Transitions among health states, using 12 different measures of health
7-8-2011
recup_44.doc
Paula Diehr and Stephen Thielke
Abstract
Introduction
A population may be conceptualized as comprising 3 states: healthy, sick, and (over
time) dead. Persons move among those states with certain probabilities, which may
vary by age and gender. There are many ways of defining the states, and transition
probabilities are seldom available.
Methods
From a longitudinal study of older adults, we analyzed twelve different variables:
self-rated health, ADL, IADL, depression (CESD), cognition (3MSE), time to walk 10
feet, number of days spent in bed, number of blocks walked, extremity strength, recent
hospitalizations, feeling that life is worthwhile, and satisfaction with the purpose of
life. We dichotomized responses for each variable into “healthy” or “sick”, and
estimated transition probabilities among the states. We examined patterns in the
prevalences and the probabilities by age, sex and variable type.
Findings
All 12 health variables had similar behavior. There were monotonic age effects, in the
expected directions, which were non-linear except for the probability of resilience or
of remaining sick. Men had a higher death rate than women, but men also had a higher
healthy prevalence for most variables. Women were more likely to become and
remain sick, and were less likely to recover on variables measuring aspects of physical
health.
Discussion
The age patterns were expected. Women were usually favored for mortality, and men
for the other variables. The only measures that favored women, COG and HOSP, were
determined externally rather than self-reported. Perhaps men are clueless (stoic) while
women are whiney (in touch with their feelings/bodies/etc.). Men are more
rectangular.
Conclusion
Older adults were likely to be healthy and to maintain their health or to recover from
the sick state, no matter how health was measured. There were substantial differences
in the gender patterns of prevalence and transition probabilities for the differing health
measures. By most measures, men were healthier, in spite of having a higher mortality
rate. Women may self-report worse health than is appropriate.
(315 words)
1
Transitions among health states, using 12 different measures of health
1 Introduction
A population may be conceptualized as comprising 3 states, healthy, sick, or (if
followed over time) dead. For example, for Activities of Daily Living (ADL),
“healthy” may be defined as having no ADL difficulties, and “sick” may be defined as
having one or more difficulties. Persons move among those states with certain
probabilities, which may vary by age and gender. Figure 1 shows the 6 one-year
transition probabilities for ADL (from a dataset described later), by age, for women.
In order from the top are the probability of staying healthy from one year to the next,
P(H to H); the probability of staying sick, P(S to S); the probability of getting sick,
P(H to S); the probability of dying from the sick state, P(S to D); and the lowest is the
probability of dying from the healthy state, P(H to D). Not surprisingly, P(H to H)
and P(S to H) decline with age, while the other probabilities increase with age. At the
oldest ages, P(S to H) is lower than P(S to D), meaning that a sick person is then more
likely to die than to recover. Men had similar patterns (not shown).
[Figure 1 about here]
Figure 2 shows the prevalence of the healthy state (healthy prevalence) and
two of the transition probabilities. The two heaviest lines represent the healthy
prevalence (proportion of the living who had no ADL difficulties), with a solid line for
males and a dotted line for females. The healthy prevalence is higher for men than for
women. It declines over time, and the slope becomes steeper with age. The
lowermost two lines represent the probability of recovering from the sick state to be in
the healthy state one year later, P(S to H). The probability is initially near 0.4,
2
declines approximately linearly with age, and is higher for women than for men. The
two topmost lines in the graph represent the probability of staying in the healthy state,
P(H to H). This probability is initially about 0.9, but declines with age and is higher
for men than for women. Figure 1 and Figure 2 suggest some hypotheses of interest
about healthy prevalence and transition probabilities.
[Figure 2 about here]
“Healthy” may be operationalized in many other ways, such as having no
IADL difficulties, or having fewer than 10 points on a scale of depressive symptoms.
Transition probabilities are often used in life-table calculations and other analyses that
model longitudinal health. The probabilities themselves, however, are rarely
published. Transition probabilities based on ADL, IADL, or self-rated health have
been published.
9 10
1234567
Transition probabilities are also available for disability, 8
depression, 11 exhaustion, 12 and body mass index.[2] To explore transition
probabilities further, we will present and describe the transition probabilities for 12
different health variables commonly used in studies of older adults.
[Stephen to write something about sex and old age here?]
We hypothesize that healthy prevalence and transition probabilities will
become less favorable with older age; that the changes will not be linear in age, but
steeper at older ages; that transition probabilities will be different for men and women;
that P(S to S) may not be monotone in age , based on relationships seen for self-rated
health. [nsick paper 3] ; and that age and sex patterns for probabilities will depend on the
particular definition of “Healthy” or “Sick”.
2 Methods
3
2.1 Data
Data came from the Cardiovascular Health Study (CHS), a populationbased longitudinal study of risk factors for heart disease and stroke in 5888 adults aged
65 and older at baseline.13 Participants were recruited from a random sample of
Medicare eligibles in four U.S. communities, and extensive data were collected during
annual clinic visits and telephone calls. The original cohort of 5201 participants,
recruited in about 1990, had up to ten annual clinic examinations. A second cohort of
687 African Americans, enrolled in about 1993, had up to seven annual examinations.
Follow-up was virtually complete for surviving participants.14
The twelve variables used in this study, common descriptors of aging that were
measured annually, are shown in Table 1. Each value was dichotomized into
“Healthy” and “Sick”, using standard thresholds where available, or choosing new
thresholds that ensured sufficient data for estimating transition probabilities.
Definitions of “healthy” are as follows: not being hospitalized in the previous year
(HOSP); no days spent in bed in the previous two weeks (BED); a score of 1 to 4 on a
10-point scale rating satisfaction with the purpose of life (SPL); a Center for
Epidemiologic Studies Short Depression score < 10 (DEP);15 16 no difficulties with
activities of daily living - walking, transferring, eating, dressing, bathing, or toileting
(ADL); a score of 1 to 3 on a 6-point scale rating whether life was worthwhile; no
problems with extremity strength - lifting, reaching, or gripping (EXSTR); being in
excellent, very good, or good self-reported health (EVGG); able to walk 15 feet in
less than 10 seconds (measured) (TWLK); no difficulties with instrumental activities
of daily living—heavy or light housework, shopping, meal preparation, money
4
management, or telephoning (IADL); having a Modified Mini Mental State
Examination score above 89 (COG);17 and walking more than 4 blocks per day, on
average (BLK). Missing data were imputed, as explained in Appendix A.
Age was divided into three categories 65-74, 76-84, and 85-94, in accordance
with the common definitions of “young old”, “old old”, and “oldest old”. These
groups are sometimes referred to by their midpoints, 70, 80, and 90. Persons could
contribute data to more than one age category. The unit of analysis was the transition
pair, defined as two measures of a variable, one year apart, for the same person.
2.2 Analysis
The healthy prevalence of each variable was calculated as the percent of living
persons who were healthy. The one-year probabilities of transitioning from state to
state were estimated from crosstabulation of data collected one year apart, combining
data from all years. General patterns were described. The associations of the
prevalences and probabilities with age and sex were tested using cross-sectional time
series logistic regression (XTLOGIT in Stata), which accounts for persons having
contributed multiple observations to the prevalence and transition data.
3 Findings
3.1 Prevalence
The first two lines of Table 1 show the sample size (number of transition pairs)
and mean age, by age and sex. Mean age was similar for men and women. The
following 12 lines show the healthy prevalence of each variable. For example, on line
3 (HOSP), 91.3% of the women aged 65-74 were “healthy”, defined as “having no
hospital days”. For men in the same state, healthy prevalence was 88.0%. Over the
5
three age groups, women’s prevalence for HOSP declined from 91.3% to 87.8% to
84.9%. Not surprisingly, all of the prevalences in Table 1 decline with age. There
was usually a significantly steeper (non-linear) decline from age 80 to 90 than from
age 70 to 80. This non-linearity was statistically significant for EXSTR, TWLK,
COG, and BLK (men and women) and BED and IADL (men only).
