Education, wealth, and duration of life expected in various degrees of frailty

Abstract

Multistate life tables are used to estimate life expected in three frailty states: frailty free, mild/moderate frailty, severe frailty. Estimates are provided for the combination of education and wealth by age, stratified by sex. Data consider 17,115 cases from the Health and Retirement Study, 2000–2014. Frailty is measured using a 59 item frailty index based on deficit accumulation. Estimates are derived using stochastic population analysis for complex events. Population-based and status-based results are reported. Findings confirm a hypothesis that the combination of higher education and wealth results in longer lives in more favorable degrees of frailty. Also, as hypothesized, wealth generally affords a greater advantage than does education among those with severe frailty at baseline. For instance, high wealth provides a 70-year-old woman with severe frailty at baseline 0.70 more total years and 0.81 more frailty free years then her counterpart with low wealth, compared to gains of 0.39 and 0.54, respectively, for those with high education. Unexpectedly, wealth also has a greater role among those frailty free at baseline. A 70-year-old woman frailty free at baseline with high wealth lives 3.19 more net years and 4.13 more years frailty free than her counterpart with low wealth, while the same comparison for high versus low education indicates advantages of 2.00 total and 1.96 frailty free years. Relative change ratios also indicate more robust results for wealth versus education. In sum, there is evidence that inequality in duration of life in degrees of frailty is socially patterned.

Electronic supplementary material

The online version of this article (10.1007/s10433-020-00587-2) contains supplementary material, which is available to authorized users.

Introduction

All definitions of frailty refer to a state of physiological deterioration across multiple health domains, and increased vulnerability to adverse health outcomes including disability, poor quality of life, hospitalizations, and death (Gobbens et al. 2010a; Rockwood 2005). Those living with more severe degrees of frailty are therefore at greater risk of physical deterioration and death and in greater need of formal and informal care. The prevalence of frailty increases with age, and living with severe frailty is common among the very old, (e.g., age 85 + (Clegg et al. 2016; Fulop et al. 2010; Gobbens et al. 2010b; Jürschik et al. 2012; Rockwood 2005). Worldwide, countries are experiencing population aging, a rapid expansion in numbers, and proportions of very old, which is in part due to long-term trends in longevity (Rowland 2009). Because frailty increases with age, population aging propels a concomitant rise in prevalence of those living with higher degrees of frailty and subsequently in chronic disease, disability, functional limitation, falls, and a host of other conditions that generate frailty and therefore increase the need for formal, informal and long-term care, and institutionalization. For how long older adults can expect to live in milder and more severe degrees of frailty, and the way in which these fluctuate by risk factors, is relevant in assessing societal costs associated with population aging (Clegg et al. 2013).

Health expectancy analysis increasingly is used to assess expected years in states of health (Mathers 2002; Saito et al. 2003, 2014). Using longitudinal panel data and applying multistate life table techniques, health expectancy analysis combines morbidity and mortality into estimates of life duration in greater and lesser health states for those of a particular age, sex and given set of characteristics. Estimates of disability-free life expectancy have been particularly valuable, for instance, in investigating how total and disability-free life varies, for example, in men and women, in people of different countries and regions, or by socioeconomic status (Berthelot et al. 2002; Crimmins et al. 2016; Minicuci et al. 2004; Robine et al. 2001; Rogers et al. 1992; Solé-Auró et al. 2015; Wohland et al. 2014; Zimmer et al. 2015). Analyses of life expectancy across degrees of frailty would be similarly useful, but thus far there are few such studies. Exceptions include Romero-Ortuno et al. (2013), who compared life expectancy with and without frailty at age 70 in European countries and Herr et al. (2018), who estimated life expected in several degrees of frailty among those 70 and older enrolled in France’s supplementary pension fund. These studies showed proportion of life expected with greater degrees of frailty is greater for women than men and some cross-national variations. Apart from these studies, published estimates of life expected in different degrees of frailty are absent. None consider socioeconomic variations.

Frailty prevalence studies suggest an advantage for those with more favorable socioeconomic characteristics and those living in countries with stronger economic indicators (Andrew et al. 2008; Brothers et al. 2014; Casale-Martinez et al. 2012; Gobbens et al. 2010b; Jürschik et al. 2012; Szanton et al. 2010; Theou et al. 2013; Woo et al. 2005). Further studies of other health expectancy outcomes, particularly disability-free life expectancy, show more net and relative years of health for those with greater education and wealth or income (Cambois et al. 2001; Chris White 2010; Rogers et al. 1992; Solé-Auró et al. 2015). Our goal now is to extend prior work to analyses of heath state transitions and determine years and proportion of life expected in various degrees of frailty by age and sex. Expecting similar findings with life in degrees of frailty we hypothesize that higher education and greater wealth associate with a greater number of frailty free years, fewer years with severe frailty, and a greater proportion of life frailty free and in less severe degrees of frailty. In other words, we expect education and wealth to associate with both net (years) and relative (proportion) years in various degrees of frailty.

