 143, No. 8, 1996
Physical Function in Older Persons
771
TABLE 5. Longitudinal change In Rosow-Breslau scale: results of random effects models based on
1982-1991 data, Established Populations for Epidemlologic Studies of the Elderly
Center
Parameter
East
Boston,
MA
Iowa
New
Haven,
CT*
North
Caroflnat
Estimated mean baseline score (a coefficients)^
Women survivors, age 65 years (a,,)
Effect on baseline score
Age past 65 years (a,)
Age past 65 years (oj)
Male sex [a^)
Nonsurvtvor (ct4)
2.64*
-0.013*
-0.00113*
0.183*
-0.528*
2.47*
2.26*
2.08*
-0.0309*
-0.0006*
0.376*
-0.554*
0.0010
-0.0010*
0.275*
-0.477*
-0.016*
-0.0006*
0.355*
-0.749*
Estimated mean, change per year (J3 coefficients)
Women survivors, age 65 years (Pg)
Effect on change per year
Age past 65 years (p,)
Male sex (P2)
Nonsurvivor (Pj)
-0.065*
-0.068*
-0.066*
-0.118*
-0.0048*
0.0299*
-0.0997*
-0.0036*
0.0008
-0.0595*
-0.0085*
0.0211*
-0.0966*
-0.003*
0.0027
-0.110*
* Adjusted for housing stratum.
t Adjusted for African-American stratum.
* Significant at a = 0.05.
TABLE 6. Longitudinal change in Nagi scale: results of random effects models* based on 1982-1991
data, Established Populations for Epldemiologlc Studies of the Elderly
Center
East
Boston,
MA
Parameter
Iowa
New
Haven,
CT*
Estimated mean baseline score (a coefficients)^
Women survivors, age 65 years (a,,)
Effect on baseline score
Age past 65 years (a,)
Age past 65 years (otj)
Male sex (oj)
Nonsurvivor (c^)
3.71*
-0.009
-0.00038*
0.204*
-0.297*
3.54*
3.21*
-0.0095
-0.0009*
0.424*
-0.368*
0.0191*
-0.0012*
0.372*
-0.337*
Estimated mean change per year (fS coefficients)
Women survivors, age 65 years (p0)
Effect on change per year
Age past 65 years (p,)
Male sex (p2)
Nonsurvivor (pj)
-0.065*
-0.058*
-0.055*
-0.0049*
0.0233*
-0.1112*
-0.0035*
0.0097
-0.0728*
-0.0085*
0.0234*
-0.0915*
* Nagi results were not included for North Carolina site because only three Nagi items were asked of all sample
members.
t Adjusted for housing stratum.
* Significant at a = 0.05.
a single number. The estimated effect of age on
change in function is illustrated in figure 1 for the
Rosow-Breslau scale in the Iowa subjects who survived the entire study period.
The random effects models, by providing both
cross-sectional and longitudinal estimates of change
per year, permitted a comparison of the effects of age
obtained from these two approaches. The cross-secAm J Epidemiol
Vol. 143, No. 8, 1996
tional decrease in physical function with age not only
was confirmed but also was seen to underestimate the
decline with age, as can be seen in figure 1. The
average rate of decline seen during follow-up was in
fact greater than would be predicted from cross-sectional models. This may be due in part to selective
exclusion from the baseline population, but not from
follow-up, of individuals in institutions.
772
Beckett et al.
TABLE 7. Annual change in KaU physical function scale: results of Markov model for transitions
based on 1982-1991 data, Established Populations for Epidemlologlc Studies of the Elderly
Center
Parameter
Iowa
East
Boston,
MA
New
Haven,
CT«
North
CaroUnat
Estimated log odds (natural logarithm of odds) of becoming disabled
Women survtvors, age 65 years
-9.74*
-8.32*
-7.89*
-7.40*
Effect on log odds (natural logarithm of odds) of becoming disabled
Age past 65 years
Male sex
Nonsurvivor
0.093*
-0.20*
1.12*
0.077*
-0.34*
1.21*
0.071*
-0.26*
1.04*
0.064*
-0.25*
1.17*
Estimated log odds (natural logarithm of odds) of remaining disabled
Women survivors, age 65 yeare
4.08*
2.76*
1.29*
2.21*
Effect on log odds (natural logarithm of odds) of remaining disabled
Age past 65 years
Male sex
Nonsurvivor
-0.061*
-0.032
-1.12*
-0.046*
0.254*
-1.21*
-0.030*
0.261*
-1.04*
-0.041*
0.067
-1.17*
• Adjusted for housing stratum.
t Adjusted for African-American stratum.