The bolded entries in Table 1 show the situations where women had a higher
healthy prevalence than men. This occurred only for COG and HOSP. The
XTLOGIT analysis of prevalence for individual variables confirmed that women were
significantly healthier than men only for HOSP and COG. (See also appendix table 1).
[Table 1 about here]
3.2 Transition probabilities
3.2.1
Transition probabilities for Sick persons
Table 2 shows the transition probabilities for persons who were initially in the
sick state. For example, P(S to H) for the youngest women is .677 when the health
measure is HOSP, and the corresponding P(S to S)= .262 and P(S to D) = .061. The
three probabilities sum to 1.0. Columns 4-6 show those probabilities for age 75-84,
and columns 7-9 show the probabilities for age 85-94. The lower half of the table
shows the same quantities for men. The bolded entries in the top half indicate
probabilities of resilience or death that were favorable to women (more likely to
recover, or less likely to die).
[Table 2 about here]
3.2.1.1 P(S to D)
6
P(S to D) always increased monotonically with age. As suggested above in
Figure 1, in the oldest age group, especially for men, P(S to D) is often greater than
P(S to H). Women were always less likely to die than men, no matter how the health
states were defined.
3.2.1.2 P(S to H)
P(S to H) always declined with age. The trend was fairly linear, but there
was significantly more decline after age 80 (non-linearity) for TWLK, COG and BLK
for women, and for EXSTR, TWLK, and COG for men.
Women were more likely than men to recover from the sick state for about
half the variables. Based on the XTLOGIT analysis, P(S to H) was significantly
higher for women than for men in at least one age category for HOSP, BED, DEP,
ADL, FLW, and EVGG. Men had significantly higher P(S to H) in at least one age
group for EXSTR, TWLK, and BLK. (See also appendix table 2a).
3.2.1.3 P(S to S)
We also analyzed the probability of staying sick, P(S to S). (See appendix
table 2b). The age relationships for P(S to S) were complex. In half (12) of the
comparisons there was no significant age relationships. In the other 12, age 70 was
always significantly less than 80, meaning that P(S to S) increased from 70 to 80.
However, compared to age 80, P(S to S) at age 90 was significantly lower for 2
variables, significantly higher 3 times, and not significantly different for 7 variables.
This lack of monotonicity is not easy to summarize.
7
There was a strong gender effect, with women significantly more likely to
stay sick then men in most cases. However, there was not a significant gender effect
for HOSP, BED, and FLW, nor for ADL and COG at age 70.
3.2.2 Transitions probabilities for healthy persons
Table 3 shows the transition probabilities for persons who were initially in the healthy
state. For example, P(H to H) for the youngest women is .917 when the health
measure is HOSP (column 1), and the corresponding P(H to S)= .075 and P(H to D) =
.008 (columns 2 and 3). Columns 4-6 show those probabilities for age 75-84, and 7-9
show the probabilities for age 85-94. The lower half of the table shows the
corresponding values for men. The shaded entries represent probabilities that favored
women (higher probability of remaining healthy or lower probability of becoming sick
or dying).
[Table 3 about here]
3.2.2.1 P(H to D)
P(H to D) increased with age, was always higher for men, no matter how the
healthy state was defined.
3.2.2.2 P(H to H)
P(H to H) declined with age. The decline usually accelerated significantly
with older age, but was not significantly non-linear for HOSP and TWLK (women)
and for ADL, EVGG, TWLK, and BLK (men).
Women generally had less favorable P(H to H) than men. The XTLOGIT
analysis found significant effects favoring women in at least one age category for
8
HOSP, FLW, and COG. Significant effects favoring men were found in at least one
age category for DEP, ADL, EXSTR, TWLK, IADL, and BLK (See also appendix
table 3A).
3.2.2.3 P(H to S)
P(H to S) increased with monotonically age. There was significant nonlinearity for SPL, FLW, and BLK (women) and for IADL and COG (men).
Women had favorable values of P(H to S) for HOSP and COG, and at some
ages for FLW and EVGG. Women were significantly favored for at least one age
category for HOSP and COG. There was no significant gender effect for P(H to S)
when defined by FLW, at any age. For the remaining variables, women were
significantly more likely to get sick than men in one or more age categories. (Also
see appendix table 3B).
3.3 Initial State
From Table 2 and Table 3, it can be seen that those in the healthy state were more
likely to be healthy in the following year, and less likely to be sick or die. This was
true for all variables. There was never a significant interaction between initial state
and gender. Therefore “healthy” and “sick” mean substantially the same in predicting
mortality for men and for women.
3.4 Principal Components and factor Analysis
To further examine the similarities of the variables, we performed a principal
component (PC) analysis of all twelve measures (not shown). (See appendix table 13).
The first PC accounted for 32% of the variation, and the loadings for all variables had
9
the same sign. This supports findings seen above for the similarities of the variables.
(see appendix table 13)
The second PC also had an eigenvalue greater than one, and retaining it
accounted for 42% of the variation. After a varimax rotation, and the first factor
comprised TWLK, IADL, ADL, EXSTR, BLK, EVGG (loadings > .5). The second
factor comprised FLW, DEP, SPL, and BED (loadings > .5). COG was also correlated
with factor 1 (loading = .45). ADL, EVGG, and HOSP were also correlated with
factor 2 (loadings 0.3 to 0.5). The two rotated factors could be taken, very loosely, as
summaries of physical and mental health, respectively. Interestingly, the variables
where women had a higher P(S to H) than men loaded most highly on factor 2 (mental
health) and the variables that favored men were those that loaded on factor 1 (physical
health). The average factor scores were higher for men than for women.
4 Discussion
4.1 Summary
Analyses comparing patterns among the 12 health variables found many
similarities. There were strong age effects in the prevalence and probabilities, in the
expected direction, which were linear only for P(S to H). The exception was P(S to S)
which often was not monotone in age. Men had a higher healthy prevalence for 10 of
the variables, with women healthier only for COG and HOSP. In spite of their better
health, men had a higher death rate in all but one comparison. Women were usually
more likely to become sick and to stay sick. They were less likely than men to recover
from sick states defined by the “physical health” variables, and more likely than men
to recover on the “mental health” variables.
10
4.2 Prevalence and Probabilities
The equilibrium - or steady state – healthy prevalence of a system can be
calculated from the transition probabilities. 18
19
The equilibrium prevalence of the
healthy state is K/(1+K), where
K
P( HtoH )  P( StoS )
[ P( HtoH )  P( StoS )]2 P( StoH )
.


2 P( HtoS )
[2 P( HtoS )]2
P( HtoS )
{1}
If we may consider the CHS sample over time to be approximately at equilibrium,
these relationships may help to explain some of the findings. To support this
assumption, we noted that the observed healthy prevalence was fairly close to the
calculated equilibrium prevalence, with the worst discrepancy being at age 90 for
IADL. (See appendix table 4 and table 4b for detailed calculations for each health
variable).
The equilibrium prevalence increases with K. P(H to S) is in the denominator
of every term, and is therefore a key component of healthy prevalence. The variables
with the lowest P(H to S) in Table 3 (e.g., FLW, BED, and HOSP for the young-old
women) should have the highest healthy prevalence in Table 1, which is the case.
Table 3 also shows that P(H to S) is higher for men than for women only for HOSP
and COG (and occasionally for EVGG). Because higher P(H to S) leads to lower
healthy prevalence, it follows that HOSP and COG are the two variables for which
women had a higher healthy prevalence.
In the first term of equation {1}, P(H to H) – P(S to S) is in the numerator.
This quantity is usually positive, meaning that a healthy person is more likely to
remain healthy than a sick person is to remain sick. The term is negative, however,
11
for BLK, meaning that a person who is sick (inactive) is more likely to remain
inactive that a person who is healthy (walks 4+ blocks a day) is to remain active. This
term is more likely to be negative for the oldest old, meaning that, with increasing age,
the probability of staying healthy becomes lower than the probability of staying sick.
The second term under the radical in equation {1} is the ratio of P(S to H) to
P(H to S). This ratio is greater than 1.0 for the young old (except for BLK), meaning
that they are more likely to recover than to get sick. The ratio is below 1 for TWLK
and COG at age 80, and is below 1 more than half the time at age 90. The relative
probabilities of recuperating and getting sick thus change over time, as a feature of
aging.