We also test whether education and wealth have unique roles in determining expected years in degrees of frailty. Some research has indicated that education and wealth affect the onset of disability and other health outcomes, whereas wealth is more influential in progression and recovery (Herd et al. 2007; Zimmer and House 2003). In short, different resources derived from socioeconomic standing have different consequences for health. Why this is so has not yet been closely examined; if knowledge versus money affect different stages of health transition differently, health expectancies could differ by baseline status. Therefore, we estimate two types of health expectancies. Population-based estimates provide years of life in various status of health for a total population. Status-based estimates stratify results by baseline health status. Frailty is subject to deterioration and recovery, although complete recovery from severe frailty is rare (Mitnitski et al. 2007; Rockwood and Mitnitski 2007). If education impacts onset, we expect it to be strongly associated with life expected in degrees of frailty among those not frail at baseline. If wealth impacts progression, we expect it to be strongly associated with life expected among those that have already experienced frailty, or those that are in some state of frailty at baseline.

Methods

Data

Multistate life table (MSLT) estimations of life expected in degrees of frailty require longitudinal panel data where each individual is present for at least two data collection waves and therefore contributes at least one baseline and follow-up observation, with the follow-up being either a measure of frailty or an observation of death. The probability that someone with a baseline frailty state ends up in a specific follow-up frailty state or deceased is referred to as a transition probability. If an individual is present for more than two waves of data collection, they may contribute more than one transition in order to estimate transition probabilities. Probabilities are used as inputs into MSLT calculations. Our study obtained probabilities using data from the Health and Retirement Study (HRS). We began with the sample of 17,397 aged 55 + that participated in the 2000 HRS and followed these individuals for eight biennial waves of data collection to 2014. Deleting 27 cases due to missing frailty information in 2000 and another 255 that did not die but had no follow-up frailty information, we end up with a valid sample of 17,115. This sample includes about 1,900 proxy respondents that completed questionnaires on behalf of an identified respondent. HRS records mortality using the National Death Index (NDI).

Although HRS, and its sister study AHEAD, originated in 1992 and 1993, respectively, we began with 2000 data because in that year weights began to be provided for nursing home residents. About 2½ % of the 2000 sample was living in a nursing home. About 10% not in a nursing home in 2000 moved into a nursing home at some point during the observation period. Given that nursing home residents are far frailer than are those living in the community, appraisal of frailty prevalence and life expected severely frail would be greatly underestimated if the nursing home sample was omitted. Detailed information, documentation, and data user guides for HRS can be found on their website (Health and Retirement Study 2015a, b).

Each individual was potentially observed eight times between 2000 and 2014. Each observation except for the last provides a baseline measure of frailty, with the subsequent being a follow-up. This means that any individual has the potential of being observed for seven transitions if they survive to 2014 and have no missing data, or they survive to 2012 with no missing information and die prior to 2014. In total, the aggregate data contain 87,362 transitions; 8221 of these are from a state of frailty to death, and 79,141 are from a state of frailty to a surviving state of frailty.

Measures

While the concept of frailty as a state of physical vulnerability and deterioration and as an indicator of aging and propinquity of death is accepted, there are different stylized and formalized approaches to its measurement (Dent et al. 2016; Fried et al. 2001; Rockwood and Mitnitski 2011). We employed the common deficit accumulation approach (Mitnitski et al. 2001; Rockwood and Howlett 2019; Rockwood and Mitnitski 2007). Deficits are indicators representing multifactorial domains of health. Multiple items for each domain are first dichotomized as being present or not, with 59 dichotomized items in total. The frailty index score (FI) is then calculated as the proportion of deficits reported (therefore ranging from 0.00 to 1.00). The domains (and number of items used for each in parentheses) are: medical conditions, symptoms, and procedures (13), system utilization (11), functional limitation (9), activities of daily lving (6), receiving assistance with activities of daily living (6), instrumental activities of daily living (4), medication use (4), sensory problems (3) equipment use (2) and a global measure of health (1). An FI was calculated for an individual in a given wave as long as valid responses existed for 80% of the deficit items. The FI is a continuous measure between 0 and 1, but MSLT approaches require that we distinguish frailty states and therefore we divide the resultant FI into categories as follows: frailty free (0.00–0.19), mild/moderate frailty (0.20–0.39), and severe frailty (0.40–1.00). Note that the theoretical limit of the index is 1.00, but because frailty and mortality are linked, it is rare to see very high scores; here only four cases have FI scores above 0.80 in the 2000 baseline data. Although there is no single standard cut-off for defining frailty states using the deficit accumulation approach, these divisions—which are data dependent—are roughly consistent with other studies that have attempted to match this approach with other discrete measures of frailty (Kulminski et al. 2008; Romero-Ortuno 2013).

Other variables in the models include age, sex, education, and wealth. Age was calculated using date of birth and date of interview. Sex was coded as male or female. HRS provides education codes, which we divided into three categories: did not complete high school; completed high school or equivalent (general educational development or GED); some or completed college. A wealth measure was constructed using HRS wealth imputation files (Bugliari et al. 2019; Pantoja et al. 2016). The imputation combines savings, goods, stocks, mutual funds, and other assets except for the house in which the individual resides. We determine the average wealth for each individual across waves by first converting each wave to the 2014 dollar value equivalent using the consumer price index (Bureau of Labor Staistics 2014). This was then divided into tertiles and labeled low, mid or high wealth. Based on 2014 standard dollar values, low is those with under about $25,000, high is over about $200,000, and mid wealth is in between. In part of our analysis, we compare the strength of associations of education versus wealth with duration of life in degrees of frailty. While categories of education and wealth are not strictly comparable, Table 1, which provides distributions for study variables, shows that there is a relatively good distribution for both men and women across categories of education and income.

Table 1.