* Significant at a = 0.05.
TABLE 8. Annual change In Rosow-Sreslau physical function scale: results of Markov model for
transitions based on 1982-1990 data, Established Populations for Epldemlologlc Studies of the Elderly
Center
Parameter
Iowa
East
Boston,
MA
New
Haven,
CT*
North
Carolinat
Estimated log odds (natural logarithm of odds) of becoming disabled
Women survivors, age 65 years
-8.33*
-7.29*
-6.60*
-4.45
Effect on tog odds (natural logarithm of odds) of becoming disabled
Age past 65 years
Male sax
Nonsurvivor
0.091*
-0.51*
0.85*
0.084*
-0.26*
0.81*
0.074*
-0.37*
0.72*
0.040*
-0.45*
1.09*
Estimated log odds (natural logarithm of odds) of becoming disabled
Women survivors, age 65 years
3.15*
2.33*
2.86*
1.63*
Effect on log odds (natural logarithm of odds) of remaining disabled
Age past 65 years
Male sex
Nonsurvivor
-0.057*
0.53*
-0.93*
-0.053*
0.60*
-0.78*
-0.054*
0.43*
-0.77*
-0.044*
0.39*
-0.84*
• Adjusted for housing stratum.
t Adjusted for African-American stratum.
* Significant at a = 0.05.
Differences in mean rate of change between men
and women
For all sites and all scales, the average rate of
decline was estimated to be less for men than for
women of similar ages (/Jj), although this difference
was not statistically significant in all cases (tables
4-6). This increased rate of decline was in addition to
me
lower mean baseline function for women. This
difference can be seen in figure 1, for men and women
aged 65, 70, 75, 80, and 85 years at baseline who
Am J Epidemiol
Vol. 143, No. 8, 1996
Physical Function in Older Persons
773
TABLE 9. Annual change In Nagi physical function scale: results of Markov model for transitions*
basad on 1982-1991 data, Established Populations for Epidemioiogic Studies of the Elderly
Center
Parameter
East
Boston,
MA
Iowa
New
Haven
CTt
Estimated log odds (natural logarithm of odds) of becoming disabled
Women survivors, age 65 years
-5.79*
-5.23*
-4.20*
Effect on log odds (natural logarithm of odds) of becoming disabled
Age past 65 years
Male sex
Nonsurvlvor
0.058*
-0.49*
0.58*
0.055*
-0.71*
0.70*
0.043*
-0.56*
0.67*
Estimated log odds (natural logarithm of odds) of becoming disabled
Women survivors, age 65 years
1.31*
1.40*
1.43*
Effect on log odds (natural logarithm of odds) of remaining disabled
Age past 65 years
Male sex
Nonsurvtvor
-0.025*
0.60*
-0.83*
-0.033*
0.65*
-0.74*
-0.037*
0.50*
-0.37*
* Nagi results were not included tor the North Carolina site because only three NagI Items were asked of all
sample members.
t Adjusted for housing stratum.
* Significant at a = 0.05.
eo
u
«
2-
1
&
•o
I
1-
65
70
75
80
85
90
95
Age of participant (years)
FIGURE 1. Predicted Rosow-Breslau scores and longitudinal changes by age and sex: Iowa Established Populations for Epidemioiogic
Studies of the Elderty. Mean scores predicted at baseline for subjects according to their Initial age:
, men;
, women.
, average decline predicted by the model for men or women of that age, followed for 5 years.
survived the entire follow-up period. (A corresponding
figure for those who died would show lower function
Am J Epidemiol
Vol. 143, No. 8, 1996
at baseline and greater rates of decline, but a similar
pattern of differences between males and females,
774
Beckett et aJ.
over the period before death.) Thus, the cross-sectional
report of greater disability in women was supported by
greater estimated decline per year over the follow-up
period, even after adjusting for age and survivorship
status. A detailed examination of interaction terms
indicated that the greater rate of decline for women
was consistent across age groups and among survivors
and nonsurvivors.