4.3 Age effects
Healthy prevalence and five of the transition probabilities declined
significantly in the expected direction with age. For P(S to H) only, the decline was
linear. The other measures tended to show a significantly larger change after age 80.
The one discrepant probability was P(S to S), which was often highest in the middle
age group. A similar pattern was noted elsewhere, based on self-rated health. [3] P(S
to S) increased from birth until about age 60, after which it declined. This pattern is
caused by the different alternatives for a sick person with increasing age. At younger
ages, the most likely change is to recuperate, but as P(S to H) decreases with age, P(S
to S) increases. At the oldest ages, however, the most likely change from the sick state
is death, and as the P(S to D) increases, P(S to S) decreases. The sick state thus has a
somewhat ambiguous meaning, since it represents a failure to recuperate for younger
persons (bad) but a resistance to dying for older persons (good).
12
4.4 Gender effects
It is puzzling that although men always had a higher death rate, they usually
also had a higher healthy prevalence (except for HOSP and COG). The findings
suggest that men are closer than women to achieving the ideal of the compression of
morbidity. 20 Sick women had a higher P(S to S) in 34 of 36 comparisons. Men had a
higher P(H to H) in 23/36 comparisons, and higher P(S to H) in 21 of 36 comparisons.
Women had a higher P(H to S) in 25 of 36 comparisons.
Thus, most of the non-death
transition probabilities tended to favor men.
Similar observations have been made by Leveille et al. [8] That study defined
“healthy” as being able to walk to miles and climb two flights of stairs without help.
They found that men were more likely to die but also to remain healthy and to recover,
while women were more likely to become sick and remain sick. They used life-table
calculations, modifying various parameters, to conclude that the most important
explanatory factor was that the probability of incidence, P(H to S) was higher for
women. We extended that finding by using 12 different measures of health. We also
used equation {1} to illustrate the key role of P(H to S) in determining the healthy
prevalence. Finally, we determined that all of the non-death transition probabilities
favored men somewhat, not just the probability of incidence. For example, we found
that P(S to S) was higher for women in every case.
Hardy [9] in a similar study (based on ADL disability, with 1 or 2 areas
considered mild disability and 3 or more severe disability) found that the higher
prevalence of disability in women versus men is due to a combination of higher
incidence and longer duration, resulting from lower rates of recovery and mortality
13
among disabled women. We found also that women were less likely to recover from
ADL difficulties.
Resilience, P(S to H), is a major feature of aging theory.[ref?] Based on the
principal components analysis, it may be appropriate to say that women have higher
resilience for mental variables and men had higher resilience for physical variables.
Equation {1} shows that healthy prevalence does not depend strictly on P(S to H), but
rather on the ratio of P(S to H) to P(H to S). Healthy prevalence does depend directly
(inversely) on P(H to S).
Women had significantly higher P(H to H) than men only for HOSP and
COG, and had lower P(H to S) only for HOSP and COG.
This helps to explain why
HOSP and COG were the only variables where women had a higher healthy
prevalence than men.
It may be that older women really are sicker than older men. Alternatively,
women may have a more nuanced understanding of their health, or may be more
willing to assume the sick role than men. [refs?] This possibility is supported by the
fact that HOSP and COG, the only variables that favored women, are similar only in
that neither was self-reported. If these variables had instead been measured by selfreport, perhaps women would have reported worse health on these measures as well.
However, the third externally measured variable, the timed walk, favored men. It
would be useful to repeat these analyses using other variables, datasets, and age
groups.
4.5 Variables were similar
14
The twelve health-related variables included measures of physical
and mental health, quality of life, and health behaviors. Some were self-reported, and
some were reported by others. Some were completely subjective while others were
based on structured responses. We had expected some of these features to make a
difference, but 10 of the 12 variables behaved in very similar ways. Two published
analyses of transitions in physical function also showed the same patterns,
[leveille] [hardy]
We had no longitudinally-collected measures of social, environmental or occupational
health. It is likely that such measures would have similar behavior to those shown
here. The principal components analysis supported the similar behavior of the various
measures, and suggested that most of the information in the 12 variables could be
summarized into 2 or 3 dimensions.
4.6 Healthy Aging
One measure of healthy aging is the probability of resilience, P(S to H). We
found that resilience was reasonably high but declined with age, and tended to be
higher for women than for men. The “one hoss shay” model suggests that all
dimensions of health might stay perfect until death, at which time all dimensions
would crash “all at once and nothing first”. That model was not supported here,
although the various measures did tend to decline in similar ways. A related model is
the compression of morbidity [fries] which has the goal of spending most of the years
before death in the healthy state. We found that the healthy prevalence declined with
age, and was usually higher for men than for women, despite the higher death rates for
men. Thus the goal of healthy aging was closer to being met for men than for women,
for 10 of 12 measures of health.
15
4.7 Limitations.
The significance tests that are reported here should be considered as descriptive
only, due to the very large number of comparisons that were made in this analysis.
The healthy states had different prevalences because of the way that “healthy” was
defined. If all measures had been continuous, we could have chosen thresholds that
would make all of the prevalences the same, but that was not possible here. We
initially planned to study a thirteenth variable, whether a person had a flu shot in the
past year. This measure was found to be essentially unrelated to health and mortality
on other measures, and so was not included here. Because the goal of this paper was
to compare twelve different measures of health, the amount of discussion given to
each measure had to be limited.
5
Summary and Conclusion
Transition probabilities among states of health are important for the study
of aging, but are rarely reported. We provided transition probabilities for healthrelated variables that had not previously been studied, and that addressed different
domains of health. In general these variables behaved in the same way. Healthy
prevalence and all of the transition probabilities changed in the expected way with age
and were usually more favorable for men that for women.
If women have a more
nuanced view of their health than men do, these gender differences could be partially
explained. Extension of these findings to other health-related variables would be of
interest.
16
Table 1
Healthy prevalence
Table 1, Prevalence
N
Mean Age
HOSP: No hospital days
BED: No bed days
SPL: Satisfied with Purpose of Life
DEP: Not depressed
ADL: No ADL difficulties
FLW: Feel life is worthwhile
EXSTR: Good extremity strength
EVGG: Exc/ Very Good/ Good health
TWLK: Walk 10 feet < 10 seconds
IADL: No IADL difficulties
COG: 3MSE > 90
BLK: Walked 4+ blocks per day
*tables_graphs_paper_05.sps 4-23-2011
Sheet 3
Sex
Female
Male
65-74 75-84 85-94 65-74 75-84 85-94
12261 12433 2183 7801 8867 1752
71.0 78.6 87.5 71.1 78.6 87.7
91.3 87.8 84.9 88.0 85.6 81.7
94.3 92.3 89.3 95.9 94.6 91.3
75.7 69.8 59.6 80.7 75.2 67.4
80.2 73.8 64.3 87.6 81.4 70.9
86.3 76.1 56.7 90.2 82.7 67.6
94.4 91.0 83.6 95.3 91.7 85.6
67.6 57.6 42.1 84.6 78.8 65.4
79.0 70.8 60.7 80.0 73.6 64.7
64.3 44.5 16.9 73.8 58.6 30.0
71.8 58.7 39.5 80.9 70.5 50.7
70.9 54.6 27.6 67.2 53.1 25.7
33.3 20.9
8.5 47.7 37.8 22.3
Bolded entries favor women.