Distribution of study variables at wave 1, stratified by sex

	Women	Men
N	9763	7352
Frailty status
Frailty free	64.6	75.9
With mild/moderate frailty	25.8	18.6
With severe frailty	9.6	5.5
Total	100.0	100.0
Age
55–59	21.0	25.2
60–64	16.8	19.0
65–69	15.9	16.9
70–74	15.0	14.6
75–79	13.0	12.2
80–84	9.8	7.4
85+	8.5	4.7
Total	100.0	100.0
Education
Less than high-school	32.9	23.1
Completed high-school or GED	33.6	34.5
Some or completed college	33.5	42.3
Total	100.0	100.0
Wealtha
Low (< $25,000)	24.3	22.9
Middle ($25,000-$200,000)	39.2	32.7
High (> $200,000)	36.5	44.4
Total	100.0	100.0
Combined education and wealth
Less than high school and low wealth	17.4	13.1
Less than high school and mid wealth	6.9	8.3
Less than high school and high wealth	2.6	3.9
Completed high school (or GED) and low wealth	12.0	7.7
Completed high school (or GED) and mid wealth	14.9	13.3
Completed high school (or GED) and high wealth	11.5	11.5
Some or completed college and low wealth	6.3	4.8
Some or completed college and mid wealth	11.1	12.8
Some or completed college and high wealth	17.2	24.6
Total	100.0	100.0

^aBased on 2014 standard dollar values

We analyzed the combined effects of education and wealth and therefore present results across nine categories. Conceptually, the lowest socioeconomic category is a combination of those with less than completed high school and low wealth; the highest is those with some or completed college and high wealth. The distribution of these categories, as well as the distribution of age and frailty status in the year 2000, stratified by sex, is provided in Table 1. Age in this table is categorized into five-year age groups, although for MSLT calculations we use single years. Except for N’s reported in this table, all results that follow apply HRS weights, which allow the findings to be representative of the population aged 55+.

Analytical strategy

We present estimates for years of total life expected (Total) divided into frailty free (FF) life expectancy, mild/moderate frailty (MMF) life expectancy, and severe frailty (SF) life expectancy, by sex, across nine categories that combine three levels of education and three levels of wealth. We also show the percentage of life expected FF, MMF, and SF. In this way, we provide estimates for the net years and relative proportion of years expected in different states.

To provide an interpretation of results which facilitates comparison of education versus wealth, we use the life expectancy estimates to derive two additional summary measures. First, we calculate the net change in years, which is the difference in life expectancy estimates between highest and lowest levels of education or wealth holding the other measure constant. For education, we subtract estimated years expected for those with less than high school from years expected for those with college education among those with mid-level wealth; for wealth, we subtract estimates for low from high for those with competed high school education. Net change does not always provide a full understanding of the association since this can be interpreted relative to estimated number of years expected. For instance, those with severe frailty at a given age will live many fewer years in total than those frailty free at the same age. A one-year gain in total years of life will mean a greater relative change among those shorter as opposed to longer lived. Therefore, we present the relative change ratio as a second summary measure, which is calculated as the expected number of years in the highest level of education or wealth divided by number of years in the lowest level, holding the other measure constant at its mid-level. Ratios greater than one indicate that higher education or wealth increase total years or years in a given frailty state, and the larger the ratio the greater the relative association. For instance, a ratio of say 1.10 relates to a 10% increase in relative number of years, while a ratio of 2.00 relates to a 100% increase or doubling in relative number of years.

Computations are presented for two types of estimates. The first is population-based, which consider all observations regardless of baseline frailty state. Population-based results are the most commonly reported results in analyses of health expectancy. To evaluate whether education or wealth associate differently with onset versus progression of life expected in degrees of frailty, we also present status-based results. These stratify estimates by baseline frailty state. To provide the most unambiguous contrast, we compare results for two groups: those that are frailty free and those living with severe frailty at baseline. If, as hypothesized, education mostly associates with onset while wealth has a greater association with progression, we would expect status-based findings to show education associating strongly among those frailty free at baseline and wealth associating more strongly among those with severe frailty at baseline.

We computed these estimates using the stochastic population analysis for complex events (SPACE) software (Cai et al. 2010; Chiu 2018). SPACE involves a two-step procedure. First, is an estimation of the annual probability of making a transition from a baseline frailty state to a follow-up state, or being deceased by follow-up, with the sum of the probabilities from any baseline state equal to 1. Second, probabilities are used as inputs for micro simulation to estimate MSLT functions. Transition probabilities are derived using a multinomial logistic regression model. The multinomial equations assume transitions are a function of age, education, wealth, and the interaction of education by wealth, stratified by sex. Supplementary Materials (Supp Table 1) show unadjusted probability transitions from baseline to follow-up states, and these run-in expected directions. For instance, the probability of being frailty free at follow-up depends greatly on being frailty free at baseline, while the probability of dying increases substantially with increasingly severe frailty states.

The simulation takes a hypothetical cohort of 100,000, applies an initial frailty status based on the baseline probability of being frailty free, or living with mild/moderate frailty or severe frailty, and applies annual transition probabilities to each hypothetical person, who is tracked year by year until death. Summary statistics for simulations result in total, FF, MMF, and SF estimates. For each estimate, a standard error is calculated with a bootstrapping method. This study uses a bootstrap of 100, which through experience is deemed sufficient to produce stable standard errors.