Effects of survivorship on mean rate of change
Those who did not survive the entire study period
were estimated to be declining at a significantly faster
rate during the period before their deaths, regardless of
age and sex, for all sites and all scales (tables 4 - 6 ,
/33). They also were found to have lower levels of
physical function at baseline regardless of age and sex
Additional variation in mean rate of change
Another contribution of the random effects model
was a characterization of the variation from the mean
changes over time. The observations for a specific
person would not be expected to follow the predicted
curve exactly. The random effects model assumed
three sources for this variability. First, individuals
might start at a different baseline level than would be
predicted for their age, sex, and survivorship status.
This effect, denoted At in the equation, was assumed to
have a constant standard deviation across age, sex, and
survivorship. Substantial otherwise unexplained variation was observed, with standard deviations of about
0.5 items for the Nagi and Rosow-Breslau scales and
slightly more for the Katz scale. Second, individuals
might decline at a faster or slower rate than would be
predicted for someone of their age, sex, and survivorship status; the variance for the person-specific declines, B,, ranged from 0.1 to 0.2 items per year of
change. Finally, the value observed in a specific year
might differ from that predicted by a person's own
mean rate of change and starting point. The standard
deviations of the within-person errors, etp were between 0.5 and 0.7 items for each of the three scales,
consistent with results in a previous short-term variability study (27).
Transitions between disability and recovery
The declining mean level of physical function does
not imply that all subjects followed a steady course of
decline during the follow-up period. Some subjects
recovered from disability, even at the oldest ages.
Markov models provided estimates of the effects of
age at baseline, sex, and survivorship on the risk of
becoming disabled and on the chance of recovery from
disability by the next year, based on all subjects who
had physical function data at 2 or more study years.
Women 65 years old who survived for the entire study
period were chosen as the comparison group, and the
coefficients were the average change in the log odds of
becoming disabled or of recovery for each year of age
beyond 65 years, for males and for those who did not
survive until the end of the study period (tables 7-9),
as in a logistic regression model.
The probability of becoming disabled by the next
year increased significantly with age for each of the
three scales for all four sites, and the probability of
recovery from disability decreased with age. Males
were significantly less likely than females to report
new disability for all sites and all scales and significantly more likely to report recovery for all except the
Katz scale at the Iowa site. Finally, those who did not
survive the study period were substantially more likely
to become disabled while under observation and less
likely to recover if they had been disabled the preceding year.
Because the coefficients in the Markov model represent the change in the log odds of a transition, direct
interpretation is complicated. In figure 2, the estimated
transition probabilities for the Iowa site can be seen.
The probability of recovery from selfreported disability was large for the youngest groups but declined with
increasing age, whereas the probability of new disability increased. Thus, for the four sites studied here, the
decline in mean function seen over the 6 years and
with increasing age is consistent with the combined
influence of more people becoming disabled and fewer
recovering. Because more people were not disabled at
the beginning of the interval for most ages, the absolute number who became disabled was larger than the
number recovering, leading to a net increase in number disabled.
Model validation and limitations
Two limitations to the random effects model approach that was used should be noted. First, the maximum likelihood estimates have not been adjusted
directly for the complex sample design used at the
New Haven and North Carolina sites. Instead, the
effects of the sample design have been addressed by
including terms in the regression model for stratum at
these two sites. Related work for linear regression
models has suggested that this approach is adequate in
many settings (35). Second, the maximum likelihood
estimation procedure assumed that the observations of
a person followed a multivariate normal distribution.
All of the physical function scales in fact had substantial ceiling effects, with most individuals having little
Am J Epidemiol
Vol. 143, No. 8, 1996
Physical Function in Older Persons
775
0.70
0.65
0.60
0.S5
0.50
0.45
0.40
3
0.35'
2
a.
0.BO-
0.20-
0.15-
o.io0.05-
o.oo(5
70
75
80
15
«0
Age (years)
FIGURE 2. Transition probabilities to disability: Rosow-Breslau scale, Iowa Established Populations for Epidemloiogic Studies of the Bderty
site. Group and status:
. women, survived entire study; . . . . . . . . women, died before end of study;
, men, survived
entire study;
, men, died before end of study.
or no disability at the youngest ages. The estimates of
effect on mean change are unlikely to have been
affected by nonnormality; however, the estimates of
variation among persons did not fully reflect the observed, skewed variation.