17
Table 2
Transition probabilities for sick persons
Table 2
Transition Probabilities for Initially Sick Persons *
1
2
Young Old (65-74)
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
3
4
Old Old (75-84)
5
6
7
8
Oldest Old (85-94)
9
P(S TO H) P(S TO S) P(S TO D) P(S TO H) P(S TO S) P(S TO D) P(S TO H) P(S TO S) P(S TO D)
0.677
0.262
0.061
0.605
0.290
0.105
0.535
0.267
0.198
0.550
0.370
0.080
0.443
0.408
0.148
0.335
0.369
0.296
0.367
0.601
0.031
0.297
0.640
0.063
0.235
0.607
0.158
0.345
0.620
0.034
0.286
0.642
0.073
0.203
0.628
0.169
0.359
0.589
0.051
0.253
0.667
0.080
0.151
0.703
0.146
0.370
0.541
0.089
0.291
0.562
0.147
0.175
0.532
0.292
0.314
0.661
0.026
0.230
0.717
0.053
0.140
0.736
0.124
0.314
0.644
0.042
0.253
0.674
0.073
0.239
0.608
0.154
0.293
0.678
0.029
0.157
0.795
0.048
0.058
0.841
0.101
0.295
0.674
0.032
0.221
0.727
0.052
0.156
0.732
0.112
0.274
0.700
0.026
0.169
0.779
0.052
0.070
0.825
0.105
0.140
0.842
0.018
0.084
0.878
0.038
0.025
0.884
0.091
0.632
0.494
0.411
0.373
0.311
0.293
0.368
0.323
0.338
0.335
0.271
0.208
0.286
0.353
0.528
0.543
0.586
0.548
0.566
0.598
0.609
0.590
0.685
0.756
0.082
0.153
0.061
0.084
0.103
0.159
0.066
0.078
0.053
0.075
0.043
0.036
0.560
0.329
0.315
0.271
0.229
0.200
0.306
0.250
0.207
0.243
0.176
0.142
0.278
0.356
0.562
0.568
0.603
0.518
0.556
0.623
0.699
0.639
0.742
0.786
* Bolded entries for P(H) and P(S) favor women.
table2_tests_08.xslx , sheet 3
18
0.162
0.315
0.123
0.161
0.168
0.282
0.138
0.127
0.094
0.118
0.082
0.072
0.489
0.257
0.243
0.175
0.134
0.151
0.196
0.178
0.077
0.166
0.071
0.078
0.227
0.329
0.535
0.576
0.630
0.456
0.563
0.586
0.764
0.643
0.779
0.769
0.283
0.414
0.222
0.250
0.236
0.393
0.241
0.236
0.159
0.191
0.150
0.153
Table 3
Transition probabilities for healthy persons
Table 3
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
Transition Probabilities for Initially Health Persons
1
2
3
4
5
6
7
8
9
Young Old (65-74)
Old Old (75-84)
Oldest Old (85-94)
P(H TO H) P(H TO S) P(H TO D) P(H TO H) P(H TO S) P(H TO D) P(H TO H) P(H TO S) P(H TO D)
0.917
0.075
0.008
0.876
0.102
0.021
0.804
0.130
0.066
0.947
0.045
0.009
0.921
0.058
0.021
0.858
0.082
0.061
0.849
0.145
0.007
0.804
0.178
0.018
0.697
0.266
0.037
0.883
0.110
0.007
0.844
0.140
0.017
0.769
0.192
0.039
0.904
0.090
0.007
0.846
0.138
0.016
0.722
0.238
0.040
0.956
0.036
0.008
0.922
0.058
0.020
0.850
0.105
0.045
0.826
0.167
0.006
0.770
0.214
0.016
0.664
0.304
0.033
0.902
0.296
0.005
0.846
0.370
0.014
0.730
0.395
0.042
0.826
0.170
0.004
0.717
0.272
0.011
0.537
0.453
0.011
0.848
0.147
0.005
0.772
0.211
0.017
0.606
0.349
0.045
0.864
0.129
0.007
0.806
0.180
0.014
0.666
0.299
0.035
0.650
0.013
0.002
0.546
0.011
0.007
0.486
0.027
0.027
0.884
0.947
0.860
0.905
0.921
0.950
0.899
0.893
0.850
0.875
0.831
0.724
0.098
0.033
0.123
0.078
0.062
0.031
0.083
0.350
0.134
0.111
0.153
0.017
0.018
0.020
0.017
0.017
0.017
0.019
0.018
0.012
0.016
0.014
0.017
0.014
0.850
0.921
0.817
0.864
0.865
0.916
0.847
0.839
0.762
0.811
0.780
0.629
0.116
0.042
0.155
0.109
0.108
0.053
0.124
0.343
0.216
0.165
0.195
0.021
0.033
0.037
0.028
0.027
0.028
0.031
0.029
0.025
0.022
0.024
0.025
0.018
* Bolded entries favor women.
table3_tests_08.xslx , sheet 3
19
0.758
0.836
0.712
0.763
0.749
0.819
0.738
0.747
0.611
0.641
0.618
0.541
0.154
0.066
0.210
0.163
0.179
0.101
0.198
0.446
0.343
0.298
0.329
0.038
0.088
0.098
0.078
0.074
0.072
0.080
0.064
0.064
0.046
0.061
0.053
0.026
Figure 1, transition probabilities for ADL for women by age
20
Figure 2.
Prevalence and Probabilities of Maintenance and Resilience
for Activities of Daily Living By Age and Sex
21
Appendices
A
Tables
1
Missing Data
1 Significance tests for prevalence
1a summary comparisons for prevalence
2a significance tests for P(S to H)
2b significance tests for P(S to S)
3a significance tests for P(H to H)
3b significance tests for P(H to S)
4 calculations from equation {1}, equilibrium prevalence
4b prev_obs minus prev_equil
5 probability differences, female minus male
6 age differences on probability of getting sick 70-80, 80-90, dif dif
7 age differences on probability of staying sick
8 summary of sex results for all probabilities (#positive)
9 summary of age results for all probabilities (# positive)
10 summary of sex results for all healthy variables (sum of #8)
11 summary for age results for all healthy variables (sum of #9)
12 interaction of age and initial state in predicting mortality
13 principal components/factor analysis.
22
Appendix A.
Missing Data
In CHS, most measures were taken annually from 1990 to 1999. However, self-rated
health was measured semi-annually from 1990 to 2005, and complete mortality was available
(for the current analysis) through 2007. We imputed missing self-rated health data and used
that, where necessary, to help impute data for the other variables. For self-rated health, we
coded the original response categories (excellent, very good, good, fair, poor) to 95, 90, 80,
30, and 15. These values represent approximately the percent probability that a person in this
state with be in excellent, very good, or good health in the following year. Under the
assumption that a dead person is not healthy, and will not be healthy next year either, we can
assign a value of 0 to values that were not made because the person had died. After this
recoding, we imputed missing data by interpolation over time, whenever there was a valid
value before and a valid value or death after the missing data. The remaining unimputed data,
for persons alive but missing at the end of the sequence, we used last observation carried
forward. Because so much information was collected after 1999, we rarely had to impute
missing data from 1990 to 1999 by extrapolation (less than .3% of the time). We are thus
comfortable with the imputation for EVGGFP.
For the other variables, each variable was transformed to a new scale representing the
probability of being in excellent, very good, or good health, deaths were set to zero, and data
were interpolated. Data missing at the end of the sequence for persons still alive was imputed
as the average of the last available observation from the variable of interest and the estimate
from self-rated health at that time. These were both on the same scale because of the
transformation. After imputation, the variables were transformed back to the original scales.