SPACE has several advantages over other MSLT approaches (Saito et al. 2014). First, similar to MSM in R, it allows specific transition probabilities to be set to zero. This is necessary since the data show the probability of moving from severe frailty to frailty free is near zero (see Supp Table 1). Second, SPACE provides flexibility in controlling for covariates. Third, its bootstrapping procedure allows for standard errors and confidence intervals to be estimated both for point estimates and differences in estimates across characteristics. SPACE is a recent addition to the suite of MSLT approaches but has already been used effectively in health expectancy studies (Chiu et al. 2019; Tareque et al. 2019).

We show our main results only for those aged 70, which is close to the mean age in wave 1. Patterns for those at other ages run in parallel to those aged 70. Complete results showing life expectancy estimates, proportion of life expected in each state, and 95% confidence intervals, are provided in Supplementary Materials (Supp Tables 2, 3 and 4, respectively).

Results

Years and percentage of life expected in frailty states

The prevalence of frailty free, mild/moderate, and severe frailty varies by age and sex (percentages in frailty states at baseline by age and sex shown in Supp. Table 5). This is seen in Fig. 1, which presents SPACE estimates for frailty state-specific expectancies and percentage of remaining life expected in each frailty state by age, stratified by sex, for the total population. The height of stacked bars indicates total life expectancy. For example, for a woman 55 years of age it is about 28 years and for a man aged 55 it is about 24 years. Total years and years frailty free decline precipitously with age, while years living with severe frailty remain fairly steady. This translates into the percentage of life expected with severe frailty increasing with age for both sexes, while the percentage frailty free drops. For instance, a woman age 55 can expect to live about 60% of her remaining 28 years of life frailty free, about 30% with mild/moderate frailty, and about 10% with severe frailty. If she survives to age 90, she can expect a little more than 5 additional years of life of which a little less than 20% is frailty free, 40% with mild/moderate frailty, and another 41% with severe frailty. Of his 24 years of life expectancy, a 55-year-old man can expect about 71% frailty free, 23% with mild/moderate frailty and only about 6% with severe frailty. At age 90 a man can expect to live a little over 4 years of life of which 28% is expected frailty free, 42% with mild/moderate frailty, and 29% with severe frailty. See Supplementary Materials (Supp Table 5) for more specific details related to Fig. 1.

Fig. 1.

Population-based estimates for years and proportion of life in each frailty state by age stratified by sex

Life expected in frailty-states by education and wealth: population-based estimates

Table 2 shows population-based estimates for total life expectancy and frailty state-specific expectancy for those aged 70 across a combination of education and wealth categories. The table demonstrates that higher levels of education and wealth individually and in combination associate with more total years of life, more years and percentage of life frailty free, and fewer years and percentage of life with severe frailty. For heuristic purposes, we concentrate our comparisons between the lowest combination of education and wealth (less than completed high school and low wealth) and the highest (some or completed college and high wealth). Women with the lowest levels of education and wealth are expected to live 12.48 years (SE 0.23), or until age 82.48. For those with a combination of highest education and wealth the total life expectancy is 18.38 (SE 0.30), almost a six-year life expectancy advantage. Frailty free life expectancies are also much higher for those with high versus low wealth and education. Women that have both less than high school education and low wealth can expect only 3.77 (SE 0.15) frailty free years, compared to 10.61 (SE 0.28) for women that have both some or completed college education and high wealth, whereas men can expect fewer total years of life, associations with education and wealth are similar. For instance, a 70-year-old man with the combination of both less than high school education and low wealth can expect 10.31 (SE 0.28) years of life, of which 4.26 (SE 0.22) are frailty free. His counterpart with both some or completed college education and high wealth can expect 15.96 more years (SE 0.29), 10.58 (SE 0.26) being frailty free. Although years expected to be lived with mild/moderate or severe frailty vary as well, net differences are less. For instance, years expected with severe frailty for a 70-year-old woman ranges from a high of 3.50 (SE 0.15) if she has both the lowest levels of education and wealth to a low of 1.96 (SE 0.13) among those with high wealth who have completed high school.

Table 2.

Population-based multistate life table estimates for those aged 70 by education and wealth, stratified by sex, showing life expectancy with standard errors in parentheses and percentage of life expected, in each state