Model validation included examination of alternative models both for the mean structure and for the
covariance structure. Interactions between the effects
of age and sex were not in general statistically significant. The quadratic description of mean score at baseline was adequate and had, moreover, the advantage of
corresponding to the linear change with age in mean
decline per year in the longitudinal portion of the
Am J Epidemiol
Vol. 143, No. 8, 1996
model, permitting direct comparison of cross-sectional
and longitudinal estimates of the effects of age. Simpler models considered for the variability included
compound symmetry (eliminating variation among
persons in change per year) and first-order autoregression (assuming all the person-specific change from
year to year came from a short-term process that was
not influenced by data before the most recent year).
Neither of these simpler models provided an adequate
description of the variance structure observed. Higher
order models than the linear random effects structure
did not improve substantially over the model presented
here.
776
Beckett et al.
Alternative Markov models that we considered included a quadratic term in age and interactions among
age, sex, and survivorship; however, these did not
contribute significantly. Residual analysis detected violation of one basic assumption of the Markov model
in that the transition probabilities were not constant
over the period of study but instead, shifted with age,
as might be expected. Thus, the coefficients shown
represent the mean transition probabilities over the
study interval. Modeling changes over the study interval was not possible with existing software. Finally,
the estimates for the New Haven and North Carolina
sites have not been adjusted for the complex sample
design, although the stratum has been included in the
regression model. In alternative analyses (not shown),
logistic regression models adjusted for the complex
sample design were fitted to each pair of years, and
similar parameter estimates and conclusions were obtained.
DISCUSSION
Three findings of this study are noteworthy. The
first finding is that, on average, decline in physical
function associated with age is greater than has been
appreciated from previous cross-sectional studies. The
average pattern of decline appears not to be linear but
to accelerate with increasing age. The second finding
is that there is much individual variation. The average
pattern of decline is the result of many persons experiencing declines in physical function and a smaller
but substantial proportion of the population experiencing recovery of lost function. The third finding is that
individual decline in reported physical function appears consistently greater for women than for men at
all ages. In addition to being more likely to experience
decline in function, women are less likely to recover
from disability. These results were quantitatively and
qualitatively consistent across four study sites in
widely separated and diverse locations.
Decline in average physical function associated with
increasing age has long been appreciated. Attempts to
quantify this change with age have come largely from
cross-sectional studies that, although not directly measuring change in function, have inferred change from
measurements made at a single time for persons of
different ages. For example, the difference between
the function of those 75 years old and those 80 years
old is assumed to represent the average decline in
function between 75 and 80 years of age. In general,
these cross-sectional studies have suggested a linear
pattern of average decline, similar to that seen in
cross-sectional data from each center of the present
study (table 3). Self-reported individual changes in
function seen in this study are, on average, substan-
tially greater than would be inferred from these crosssectional data. The most likely explanation is that
cross-sectional community-based studies of physical
function are subject to underrepresentation of persons
with poor function because the latter are selectively
removed from the population due to placement in
long-term care institutions. Their absence as study
participants distorts the true relation between physical
function and age because the older age groups of the
cross-sectional sample do not include many of those
with more severe loss of function. Several longitudinal
studies have also examined physical function among
older persons but have not focused on directly estimating average decline in function with age. Unlike
the present study, in which repeated measures of physical function were made at six annual interviews, as
pointed out earlier, most previous longitudinal studies
have either examined physical status at a single point
(relating it to previously measured predictors) (7-10)
or at two points, 2-25 years apart (11-20). Only one
study, which examined function at six points over 10
years, characterized change over time (22, 23).
Variation in individual patterns of change in physical function has not been extensively studied in population-based samples of older persons. The results of
this study indicate that the average pattern of decline
in function is not uniform; some individuals do not
experience this decline. Many persons maintain good
function to advanced ages, and many persons who
experience disability recover from it, even among the
older age groups. The average estimate of decreasing
physical function with increasing age reflects both
increasing likelihood of experiencing disability and
decreasing Likelihood of recovery (figure 2).
This evidence of recovery is especially important
because it indicates the potential to reverse disability
even in the oldest age groups. Some evidence suggests
that a greater proportion of people may be experiencing continued good function or reversal of disability;
recent estimates (36) of the prevalence of disability in
the United States population in 1982, 1984, and 1989
suggest that the age-standardized prevalence of disability decreased over this period. However, the number of disabled older persons in the population was
estimated to have actually increased over this time
because this trend was not sufficient to compensate for
the increasing number of persons in the oldest age
groups over this same period.