23
Appendix Table 1, includes the significance tests
appendix table 1, prevalence (results of xtlogit)
F>M
b
a
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
70
a
c
80
b
90
70
f
80
90
c
d
d
d
d
e
e
e
e
d
e
e
e
e
d
d
a
M>F
e
d
terminal drop
early
late
g
g
f
f
f
g
f
g
f
f
g
b
d
e
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
f
g
g
g
g
g
g
g
g
24
Appendix table 1a, summary of stuff about the Prevalences of the Healthy States
yrs 1990-1998 only
Appendix table 1
Female minus male
Female minus male
female
male male male
a
b
a
b
70-80 80-90 b-a
70-80 80-90 b-a
ignore col labels
7801 8867 1752
ignore col labels
71.129 78.628 87.654
3.51 2.85 -0.67 2.38 3.97 1.58
2.02 2.93 0.91 1.35 3.23 1.88
5.85 10.20 4.35 5.55 7.80 2.25
6.35 9.53 3.18 6.17 10.44 4.27
10.15 19.45 9.30 7.48 15.06 7.58
3.40 7.43 4.03 3.61 6.09 2.48
9.98 15.54 5.56 5.88 13.40 7.52
8.13 10.18 2.05 6.42 8.93 2.51
19.78 27.64 7.86 15.28 28.59 13.31
13.11 19.17 6.05 10.43 19.71 9.28
16.24 27.05 10.81 14.14 27.41 13.27
-7.86 -0.04 7.82 0.00 0.00 0.00
12.45 12.43 -0.02 9.89 15.51 5.62
4.00 -4.00 -8.00 4.00 -3.00 -7.00
65-74 75-84 85-94
N
12261 12433 2183
mean age
70.999 78.561 87.503
HP: No hospital days
3.26 2.13 3.25
BD: No bed days
-1.62 -2.30 -2.00
SPL: Satisfied with Purpose of Life-5.01 -5.31 -7.71
DP: Not depressed
-7.38 -7.55 -6.63
ADL: No ADL difficulties
-3.91 -6.58 -10.97
FLW: Feel life is worthwhile
-0.94 -0.73 -2.06
XS: Good extremity strength
-17.02 -21.12 -23.26
VG: Exc/ Very Good/ Good health-1.06 -2.77 -4.02
TW: Walk 10 feet < 10 seconds -9.51 -14.00 -13.05
YD: No IADL difficulties
-9.07 -11.75 -11.21
CG: 3MSE > 90
3.63 1.53 1.89
FH: Flu shot last year
-0.67 -4.17 -1.59
BK: Walked 4+ blocks per day -14.31 -16.87 -13.79
no pain
-12
-12
-11
plus
minus
2
10
2
10
2
10
12
0
25
12
0
11
1
12
0
12
0
12
0
Appendix Table 2a P(S to H)
appendix table 2a, recuperation (XTLOGIT)
f>m
b
a
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
70
c
80
f<m
e
d
90
70
terminal drop
terminal drop
early
late
g
g
f
80
90
b
b
a
b
b
b
d
e
f
d
d
e
g
e
g
g
c
d
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
f
g
g
g
26
Appendix Table 2b P(S to S)
appendix table 2b, stay sick (XTLOGIT)
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
a
70
a
a
a
a
a
a
a
f>m
b
80
c
90
b
b
b
c
c
c
b
b
b
b
b
b
sig drop
c
c
c
c
c
c
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
signs
n
n,n
n
n
n
n
n
n,n
n,p
n,n
n,p
n,p
n
n,p
male
male
HOSP
HOSP
BED
BED
SPL
SPL
DEP
DEP
ADL
ADL
FLW
FLW
EXSTR
EXSTR
EVGG
EVGG
n
n,n
TWLK
TWLK
IADL
IADL
COG
COG
BLK
BLK
n
n,n
a, b, c, women more likely to stay sick n=negative
p=pos
ns = not significant
27
sig
f
ns,ns
ns,ns
n,ns
ns,ns
n,ns
ns,ns
n,ns
n,n
n,p
n,ns
n,p
n,ns
m same
ns,ns
x
ns,ns
x
ns,ns
0
ns,ns
x
ns,ns
0
ns,ns
x
ns,ns
0
ns,ns
0
n,p
x
n.ns
x
n,ns
0
n,ns
x
ns,ns
ns,ns
ns,ns
ns,ns
ns,ns
ns,ns
ns,ns
ns,ns
n,p
n.ns
n,ns
n,ns
x, m=f
Appendix Table 3a P(H to H)
appendix table 3A, maintaining health (XTLOGIT)
F>M
b
a
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
70
A
c
80
B
F<M
e
d
90
70
f
80
90
C
D
D
E
E
D
E
F
D
D
E
E
F
D
E
C
A
terminal drop
terminal drop
early
late
g
H
B
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
28
Appendix table 3b, xtlogit analysis of P(H to S)
appendix table 3B, get sick (based on table 3) (XTLOGIT)
F>M
M>F
a
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
b
70
c
80
d
90
70
D
A
A
A
A
B
B
B
B
e
f
80
E
C
terminal drop
terminal drop
early
late
g
H
90
F
H
C
H
A
B
A
A
B
B
C
C
C
C
D
A
H
B
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
H
H
29
Appendix Table 4, Mystery of Sex Differences
table4_mystery_08.xlsx
Young Old
d (65-74)
Old Old (75-84)
Oldest Old (85-94)
f
d
w
q prev_equil
k
d
w
q
k
prev_equil
d
w
q
k
p_eq
HP 0.65
4.4 9.01 9.65 0.91 0.59 2.86 5.91 6.62 0.87 0.54 2.06 4.12 4.96 0.83
BD 0.58
6.4 12.29 13.78 0.93 0.51 4.43 7.66 9.65 0.91 0.49 3.00 4.11 6.62 0.87
SPL 0.25
0.9 2.54 2.66 0.73 0.16 0.46 1.67 1.83 0.65 0.09 0.17 0.88 1.13 0.53
DP 0.26
1.2 3.14 3.33 0.77 0.20 0.72 2.05 2.33 0.70 0.14 0.37 1.05 1.46 0.59
XD 0.31
1.8 4.01 4.42 0.82 0.18 0.65 1.83 2.14 0.68 0.02 0.04 0.63 0.84 0.46
FLW 0.41
5.7 10.20 12.25 0.92 0.36 3.13 5.05 6.98 0.87 0.32 1.51 1.67 3.50 0.78
XS 0.17
0.5 1.87 1.95 0.66 0.05 0.12 1.08 1.17 0.54 -0.07 -0.12 0.46 0.57 0.36
VG 0.26
1.4 3.36 3.67 0.79 0.17 0.61 1.81 2.09 0.68 0.12 0.27 1.05 1.33 0.57
TW 0.15
0.4 1.72 1.82 0.64 -0.08 -0.14 0.58 0.63 0.39 -0.30 -0.34 0.13 0.15 0.13
YD 0.17
0.6 2.00 2.13 0.68 0.04 0.11 1.04 1.13 0.53 -0.13 -0.18 0.45 0.51 0.34
CG 0.16
0.6 2.13 2.23 0.69 0.03 0.07 0.94 1.05 0.51 -0.16 -0.27 0.23 0.29 0.22
BK -0.19 -0.3 0.40 0.42 0.29 -0.33 -0.37 0.19 0.20 0.17 -0.40 -0.41 0.05 0.06 0.05
pain -0.06 -0.1 0.79 0.79 0.44 -0.07 -0.12 0.76 0.76 0.43 -0.01 -0.02 0.96 0.96 0.49
leveille
0.18
0.2 0.58 1.01 0.50 0.01 0.01 0.67 0.83 0.45 -0.25 -0.30 0.13 0.16 0.14
m
dw
q
k
prev_equil
d
w
q
k
d
w
q
k
prev
HP 0.60
3.0 6.44 7.01 0.88 0.57 2.46 4.81 5.75 0.85 0.53 1.72 3.17 4.19 0.81
BD 0.59
9.1 15.14 19.01 0.95 0.57 6.73 7.84 14.02 0.93 0.51 3.83 3.87 8.13 0.89
SPL 0.33
1.3 3.34 3.62 0.78 0.26 0.83 2.04 2.47 0.71 0.18 0.42 1.16 1.58 0.61
DP 0.36
2.3 4.78 5.50 0.85 0.30 1.37 2.49 3.45 0.78 0.19 0.58 1.08 1.77 0.64
XD 0.33
2.7 4.99 6.18 0.86 0.26 1.21 2.13 3.11 0.76 0.12 0.33 0.75 1.26 0.56