Education	Less than high school			Completed high school or GED			Some or completed college
Wealth	Low	Mid	High	Low	Mid	High	Low	Mid	High
Life expectancy
Women
FF	3.77 (.15)	5.37 (.30)	7.68 (.56)	4.31 (.22)	7.11(.27)	9.50 (.31)	5.03 (.38)	7.98 (.27)	10.61 (.28)
MMF	5.21 (.17)	6.11 (.29)	5.95 (.51)	5.71 (.21)	6.72 (.24)	5.60 (.27)	5.78 (.32)	6.38 (.27)	5.50 (.19)
SF	3.50 (.15)	2.75 (.20)	2.69 (.42)	3.09 (.19)	2.51 (.18)	1.96 (.13)	2.96 (.26)	2.20 (.19)	2.27 (.17)
Total	12.48 (.23)	14.23 (.39)	16.31 (.72)	13.11 (.28)	16.34 (.30)	17.06 (.37)	13.78 (.48)	16.56 (.36)	18.38 (.30)
Men
FF	4.26 (.22)	6.01 (.28)	7.80 (.43)	4.57 (.29)	6.98 (.24)	9.22 (.39)	5.34 (.47)	7.98 (.30)	10.58 (.26)
MMF	3.98 (.17)	4.58 (.25)	4.64 (.34)	4.16 (.27)	4.70 (.22)	4.44 (.23)	3.41 (.30)	4.41 (.28)	4.14 (.18)
SF	2.07 (.15)	1.44 (.11)	1.06 (.21)	1.53 (.17)	1.33 (.13)	1.18 (.13)	1.76 (.24)	1.23 (.12)	1.24 (.11)
Total	10.31 (.28)	12.04 (.35)	13.49 (.47)	10.26 (.43)	13.00 (.32)	14.83 (.39)	10.51 (.55)	13.62 (.36)	15.96 (.29)
Percentage of life
Women
FF	30.2	37.7	47.1	32.8	43.6	55.7	36.5	48.1	57.7
MMF	41.7	43.0	36.4	43.6	41.1	32.8	42.0	38.3	30.1
SF	28.1	19.3	16.5	23.6	15.3	11.5	21.5	13.6	12.2
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
Men
FF	41.3	50.0	57.8	44.5	53.6	62.1	50.9	58.6	66.3
MMF	38.6	38.0	34.4	40.6	36.2	29.9	32.4	32.4	26.0
SF	20.1	12.0	7.8	14.9	10.2	8.0	16.7	9.0	7.7
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

FF frailty free, MMF with mild/moderate frailty, SF with severe frailty

Despite total life expectancy being higher for women, the percentage of life frailty free is higher for men across all combinations of education and wealth. While net differences in duration of life with severe frailty are small relative to duration frailty free, as a percentage, severe frailty expectation vary considerably. For instance, a 70-year-old woman who has low wealth and less than high school education can expect about 28% of remaining life with severe frailty. Her counterpart with some or completed college education and high wealth expects only about 12%. Similarly, for men, those with the lowest levels of education and wealth can expect about 20% with severe frailty, compared to less than 8% if he has some or completed college education and high wealth.

Table 3 allows for comparison between education and wealth. It shows net changes in years calculated by subtracting the estimates of the lowest from highest level of education or income, and the relative change ratios calculated by dividing estimates of the highest by lowest education or income, holding the other indicator constant. Statistical significance tests for net changes are also provided. The key observation is that net and relative frailty free years expected are much greater for those with high levels of education or wealth. Even so, the advantage of wealth appears to be greater. For instance, a 70-year-old woman with high education can expect 2.61 more frailty free years than her low educated counterpart, while the same aged woman with high wealth can expect 5.19 more frailty free years than her low wealth counterpart. While high wealth and high education both result in more frailty free years, having high versus low wealth is more advantageous than having high versus low education. The ratio of frailty free years is 1.49 when comparing high to low education, but 2.20 when comparing high to low wealth. The results are similar for men. Thus, a high wealth woman and man can expect to live more than twice as many frailty free years than their low wealth counterparts.

Table 3.

Net change in years and relative change ratio in frailty specific and total life expectancy for those aged 70 by education and wealth

	Net change in years		Relative change ratio
	Education	Wealth	Education	Wealth
Women
FF	+ 2.61*	+ 5.19*	1.49	2.20
MMF	+ 0.27	− 0.11	1.04	0.98
SF	− 0.55	− 1.13*	0.80	0.63
Total	+ 2.33*	+ 3.95*	1.16	1.30
Men
FF	+ 1.97*	+ 4.65*	1.33	2.02
MMF	− 0.17	− 0.28	0.96	1.07
SF	− 0.21	− 0.35	0.85	0.77
Total	+ 1.58*	+ 4.57*	1.13	1.45

Net change in years for education and wealth subtracts years expected for those with highest minus lowest level of education or wealth when the other indicator is at its mid-level. Therefore, net change indicates the gain or loss in years in a specific frailty state, or gain or loss in total years of life, when moving from lowest to highest level of education or wealth. Relative change ratio for education and wealth is the ratio of years expected for those with highest to lowest level of education or wealth when the other indicator is at its mid-level. Therefore, relative change indicates the degree to which years of life in a specific frailty state, or total years of life, change relative to the size of the estimates

FF frailty free, MMF mild/moderate frailty, SF severe frailty, Total total life

*Net change in life expectancy is statistically significant at p < .05

Life expected in frailty-states by education and wealth: status-based estimates

Table 4, which presents findings for those frailty free and those with severe frailty at baseline, suggests there are advantages to being frailty free at baseline as well as having high education and wealth. The longest-lived persons, and the longest-lived persons in a frailty free state, are those that are frailty free at baseline and have a combination of high education and high wealth. A 70-year-old women with some or completed college education and high wealth that is frailty free at baseline can expect 19.19 (SE 0.30) more years of life of which 12.15 (SE 0.28) are frailty free and 2.07 (SE 0.16) are with severe frailty. This means that she can expect to live about 58% of her remaining years frailty free and about 12% with severe frailty. On the opposite end is one who has less than high school education and low wealth and lives with severe frailty at baseline. She can expect to live 8.85 (SE 0.30) more years, of which 0.48 (SE 0.05) are frailty free and 5.81 (SE 0.21) are with severe frailty. Therefore, this woman can expect about 6% of remaining life frailty free, compared with 66% with severe frailty. A 70-year-old man with some or completed college education and high wealth who is frailty free at baseline expects 16.64 (SE 0.29) more years of life of which 11.80 (SE 0.25) are frailty free and 1.10 (SE 0.10) with severe frailty. His counterpart with less than high school education and low wealth who lives with severe frailty at baseline will live 6.36 (SE 0.35) more years of life, of which 0.38 (SE 0.06) are frailty free and 4.41 (SE 0.25) with severe frailty. The percentage of life spent frailty free therefore is about 66% for the high educated, high wealth man frailty free at baseline and 6% for the low educated, low wealth man with severe frailty at baseline. The percentage of life with severe frailty in contrast is about 8% for the high educated, high wealth man frailty free at baseline and 69% for the low educated, low wealth man with severe frailty at baseline.