It is unclear from previous research whether older
women have lower levels of function than do older
men. Some cross-sectional studies have noted greater
prevalence rates of physical disability among women
than among men (2, 12, 37), although these sex differences appear to become apparent only in older old
Am J Epidemiol
Vol. 143, No. 8, 1996
Physical Function in Older Persons
age. In addition, sex differences are generally greater
for mobility-related activities (2) or instrumental activities of daily living (37) than for basic ADLs. Prospective research has produced equally mixed results
with regard to sex differences in incidence of disability. Most studies have failed to find any sex difference
predicting new disability after controlling for other
risk factors (9, 11-13, 17, 18, 20, 22); however, two
studies found women to be at higher risk of developing
disability (14, 16). Although the results of the current
study were not adjusted for other risk factors of functional decline, they clearly suggest a significantly elevated risk for decline among women. This effect was,
with few exceptions, consistent throughout our analyses: Women generally showed more decline in all
three measures of function when function was modeled either as continuous variables (random effects
models) or as dichotomous outcomes (Markov models).
It should be noted that biased reporting is less likely
to affect longitudinal studies of change in physical
function than cross-sectional studies. To the extent
that factors distorting report of function are constant
for each person for the initial report and for subsequent
reports, measurement of individual change in function
over time will be unaffected by these distortions. If, as
appears reasonable, any sex differences in reporting
remain constant over time, then the results of this
study suggest that women on average both are at
greater risk of developing disability than men and are
less likely to recover from it. This finding seems
somewhat paradoxical because women on average live
longer than men; however, higher levels of disability
are associated with increased risk of death among
older persons (38-41). If valid, this finding appears to
be of substantial concern because it implies that
women have both higher risk of disability and longer
average duration of disability because of longer survival.
Study strengths and limitations
This study has several strengths in comparison with
previous work in this area. The most important is the
longitudinal design with function measured on six
occasions over a 5-year period with minimal loss to
follow-up. The design and analyses focus on accurately measuring individual changes in function, including both decline and improvement. This permits
estimation of disability incidence and recovery as well
as a more detailed characterization of the time path of
physical function level. Other advantages include the
large size of the study, the presence of four geographically dispersed communities representing both urban
Am J Epidemiol
Vol. 143, No. 8, 1996
777
and rural settings, and the use of three wellcharacterized and accepted measures of function.
The results of this study also suggest that relatively
complex statistical approaches may be necessary to
address some common, clinically relevant health problems, especially in longitudinal data. The techniques
employed here use multiple, sequentially collected
measurements efficiently while avoiding bias, especially that arising from adjustment for initial level of
function. Furthermore, these approaches provide a
practical illustration of the need to use more than one
statistical approach to examine the same data set. In
these data, random effects models are an effective
means of analyzing the average change over time. For
examining the bidirectional nature of the change, with
some persons experiencing recovery from disability
and others experiencing decline in function, Markov
models are more useful than random effects models.
The two different analytic approaches are complementary in answering related questions about the health of
older persons.
This study emphasizes physical function; however,
at least to some degree, respondents' reports of disabilities may reflect cognitive as well as physical
difficulties because these scales are not pure measures
of physical function. In this regard, it is noteworthy
that the Nagi items are substantially more limited to
physical disability than are the Katz ADL items, yet
the patterns of disability with respect to age and sex on
each scale are very similar. Direct observational tests
of physical performance offer assessment that is more
limited to physical function. To date, however, they
have been used in few longitudinal studies, and they
do not provide the global assessment of function that
self-reported measures provide. Another limitation is
that the proportion of participants represented by
proxy respondents increases with increasing level of
disability, and it is possible that the reports of these
proxy respondents may be systematically different
from those of the participants themselves.
Despite their limitations, the data reported here
strongly suggest that disability among older persons is
an even greater problem than is apparent from previous cross-sectional studies. The magnitude of this public health problem will very likely continue to grow
because the oldest age groups are the most rapidly
growing segments of the populations of the United
States and of other developed countries. Disability is
also a strong predictor of utilization of institutional
long-term care and other health care services. It is
important to emphasize that the strong relation between disability and age does not necessarily imply
that age itself is responsible for the decline or that such
decline is inevitable. Substantial numbers of persons
778
Beckett et al.
experienced stable or improving function with age.
The challenge these results pose is to identify both
potentially reversible factors contributing to loss of
function and meaningful interventions for those experiencing disability.
ACKNOWLEDGMENTS
This work was supported by the following contracts with
the National Institute on Aging: N01AGO2105,
N01AG02106, N01AG02107, and N01AG12102.
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