FLW 0.40
6.5 9.48 13.69 0.93 0.40 3.72 3.75 7.92 0.89 0.36 1.80 1.50 3.98 0.80
XS 0.33
2.0 4.43 4.91 0.83 0.29 1.17 2.46 3.13 0.76 0.17 0.44 0.99 1.53 0.60
VG 0.29
1.6 3.41 3.96 0.80 0.22 0.79 1.84 2.37 0.70 0.16 0.42 0.94 1.48 0.60
TW 0.24
0.9 2.52 2.73 0.73 0.06 0.15 0.96 1.14 0.53 -0.15 -0.22 0.23 0.30 0.23
YD 0.29
1.3 3.01 3.44 0.77 0.17 0.52 1.48 1.85 0.65 0.00 0.00 0.56 0.74 0.43
CG 0.15
0.5 1.78 1.89 0.65 0.04 0.10 0.91 1.05 0.51 -0.16 -0.24 0.22 0.28 0.22
BK -0.03 -0.1 0.79 0.83 0.45 -0.16 -0.22 0.40 0.45 0.31 -0.23 -0.26 0.18 0.24 0.19
pain 0.06
0.1 1.23 1.25 0.56 0.05 0.11 1.22 1.22 0.55 0.09 0.23 1.50 1.47 0.60
leveille 0.36
2.5 4.11 5.74 0.85 0.20 0.63 1.28 1.92 0.66 -0.06 -0.08 0.30 0.47 0.32
female minus male
female minus male
female minus male
f Minus M=
d
w
q prev_equil
k
d
w
q prev_equil
k
d
w
q
k p_eq
HP 0.1
1.3 2.57 2.64 0.03 0.0 0.40 1.10 0.87 0.02 0.0 0.35 0.95 0.77 0.02
BD 0.0
-2.7 -2.84 -5.24 -0.02 -0.1 -2.30 -0.18 -4.37 -0.03 0.0 -0.83 0.23 -1.52 -0.02
0.11 -0.1
-0.5 -0.79 -0.95 -0.06 -0.1 -0.37 -0.37 -0.64 -0.07 -0.1 -0.25 -0.27 -0.45 -0.08
DP -0.1
-1.1 -1.64 -2.17 -0.08 -0.1 -0.64 -0.45 -1.13 -0.08 0.0 -0.21 -0.02 -0.31 -0.05
XD 0.0
-0.9 -0.98 -1.76 -0.05 -0.1 -0.57 -0.30 -0.97 -0.07 -0.1 -0.29 -0.12 -0.43 -0.10
FLW 0.0
-0.8 0.72 -1.45 -0.01 0.0 -0.59 1.30 -0.94 -0.01 0.0 -0.29 0.17 -0.49 -0.02
XS -0.2
-1.5 -2.56 -2.96 -0.17 -0.2 -1.05 -1.38 -1.96 -0.22 -0.2 -0.56 -0.53 -0.96 -0.24
VG 0.0
-0.2 -0.05 -0.29 -0.01 0.0 -0.18 -0.03 -0.27 -0.03 0.0 -0.16 0.11 -0.16 -0.03
TW -0.1
-0.5 -0.80 -0.91 -0.09 -0.1 -0.29 -0.38 -0.51 -0.15 -0.2 -0.11 -0.10 -0.15 -0.10
YD -0.1
-0.7 -1.01 -1.32 -0.09 -0.1 -0.42 -0.43 -0.71 -0.12 -0.1 -0.18 -0.11 -0.23 -0.09
CG 0.0
0.2 0.35 0.34 0.04 0.0 -0.02 0.03 -0.01 0.00 0.0 -0.02 0.02 0.01 0.00
BK -0.2
-0.2 -0.39 -0.42 -0.16 -0.2 -0.15 -0.21 -0.25 -0.14 -0.2 -0.15 -0.13 -0.18 -0.14
pain -0.1
-0.2 -0.44 -0.47 -0.12 -0.1 -0.23 -0.46 -0.46 -0.12 -0.1 -0.25 -0.54 -0.51 -0.11
leveille -0.2
-2.3 -3.53 -4.73 -0.35 -0.2 -0.62 -0.61 -1.09 -0.20 -0.2 -0.23 -0.17 -0.31 -0.18
30
Table 4b prev_obs – prev_equil
ADL looks bad, especially for age 90. Sample size?
others agree within 2 percentage points
Observed almost always > equilibrium
OBSERVED MINUS EQUILIBRIUM
F
M
70
80
90
70
80
90
HOSP: No hospital days
0.0068
BED: No bed days
0.0104
SPL: Satisfied with Purpose of Life 0.0298
DEP: Not depressed
0.0329
ADL: No ADL difficulties
0.0473
FLW: Feel life is worthwhile
0.0193
EXSTR: Good extremity strength 0.0149
EVGG: Exc/ Very Good/ Good health
0.0035
TWLK: Walk 10 feet < 10 seconds -0.0017
IADL: No IADL difficulties
0.0380
COG: 3MSE > 90
0.0185
BLK: Walked 4+ blocks per day
0.0401
0.0090
0.0165
0.0515
0.0392
0.0792
0.0352
0.0375
0.0316
0.0593
0.0557
0.0351
0.0428
0.0171
0.0246
0.0670
0.0503
0.1111
0.0580
0.0576
0.0363
0.0350
0.0565
0.0527
0.0303
0.0051
0.0089
0.0237
0.0295
0.0411
0.0213
0.0155
0.0016
0.0068
0.0340
0.0184
0.0228
0.0046
0.0121
0.0393
0.0385
0.0702
0.0293
0.0299
0.0331
0.0535
0.0558
0.0178
0.0676
0.0095
0.0227
0.0618
0.0711
0.1183
0.0569
0.0491
0.0494
0.0674
0.0814
0.0371
0.0317
31
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
APPENDIX TABLE 5
PROBABILITY DIFFERENCES F MINUS M TABLE 3 SHEET 2
FEMALE MINUS MALE PROBS FOR HEALTHY FOLKS TABLE 3
Young Old (65-74)
Old Old (75-84)
Oldest Old (85-94)
P(H)
P(S)
P(D)
P(H)
P(S)
P(D)
P(H)
P(S)
P(D)
0.033
-0.023
-0.010
0.026
-0.014
-0.012
0.047
-0.024
-0.022
-0.001
0.012
-0.011
-0.001
0.016
-0.015
0.022
0.015
-0.037
-0.011
0.022
-0.010
-0.013
0.023
-0.010
-0.014
0.056
-0.041
-0.022
0.032
-0.010
-0.021
0.031
-0.010
0.005
0.030
-0.035
-0.017
0.027
-0.011
-0.019
0.030
-0.012
-0.027
0.060
-0.032
0.005
0.005
-0.011
0.007
0.004
-0.011
0.030
0.005
-0.035
-0.072
0.084
-0.012
-0.077
0.090
-0.013
-0.074
0.105
-0.031
0.009
-0.054
-0.007
0.007
0.027
-0.011
-0.016
-0.051
-0.023
-0.024
0.036
-0.012
-0.046
0.057
-0.011
-0.075
0.110
-0.035
-0.027
0.036
-0.009
-0.039
0.047
-0.007
-0.035
0.051
-0.016
0.033
-0.024
-0.010
0.026
-0.015
-0.011
0.048
-0.030
-0.018
0.020
0.024
-0.012
0.014
0.029
-0.026
0.012
0.040
-0.037
-0.074
-0.004
-0.012
-0.084
-0.011
-0.011
-0.055
-0.011
0.001
-0.040
0.060
-0.020
-0.040
0.060
-0.020
0.030
0.040
-0.070
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
FEMALE MINUS MALE PROBS FOR THE SICK
TABLE 2
Young Old (65-74)
Old Old (75-84)
Oldest Old (85-94)
P(H)
P(S)
P(D)
P(H)
P(S)
P(D)
P(H)
P(S)
P(D)
0.045
-0.024
-0.022
0.045
0.012
-0.057
0.046
0.040
-0.086
0.056
0.017
-0.073
0.114
0.052
-0.166
0.078
0.040
-0.118
-0.043
0.073
-0.030
-0.018
0.078
-0.061
-0.008
0.072
-0.064
-0.028
0.077
-0.049
0.015
0.074
-0.089
0.028
0.052
-0.080
0.049
0.003
-0.052
0.023
0.064
-0.088
0.017
0.073
-0.090
0.077
-0.007
-0.070
0.091
0.044
-0.134
0.025
0.076
-0.100
-0.054
0.094
-0.040
-0.076
0.161
-0.085
-0.056
0.172
-0.116
-0.009
0.046
-0.036
0.003
0.052
-0.054
0.061
0.021
-0.082
-0.045
0.070
-0.025
-0.050
0.096
-0.046
-0.019
0.077
-0.058
-0.041
0.084
-0.043
-0.022
0.088
-0.066
-0.010
0.089
-0.079
0.003
0.014
-0.018
-0.007
0.037
-0.030
-0.001
0.046
-0.045
-0.027
0.041
-0.014
-0.018
0.029
-0.011
0.017
0.027
-0.044
-0.068
0.086
-0.018
-0.058
0.092
-0.035
-0.053
0.116
-0.062
-0.040
0.060
-0.020
-0.040
0.060
-0.020
0.030
0.040
-0.070
32
APPENDIX TABLE 6
PROBABILITY OF GETTING SICK