Table 4.

Status-based multistate life table estimates for those aged 70 by education and wealth, stratified by sex, showing life expectancy with standard errors in parentheses and percentage of life expected, in each state, for those frailty free and with severe frailty at baseline

Education	Less than high school			Completed high school or GED			Some or completed college
Wealth	Low	Mid	High	Low	Mid	High	Low	Mid	High
Frailty free at baseline
Life expectancy
Women
FF	6.96 (.20)	7.91 (.35)	9.98 (.58)	7.09 (.23)	9.34 (.26)	11.22 (.30)	7.80 (.39)	9.87 (.27)	12.15 (.28)
MMF	4.69 (.17)	5.36 (.28)	5.28 (.49)	5.18 (.20)	5.89 (.23)	4.95 (.26)	5.03 (.31)	5.70 (.26)	4.98 (.18)
SF	2.70 (.12)	2.31 (.18)	2.32 (.37)	2.47 (.15)	2.15 (.15)	1.77 (.11)	2.39 (.22)	2.01 (.17)	2.07 (.16)
Total	14.35 (.25)	15.58 (.41)	17.58 (.74)	14.74 (.30)	17.38 (.29)	17.93 (.37)	15.21 (.48)	17.58 (.36)	19.19 (.30)
Men
FF	6.87 (.25)	8.07 (.30)	9.30 (.45)	6.73 (.36)	8.54 (.24)	10.56 (.40)	7.82 (.54)	9.56 (.30)	11.80 (.25)
MMF	3.45 (.17)	3.89 (.23)	4.17 (.32)	3.60 (.27)	4.12 (.22)	3.97 (.22)	2.77 (.29)	3.90 (.27)	3.74 (.17)
SF	1.48 (.12)	1.18 (.10)	0.90 (.18)	1.15 (.14)	1.16 (.12)	1.06 (.12)	1.34 (.21)	1.05 (.11)	1.10 (.10)
Total	11.81 (.29)	13.14 (.37)	14.38 (.49)	11.48 (.50)	13.83 (.32)	15.58 (.40)	11.92 (.64)	14.51 (.36)	16.64 (.29)
Percentage of life
Women
FF	30.2	37.7	47.1	32.8	43.6	55.7	36.5	48.1	57.7
MMF	41.7	43.0	36.4	43.6	41.1	32.8	42.0	38.3	30.1
SF	28.1	19.3	16.5	23.6	15.3	11.5	21.5	13.6	12.2
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
Men
FF	41.3	50.0	57.8	44.5	53.6	62.1	50.9	58.6	66.3
MMF	38.6	38.0	34.4	40.6	36.2	29.9	32.4	32.4	26.0
SF	20.1	12.0	7.8	14.9	10.2	8.0	16.7	9.0	7.7
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
With severe frailty at baseline
Life expectancy
Women
FF	0.48 (.05)	0.59 (.12)	0.92 (.24)	0.52 (.06)	0.97 (.13)	1.33 (.22)	0.63 (.11)	1.13 (.16)	1.57 (.23)
MMF	2.55 (.20)	2.87 (.44)	2.97 (.74)	2.49 (.23)	3.58 (.34)	3.18 (.40)	2.92 (.36)	3.25 (.38)	3.28 (.38)
SF	5.81 (.21)	5.52 (.36)	5.56 (.71)	5.70 (.30)	5.88 (.37)	4.89 (.32)	5.48 (.36)	4.99 (.34)	5.49 (.32)
Total	8.85 (.30)	8.98 (.59)	9.44 (1.03)	8.70 (.34)	10.42 (.47)	9.40 (.60)	9.03 (.53)	9.37 (.56)	10.34 (.64)
With severe frailty at baseline
Life expectancy
Men
FF	0.38 (.06)	0.69 (.12)	1.26 (.36)	0.39 (.07)	1.05 (.16)	1.28 (.23)	0.42 (.10)	0.66 (.17)	1.21 (.26)
MMF	1.57 (.19)	2.28 (.35)	2.76 (.71)	1.48 (.24)	2.71 (.36)	2.97 (.42)	1.72 (.34)	1.75 (.38)	2.35 (.43)
SF	4.41 (.25)	3.87 (.29)	3.94 (.67)	3.82 (.39)	3.92 (.32)	4.14 (.42)	4.00 (.33)	4.16 (.35)	4.32 (.37)
Total	6.36 (.35)	6.84 (.44)	7.97 (.87)	5.70 (.44)	7.68 (.52)	8.39 (.59)	6.14 (.55)	6.57 (.58)	7.89 (.63)
Percentage of life
Women
FF	5.5	6.6	9.7	5.9	9.3	14.2	7.0	12.0	15.1
MMF	28.8	32	31.5	27.6	34.3	33.8	32.3	34.7	31.8
SF	65.7	61.4	58.8	66.5	56.4	52.0	60.7	53.3	53.1
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
Men
FF	6.0	10.2	15.9	6.9	13.7	15.3	6.9	10.1	15.4
MMF	24.7	33.3	34.6	26	35.3	35.3	27.9	26.6	29.8
SF	69.3	56.5	49.5	67.1	51.0	49.4	65.2	63.3	54.8
Total	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

