Sex differences in the relative heterogeneity of frailty in relation to age, frailty, health protection, and five‐year mortality

Abstract Background Previous studies have suggested that the relative heterogeneity of frailty declines with increases in age and the level of the frailty index (FI). In this study, we investigated the sex difference in the relative heterogeneity of frailty and its response to health‐protective factors, in a Chinese community sample. Methods Data used for this secondary analysis were obtained from the Beijing Longitudinal Study of Aging that involved 3257 community‐dwelling Chinese people aged 55 years and older at baseline. An FI was constructed for each indicial using 35 variables assessing health‐related problems. A protection index (PI) consisting of 27 variables assessing lifestyle and social engagement was also built. The relative heterogeneity of frailty, as measured by the coefficient of variation (CV) of the FI, was calculated as the ratio of the standard deviation to the mean FI for different age, FI, and PI groups, and for the five‐year survival status. Results The CV decreased with the increase in age (F = 20.60, P = .006) and the FI (F = 57.59, P = .001), consistent in both sexes. In each age group, the CV was higher in men than in women (t = 3.25, P = .018). A great level of protection was associated with a significantly reduced mortality, and an increased CV (t = 2.91, P = .027). Conclusions Our data demonstrate that a gender difference exists in the relative heterogeneity of frailty, which is negatively related to age and frailty as well as positively associated with health protection and the five‐year survival.

span, 10,11 leading to an irreversible process of deterioration in the body system and, finally death. During the deterioration process, older adults show highly heterogeneous health status. When the body system reaches its redundancy exhaustion (i.e. an empirical limit with an FI value around 0.7) as detected in several studies, [12][13][14] maintenance of its homeostasis becomes dysfunctional in response to stressors, leading to catastrophic health transition. 15 As people get closer to the end of life, a single extra deficit can cause the body system to fail, leaving the individual with little chance of survival.
Increased health vulnerability in older adults can be well represented by a decline in relative heterogeneity of FI. Such frailty heterogeneity can be measured by the coefficient of variation (CV), i.e. the ratio of the standard deviation to the mean FI. It declines with an increase in age, which is well applied to Ashby's law of "requisite variety" 16 and indicates that as a complicated system ages, it loses variety in the response repertoire and is accompanied by decreasing capability of perceiving disturbance, so that the system is incapable of responding to disturbances and maintaining its integrity. 17 Frailty may be treatable, benefited from numerous geriatric interventions. [18][19][20][21] Even though deterioration and death generally dominate the process of aging, short-term stabilization and also improvement in health status can occur in some individuals. 22 Using the Beijing Longitudinal Study of Aging data, we have shown that extrinsic factors related to lifestyle, behavioral, social and environmental factors can exert positive effects of protection on health outcomes. 23  In this study we investigated the age and sex differences in the relative heterogeneity of frailty and examined their relations with the level of health protection. To do so, we compared men and women of different age and frailty groups and with different fiveyear mortality outcomes. Given the extent of health changes, we separately studied subjects who were aged 55-64 years and those aged 65+ years in a well-established Chinese community sample.

| Participants and data
As described elsewhere, the Beijing Longitudinal Study of Aging is a prospective cohort study of 3257 community-dwelling Chinese population aged 55 years and older at baseline. The geographic distribution, economic status, age, and education of the sample represent the older population of Beijing, as obtained from the Fourth National Census Data. 24 As described elsewhere, 25 the cohort was assembled in 1992; the response rate was 91.2%; participants were followed every two to three years. As with previous studies, 14,23,26,27 for this analysis, variables from the baseline dataset were retrieved. In this study, the widely accepted age of 65 years as the threshold of older verses later middle-aged adults [28][29][30] was used as the cut-off age. Five-year survival outcomes were evaluated. Survival status was determined through interviews with surviving household members and neighbors and verified by death certificates and/or local police register records.
Vital status was known for 92.1% of the participants, with censoring for dates of death or dropout. Data of the subjects with missing survival information (8.4%) were excluded from survival-related analysis only.

| Frailty index
A frailty index (FI) was constructed using the baseline survey data (1992) for each participant as described elsewhere. 14,23,26,27 Each variable used in the FI satisfied the criteria of being associated with health status, accumulating with age, not saturating (i.e. not becoming present in >80% of people), and having >1% prevalence and <5% missing, and covering several systems. 31 In total 35 variables were used, which included diseases (n = 8), symptoms (n = 7), psychological problems (n = 5), basic and Instrumental Activities of Daily Living (ADL and IADL) disabilities (n = 14), the MMSE total score. 14 The variables were each coded into a value between 0 and 1; the coded values were then summed and divided by 35 (the ratio of deficits present). This operation yielded an FI ranging from a theoretical minimum of 0 (no deficits present) to a possible maximum of 1.0 (all deficits present), with higher FI values representing a higher level of frailty, representing worse health and greater vulnerability to adverse outcomes. The maximum number of missing value with any individual in the sample was 1, which was replaced using the non-missing mean.