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
TABLE3_TESTS_SHEET 2
GET SICK
Young OldOld
(65-74)
Old (75-84)
Oldest Old (85-94)
P(H)
P(H)
P(H)
dif 70-80 dif 80-90 dif-dif
0.075
0.102
0.130
-0.027
-0.028
0.000
0.045
0.058
0.082
-0.013
-0.024
0.010
0.145
0.178
0.266
-0.034
-0.088
0.054
0.110
0.140
0.192
-0.030
-0.053
0.023
0.090
0.138
0.238
-0.049
-0.100
0.052
0.036
0.058
0.105
-0.021
-0.048
0.026
0.167
0.214
0.304
-0.047
-0.090
0.043
0.296
0.370
0.395
-0.074
-0.025
-0.049
0.170
0.272
0.453
-0.102
-0.180
0.078
0.147
0.211
0.349
-0.064
-0.137
0.073
0.129
0.180
0.299
-0.051
-0.119
0.068
0.252
0.273
0.312
-0.021
-0.039
0.019
0.013
0.011
0.027
0.002
-0.017
0.019
0.280
0.290
0.240
-0.010
0.050
-0.060
0.098
0.033
0.123
0.078
0.062
0.031
0.083
0.350
0.134
0.111
0.153
0.228
0.017
0.220
0.116
0.042
0.155
0.109
0.108
0.053
0.124
0.343
0.216
0.165
0.195
0.244
0.021
0.230
0.154
0.066
0.210
0.163
0.179
0.101
0.198
0.446
0.343
0.298
0.329
0.272
0.038
0.200
-0.018
-0.009
-0.032
-0.031
-0.045
-0.022
-0.041
0.007
-0.082
-0.053
-0.042
-0.016
-0.004
-0.010
33
-0.038
-0.024
-0.055
-0.054
-0.071
-0.047
-0.074
-0.103
-0.127
-0.134
-0.134
-0.028
-0.017
0.030
0.020
0.015
0.024
0.023
0.026
0.025
0.033
0.110
0.046
0.080
0.092
0.012
0.013
-0.040
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
HP
BD
SPL
DP
XD
FLW
XS
VG
TW
YD
CG
FH
BK
pain
APPENDIX TABLE 7 FROM TABLE2_TESTS SHEET 2
PROBABILITY OF STAYING SICK BY AGE
Young OldOld
(65-74)
Old (75-84)
Oldest Old (85-94)
P(S)
P(S)
P(S)
dif 70-80 dif 80-90 dif-dif
0.262
0.290
0.267
-0.028
0.023
-0.051
0.370
0.408
0.369
-0.038
0.039
-0.077
0.601
0.640
0.607
-0.039
0.033
-0.071
0.620
0.642
0.628
-0.021
0.014
-0.035
0.589
0.667
0.703
-0.078
-0.036
-0.042
0.541
0.562
0.532
-0.021
0.030
-0.051
0.661
0.717
0.736
-0.057
-0.018
-0.038
0.644
0.674
0.608
-0.030
0.067
-0.097
0.678
0.795
0.841
-0.117
-0.046
-0.071
0.674
0.727
0.732
-0.054
-0.005
-0.049
0.700
0.779
0.825
-0.079
-0.046
-0.034
0.766
0.723
0.687
0.043
0.036
0.007
0.842
0.878
0.884
-0.036
-0.006
-0.030
0.280
0.290
0.240
-0.010
0.050
-0.060
0.286
0.353
0.528
0.543
0.586
0.548
0.566
0.598
0.609
0.590
0.685
0.725
0.756
0.220
0.278
0.356
0.562
0.568
0.603
0.518
0.556
0.623
0.699
0.639
0.742
0.694
0.786
0.230
0.227
0.329
0.535
0.576
0.630
0.456
0.563
0.586
0.764
0.643
0.779
0.660
0.769
0.200
0.008
-0.003
-0.033
-0.025
-0.017
0.030
0.010
-0.024
-0.091
-0.049
-0.057
0.031
-0.030
-0.010
34
0.051
0.027
0.027
-0.008
-0.027
0.062
-0.007
0.036
-0.065
-0.004
-0.037
0.034
0.017
0.030
-0.043
-0.030
-0.060
-0.017
0.010
-0.032
0.017
-0.061
-0.026
-0.045
-0.020
-0.003
-0.047
-0.040
appendix table 8
all_6_probs SUMMARY OF SEX RESULTS
FEMALE MINUS MALE
0
PLUS
MINUS
65-74
P(H)
4
8
P(S)
10
2
Sick
Old Old (75-84)
P(D)
P(H)
0
5
12
7
P(S)
8
4
18
6
P(S)
12
0
Healthy
Old Old (75-84)
P(D)
P(H)
0
4
12
8
0
24
2
Oldest Old (85-94)
P(S)
P(D)
P(H)
12
0
6
0
12
6
FEMALE MINUS MALE
Young Old (65-74)
0
P(H)
PLUS
4
MINUS
8
A
sumplus
8
summinus
16
panel
5/21/2011
9
15
P(D)
0
12
5
P(S)
9
3
P(D)
0
12
85-94
P(H)
5
7
P(S)
8
4
P(D)
1
11
21
3
0
24
11
13
20
4
1
23
8
Differences between healthy and sick (Sick minus Healthy)
F minus M
65-74
Old Old (75-84)
B
P(H)
P(S)
P(D)
P(H)
P(S)
PLUS
6
9
0
8
12
MINUS
6
3
12
4
0
P(D) higher for men 24, 24,A23 cases =
P(S) higher for F 18,21, 20 =
S
H
S
H
P(H) is mixed, men higher
original probabilities
Sick Minus Healthy
65-74
0
P(H)
PLUS
0
MINUS
12
PLUS
0
MINUS
12
resilience_25.sps 4-23-2011
0
sumplus
0
summin
24
34
25
21
23
P(D)
0
12
85-94
P(H)
9
3
71
59
of 72
of 72
44
of 72
P(S)
11
1
P(D)
0
12
7
P(S)
12
0
12
0
0
24
0
Old Old (75-84)
P(D)
P(H)
12
0
0
12
12
0
0
12
0
0
24
0
0
24
P(S)
12
0
12
0
0
24
0
35
Oldest Old (85-94)
P(D)
P(H)
12
0
0
12
12
0
0
12
0
0
24
0
0
24
P(S)
12
0
12
0
0
24
0
P(D)
12
0
12
0
0
24
0
Appendix Table 9 summary of age results
Appendix Table 9
all_6_probs
SUMMARY OF AGE RESTULTS
0
panel
5/21/2011
AGE
Sick
differences
3
PLUS
MINUS
PLUS
MINUS
P(H)
DROP1
70-80
11
1
11
1
sumplus
summinus
22
2
F
M
DROP2
80-90
DROPDROP
12
6
0
6
12
8
0
4
24
0
14
10
P(S)
DROP1
70-80
0
12
3
9
3
21
12
12
2
22
DROP2
80-90
0
12
0
12
DIF
12
0
10
2
0
24
0
24
22
2
Healthy
F
M
PLUS
MINUS
PLUS
MINUS
P(H)
DROP1
70-80
12
0
12
0
age differences
P(S)
DROP2
DROP1
80-90
DROPDROP
70-80
12
1
1
0
11
11
12
1
1
0
11
11
DROP2
80-90
DROPDROP
6
1
6
11
6
1
6
11
P(D)
DROP1
70-80
0
12
0
12
6
DROP2
80-90
DROPDROP
0
11
12
1
0
12
12
0
P(D)
DROP1
70-80
0
12
0
12
DROP2
80-90
1
11
0
12
DIF
11
1
12
0
sumplus
summinus
24
24
2
22
2
22
0
24
23
1
0
24
1
23
23
1
plusall
minusall
46
2
48
0
16
32
5
43
12
36
25
23
0
48
1
47
45
3
DROP2
80-90
0
12
0
12
12
0
7
5
0
24
19
5
sick minus healthy
P(H)
DROP1
70-80
F
PLUS
10
MINUS
2
M
PLUS
11
MINUS
1
sumplus
summinus
21
3
age diffs
DROP2
0
80-90
DROPDROP
4
11
8
1
1
11
11
1
5
19
22
2
DROP1
70-80
4
8
7
5
DROP2
80-90
12
0
12
0
0
12
0
12
P(D)
DROP1
70-80
0
12
0
12
11
13
24
0
0
24
0
24
36
Appendix Table 10 (was), summary for sex
TABLE 4
SUMMARY OF SEX RESULTS, OVER 12 HEALTH VARIABLES
1
2
3
4
5
6
7
8
9
10
11
12
SEX
Probabilities
start sick
1
F>M
2
F<M
3
4
start healthy
F>M
F<M
5
6
sum over initial state
F>M
F<M
70
80
90
P(H) P(S) P(D) P(H) P(S) P(D) P(H) P(S) P(D)
4 10
0
5 12
0
6 12
0
8
2 12
7
0 12
6
0 12
P(H) P(S) P(D) P(H) P(S) P(D) P(H) P(S) P(D)
4
8
0
4
9
0
5
8
1
8
4 12
8
3 12
7
4 11
8
16
18
6
all_6_probs….