FF frailty free, MMF with mild/moderate frailty, SF with severe frailty

Considering those in the same frailty state at baseline, education, and wealth still make a difference. For instance, we compare expectancies for a 70-year-old man with severe frailty at baseline. If he has low education and wealth he can expect 6.36 (SE 0.35) more years of life, 69% of which is lived with severe frailty. His counterpart with high education and wealth can expect 7.89 (SE 0.63) more years in total, 55% of which is in a state of severe frailty. For women with severe frailty at baseline the numbers are 8.85 (SE 0.30) versus 10.34 (SE 0.64) total years comparing low education and wealth to high education and wealth, of which 66% versus 53% are lived with severe frailty.

As shown in Table 5, within baseline state, education and wealth mostly matter for total length of life and years to be lived frailty free, with some variation by sex. As an example, women frailty free at baseline, with high wealth, expect 4.13 more years of life frailty free than their low wealth counterparts, holding education constant. The advantage for men with high wealth is 3.83 years. The relative change ratio is 1.58 for women and 1.57 for men, indicating that women and men live about 58% or 57% longer lives frailty free if they have high wealth versus low wealth. Education matters as well, but less so. The gain in frailty free years for women is 1.96 with a ratio of 1.25, while for men it is 1.49 with a ratio of 1.18. For those frailty free at baseline, high education and wealth result in significantly more years of total life, but years of with mild/moderate frailty and with severe frailty are not statistically different across levels of education and wealth.

Table 5.

Net change in years and relative change ratio in life expectancy for those aged 70 by education and wealth, for those frailty free and with severe frailty at baseline

	Net change in years		Relative change ratio
	Education	Wealth	Education	Wealth
Frailty free at baseline
Women
FF	1.96*	4.13*	1.25	1.58
MMF	0.34	− 0.23	1.06	0.96
SF	− 0.30	− 0.70	0.87	0.72
Total	2.00*	3.19*	1.13	1.22
Men
FF	1.49*	3.83*	1.18	1.57
MMF	0.01	0.37	1.00	1.10
SF	− 0.13	− 0.09	0.89	0.92
Total	1.37*	4.10*	1.10	1.36
With severe frailty at baseline
Women
FF	0.54	0.81*	1.92	2.56
MMF	0.38	0.69	1.13	1.28
SF	− 0.53	− 0.81	0.90	0.86
Total	0.39	0.70	1.04	1.08
Men
FF	− 0.03	0.89*	0.96	3.28
MMF	− 0.53	1.49*	0.77	2.01
SF	0.29	0.32	1.07	1.08
Total	− 0.27	2.69*	0.96	1.47

Net change in years for education and wealth subtracts years expected for those with highest minus lowest level of education or wealth when the other indicator is at its mid-level. Relative change ratio for education and wealth is the ratio of years expected for those with highest to lowest level of education or wealth when the other indicator is at its mid-level

* Net gain in life expectancy is statistically significant at p < .05

Among those with severe frailty at baseline, Table 5 suggests robust wealth associations for men. Men that are with severe frailty at baseline will live 2.69 more years if they have high versus low wealth, which is distributed as .89 more years of frailty free life, 1.49 more years of with mild/moderate frailty and .32 more years of with severe frailty. Relatively speaking, there is a more than three times gain in frailty free years for men with severe frailty at baseline. Women with severe frailty at baseline with high wealth gain a significant number of frailty free years, but wealth does not associate with net total, with mild/moderate frailty or with severe frailty years for women. Education, in contrast, is not at all significantly associated with the net change in years for those with severe frailty at baseline.

Discussion

Our study quantified duration of life in various degrees of frailty. Comporting with a couple of earlier studies in Europe (Herr et al. 2018; Romero-Ortuno et al. 2013) we find that frailty free life expectancy and the percentage of life expected frailty free each decrease with age. We also find that with age the length and percentage of life with mild/moderate frailty and severe frailty increase. Although women live longer than men, a greater proportion of their remaining years is lived with severe frailty. Our findings add to earlier computations in important ways. The hypothesis regarding how education and wealth in combination associate with duration of life in various degrees of frailty is confirmed. First, higher education and wealth associate with longer total life, longer life frailty free, and a shorter time with severe frailty. Second, those with greater education and wealth live a greater percentage of their remaining lives in more favorable degrees of frailty. Third, the combination of education and wealth is particularly important as those with high levels of both are greatly advantaged in terms of total yeas of life and years expected frailty free in comparison to those with low levels of both.

We find some unexpected results as well. Extant research suggested that wealth would have stronger impacts on those severely frail at baseline and education would be a more robust determinant for those frailty free at baseline. Our findings in fact found that while both measures of socioeconomic status are important, wealth influences duration of life expected in degrees of frailty more so than education regardless of baseline state. Particularly among men, duration of life in degrees of frailty varies greatly by wealth but not education. Table 5 for instance showed that men who have severe frailty at baseline live 2.69 more total years of life and 0.89 more years frailty free if they have high wealth, whereas high education has little impact on total or frailty free duration. Results for women who have severe frailty at baseline also indicate a higher role for wealth, although the associations are not quite as strong. Education does have a strong impact on length of life in degrees of frailty among those frailty free at baseline, but wealth is even more impactful. For instance, as reported above, a woman frailty free at baseline with high education does gain 1.96 frailty free years over her low educated counterpart, but high wealth gains her 4.13 years.