sheet 3
all_6_probs_plusprev
0
24
9
15
21
3
0
24
11
13
20
4
1
23
sum over age
P(H) P(S) P(D)
15 34
0
21
2 36
13
23
25
11
1
35
28
44
59
13
1
71
Bolded cells significant by the sign test (p<.01).
critical vals. are 11/12, 19/24, 27/36, 48/72, 34/48
37
Appendix Table 11 (was Table 5), Summary for Age Results
Table 5
SUMMARY OF AGE RESULTS, OVER 12 HEALTH VARIABLES
1
Probabilities
sick
5
6
11
12
13
14
F
PLUS
MINUS
M PLUS
MINUS
F+M
7 healthy
8
9
10
S+H
3
4
P(H)
SEX
1
2
3
4
2
PLUS
MINUS
F
PLUS
MINUS
M PLUS
MINUS
5
6
7
P(S)
8
9
P(D)
a
b
c
a
b
c
a
b
c
70-80 80-90 b-a 70-80 80-90 b-a 70-80 80-90 b-a
11
12
6
0
6
1
0
0
12
1
0
6
12
6 11
12
12
0
11
12
8
3
6
1
0
0
10
1
0
4
9
6 11
12
12
2
0
0
0
22
24 14
3
12
2
0
0
22
2
0 10
21
12 22
24
24
2
12
0
12
0
12
0
12
0
1
11
1
11
1
11
1
11
0
12
0
12
11
1
12
0
F+M
PLUS
MINUS
24
0
24
0
2
22
2
22
0
24
23
1
all
PLUS
MINUS
46
2
48
0
16
32
5
43
12
36
25
23
0
12
0
12
0
0
24
0
0
48
1
11
0
12
0
1
23
0
1
47
11
1
12
0
0
23
1
0
45
3
Bolded cells are significant by the sign test (p<.01).
Critical vals. are 11/12, 19/24, 27/36, 48/72, 34/48
a
Age 70 minus Age 80
Positive ==> decline
b
Age 80 minus age 90
Positive ==> decline
b-a
Age (80 to 90) minus (70 to 80) Positive ==> steeper with age
all_6_probs….
sheet 3
38
Appendix Table 12 interaction of healthy and gender
appendix table 12
female
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
mean
male
HOSP
BED
SPL
DEP
ADL
FLW
EXSTR
EVGG
TWLK
IADL
COG
BLK
mean
pd:s/pd:h
70
7.74
9.31
4.67
4.67
7.83
10.90
4.14
8.62
7.83
6.23
3.55
9.19
7.06
4.64
7.64
3.60
4.83
6.05
8.38
3.62
6.34
3.42
5.45
2.59
2.64
4.93
`
does "healthy" mean the same thing wrt death for men and women?
pd:s/pd:h
F-M
F/M
80
90
70
80
90
70
80
4.96
3.00
3.101
0.125
-0.217
1.668
1.026
6.92
4.89
1.677
-1.643
0.643
1.220
0.808
3.55
4.28
1.075
-0.827
1.432
1.299
0.811
4.33
4.33
-0.168
-1.671
0.954
0.965
0.721
4.94
3.68
1.788
-1.114
0.388
1.296
0.816
7.40
6.51
2.519
-1.652
1.595
1.301
0.817
3.34
3.80
0.510
-1.483
0.032
1.141
0.692
5.15
3.70
2.279
0.019
0.038
1.359
1.004
4.41
9.32
4.416
0.119
5.845
2.292
1.028
3.12
2.48
0.780
-1.757
-0.667
1.143
0.640
3.69
3.01
0.964
0.480
0.202
1.372
1.150
5.16
3.37
6.552
1.114
-2.614
3.479
1.275
4.75
4.36
2.12
-0.69
0.64
1.54
0.90
4.84
8.57
4.38
6.00
6.05
9.05
4.82
5.13
4.29
4.88
3.21
4.05
5.44
3.22
4.25
2.85
3.37
3.29
4.91
3.77
3.66
3.48
3.15
2.81
5.98
3.73
not monotonic
always > 1, s more likely to die than h
ratio higher for women than for men in 2 age groups
39
90
0.933
1.151
1.503
1.283
1.118
1.325
1.009
1.011
2.681
0.788
1.072
0.563
1.20
Appendix Table 13, principal component/factor analysis
Total Vari ance Expl ai ned
Comp onent
1
2
3
4
5
6
7
8
9
10
11
12
Tot al
3.839
1.175
.994
.942
.819
.778
.646
.629
.594
.568
.524
.492
Initial Eigenvalues
% of Variance Cumulative %
31.990
31.990
9.790
41.779
8.280
50.059
7.851
57.910
6.828
64.738
6.485
71.223
5.382
76.604
5.240
81.845
4.949
86.794
4.733
91.526
4.371
95.897
4.103
100.000
Extraction Sums of Squared Loadings
Tot al % of Variance Cumulative %
3.839
31.990
31.990
1.175
9.790
41.779
Extraction M ethod: Princip al Component Analysis.
Component Matrixa
XD_bef
YD_bef
VG_BACK_BEF
DP_bef
FLW_bef
XS-Bef
TW_bef
SPL_bef
BD_bef
CG-bef
BK_BEF
HP_bef
Comp onent
1
2
.683
.664
.658
.630
-.369
.623
-.477
.607
.580
.388
.539
-.441
.481
.431
.416
.403
.355
Extraction M ethod: Princip al Comp onent Analy sis.
a. 2 comp onents extract ed.
40
Rot ation Sums of Squared Loadings
Tot al % of Variance Cumulative %
2.614
21.783
21.783
2.400
19.997
41.779
Rotated Component Matrixa
TW_bef
YD_bef
XD_bef
XS-Bef
BK_BEF
VG_BACK_BEF
CG-bef
FLW_bef
DP_bef
SPL_bef
BD_bef
HP_bef
Component
1
2
.690
.673
.608
.349
.606
.579
.535
.391
.451
.773
.698
.690
.546
.336
Extract ion M ethod: Princip al Component Analysis.
Rotation M ethod: Varimax with Kaiser Normalization.
a. Rotation converged in 3 iterat ions.
41
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