Earlier literature supports these findings. Studies that have examined the patterning of a variety of health outcomes that are constituents of frailty, such as functional limitation, disability, and chronic health conditions, suggest education plays a role in preventing onset of poor health but indicators of wealth serve to slow both onset and the course of progression of health problems (Herd et al. 2007; Zimmer and House 2003). Herd et al. (2007) explain that education’s role may be in affecting intrinsic resources, such as psychological and social processes, that impact health throughout life. Wealth, in contrast, is more likely to impact access to health care, medication, and other factors important for managing health problems. Wealth, and its close counterpart, income, at least in the U.S. where health insurance coverage can vary greatly, may therefore be more closely linked with resources needed to moderate the impact of frailty, for example, with potentially costly procedures, medications or hiring of personal assistance.

There are policy implications to our study. Macro and micro economic research on frailty consistently shows health care costs, costs of long-term care and indirect costs of informal care to be extremely high for those with severe frailty (Butler et al. 2016; Guralnik et al. 2002; Hajek et al. 2018; Salinas-Rodríguez et al. 2019). Our status-based results show that the length of life with severe frailty can be quite long for some groups, who tend to be those with the fewest resources. For instance, although 70-year-old women overall can expect to live about 2½ years with severe frailty, if that woman has low education and wealth the number rises to 3½, and if she has severe frailty at baseline she can expect almost 6 more years living with severe frailty. Besides the likely lesser quality of life that these persons must endure, this represents an enormous cost of severe frailty among those specifically with low socioeconomic standing (Crocker et al. 2019).

There are limitations to this study that warrant mention. Chief among them is the difficulty in comparing associations of wealth versus education given that distributions of these measures are slightly different and the conceptual distance between levels of wealth may not be congruent to levels of education. As shown in Table 1, there is a fairly even distribution across education categories and across wealth categories for both women and men such that low and high levels of each contain similar proportions. However, education is capped both at the low end (no years) and high end (completed university), whereas wealth is continuous and can be any negative or positive number. This may have some impact, especially if extreme levels of wealth associate with very high or very low durations of life in degrees of frailty. Second, sensitivity tests with different numbers of categories suggested patterns are robust to number of categories, although subtler changes exist when adding categories. Third, many of the comparisons are quite large, making it difficult to imagine that differences are simply a function of measurement. Finally, tests of significance of the net change in year shows that there are instances where wealth significantly associates with life expected in a given frailty state where education does not. In the end, the evidence we provide is strong enough and the measures comparable enough to suggest our conclusions are robust, despite some questions that should be posed when comparing the strength of association of different types of measures.

Transition probabilities used as input assume that any change in status occurs at some randomly assigned time during the survey interval. In reality, we do not know when a change occurs nor how many changes occurred over time, resulting in overlooked events. This limitation becomes more acute the longer the period between contiguous observations. Because of space limitations, we concentrated in this paper on the findings for 70 year olds. However, scanning the results for those older and younger, found in Supplementary Materials, suggests generally similar conclusions across these cohorts. For our study, we began with the HRS sample present in the year 2000. Later born cohorts may physically differ from cohorts examined here, and HRS data do permit cohort analysis since samples are regularly refreshed with new participants entering every six years. Future study comparing both frailty expectancies and associations with education and wealth among newer cohorts will be useful. A number of observations in some cells, for instance low educated with high wealth, are relatively small. Nonetheless, the standard errors point to relatively tight estimation intervals. Finally, the FI scores are meant to be used as continuous measures, with each fraction increase relating to some increase in frailty. The multistate life table approach we use here, however, requires that we construct ‘states,’ and therefore we artificially categorize our outcome in a somewhat crude fashion, though one that does comport with previous analyses and interpretations of the frailty index.

In sum, this study has provided initial evidence of how duration of life in various degrees of frailty can vary by indicators of socioeconomic status. The differences are stark, providing evidence that inequality in frailty is socially patterned. Given population aging and rising longevity occurring across all classes, we may expect challenges in the future with respect to increasing years of life with severe frailty among those with the fewest resources available to address their health condition.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

ZZ conceptualized the paper, conducted the analysis and wrote the first draft. YS conducted the analysis and contributed to writing of the methodology section. OT edited the manuscript and consulted on conceptualization and interpretation. CH edited the manuscript, conducted statistical analysis and construction of variables and consulted on interpretation and development of indicators. KR edited the manuscript and consulted on the conceptualization and interpretation.

Funding

The lead author acknowledges funding from the Social Sciences and Humanities Research Council of Canada and their Canada Research Chairs program. The Health and Retirement Study receives funding from United States Department of Health and Human Services. National Institutes of Health. National Institute on Aging (NIA U01AG009740), United States Social Security Administration.

Availability of data and material

https://hrs.isr.umich.edu/data-products/access-to-public-data.

Code availability

Contact lead author.

Compliance with ethical standards

Conflict of interest

Through Dalhousie University, KR has asserted copyright of the Clinical Frailty Scale. It is free for use for education, research and not-for-profit care.