| Relative heterogeneity of frailty
The relative heterogeneity was calculated as the coefficient of variation (CV) of the frailty index (FI) based on the equation: ν = σ/〈f〉, where ν is coefficient of variation, 〈f〉 represents the mean FI and σ is its standard deviation for any given age group. 22 The coefficient of variation at a given level of FI 〈f〉 is described by a power-law formula: ν = A/〈f〉 α , where the parameters A and α, are fitted to the observed data. 22

| Protection Index
A Protection Index (PI) was constructed as the sum of 27 extrinsic factors, representing a comparably complete version of health protection assessment than previously reported. 23 Each of the items was coded in a reverse manner as with the deficits coding. For instance, for the PI, 1 = being married; satisfied with house condition; someone help housework; having someone counts for help; family or friend to count on help; financial help acquired; visit friend or relatives; traveling; help your relative to do housework; physical or outdoor leisure activities;

| Statistical analysis
Sample characteristics were described using means and standard deviations for interval variables and percentages for the categorical variables, with differences tested using analysis of variance (ANOVA) and Chi-square (Χ 2 ) respectively. The attributable risk (AR) for the five-year mortality was calculated for each protective factor as the fraction to the proportion of the risk among the exposed population lacking that protective factor that could be attributed to the exposure. 32 Fiveyear mortality rates were compared between men and women using Student t tests. Multivariable regression analysis was used to examine the relationship between the coefficient of variation (CV) with age and the FI. Based on the PI values, subjects were categorized into three groups (tertiles), with lower (1st tertile), intermediate (2nd tertile) and higher (3rd tertile) levels of protection. Age trajectories of the FI and its coefficient of variation were compared for sex and protection levels.
Data analyses were performed using SPSS v21.

| RE SULTS
Women were slightly older and had less education than men (Table 1). Compared with women, men were more likely to be married and engaged in intellectual occupation especially after 65 years of age. In both men and women, most deficits were associated with an increased risk of mortality by five years. On TA B L E 1 Characteristics of the sample as separated by sex for the younger (<65 y) and older (>65 y) groups average, women who were aged 55-64 years appeared to be frailer (FI = 0.09 ± 0.07) and had more protective factors (PI = 0.71 ± 0.09) than men (FI = 0.08 ± 0.07, PI = 0.68 ± 0.10). Women aged 65+ years also tended to be frailer than men, but with no significant sex difference in PI (0.65 ± 0.11 vs 0.66 ± 0.11, F = 1.9, P = .169).
The relative frailty heterogeneity, measured by the coefficient of variation CV of the FI, was higher in men than women in both age groups coefficient of variation (Table 1).
Considering individually the factors that make up the PI, in both 55-64 and 65+ age groups and especially the former, lack of protective factors often showed a higher risk of death in men than in women ( Table 2). For the 55-64 year-old group, lack of many protective factors appeared to be more lethal for men than for women.
This also occurred in the 65+ age group: lack of protective factors often correlated with a higher risk of death in men than in women.
Notably, several protective factors, when considered individually, seemed to have promoted mortality in the 65+ group (i.e. negative attributable risk) after 5 years. This was especially true regarding women ( Table 2). Such variables included several social support, life control factors.
Considering deficits collectively, the mean FI increased with age (Table 3a); the mean PI declined at advanced ages (Table 3b).
Significant sex difference in FI was found in all age groups except the 55-59 year-old group (Table 3a), with women being frailer than men (t = 5.20, P = .002). The sex differences in the PI were chiefly showed in the 55-64 year-old group (Table 3b), while no significant sex differences existed in the 65+ age group.
The decline of the coefficient of variation (CV) of frailty was greater in men than in women (t = 3.24, P = .018; Figure 1). The relative frailty heterogeneity also decreased with an increase of the  Table 2). Similarly, a greater level of the PI was associated with a higher level of the relative heterogeneity of frailty as measured by the CV (t = 2.91, P = .027) in the sample.

| D ISCUSS I ON
In the previous studies, women in comparison with men have lower self-rating on health and tend to accumulate more deficits. [33][34][35][36] However, women appear to tolerate more deficits and have greater capability in compensating for adverse outcomes accompanied by lower mortality rate. 14 In this study we evaluated the relative heterogeneity of frailty in a Chinese community sample, applying the deficit accumulation based frailty index (FI) approach. We studied the sex differences of the relative heterogeneity of frailty in relation to age, the FI, the protection index (PI), and the five-year mortality. By constructing an improved version of the PI that consisted of a complete set of the protective factors available in the dataset, we further examined the impact of health protection on the relative heterogeneity of frailty, providing the first investigation of this research line.
Our data confirmed that the relative heterogeneity measured by the coefficient of variation declined with increased age and FI, consistent with the previous reports. 22,33 Our data also confirmed that higher mortality rates were associated with lower levels of the relative heterogeneity of frailty. This study further extended the frailty heterogeneity analysis to include people of late middle age. As expected, the majority of the protective factors were individually associated with a decreased risk of death, meaning that a lack of protective factors increased the individual's risk of mortality ( Consistent with the previous studies, 22,33 our data showed that the relative heterogeneity of frailty declined with age and with increased deficit accumulation respectively. More interestingly, women in this study showed a lower level of the relative heterogeneity of frailty than did men in any given age group. A higher survival rate is associated with a higher level of the relative heterogeneity of frailty. This observation TA B L E 2 Absence of the protective factors and the associated attributable risks (AR) for the 5-y mortality, by sex for the younger (<65 y) and older (>65 y) groups  In conclusion, our data suggest that a gender difference exists in the relative frailty heterogeneity measured by the coefficient of variation of the frailty index. Having more health-protective factors can help decrease deficit accumulation and increase relative frailty heterogeneity among older adults, and be associated with reduced mortality rates. This finding suggests the interplay of intrinsic and extrinsic factors in determining health outcomes, which can provide insights for promoting public health in aging.

CO N FLI C T S O F I NTE R E S T
Nothing to disclose.

AUTH O R CO NTR I B UTI O N S
ZY processed and analyzed the data, prepared the result presentation, and drafted the first manuscript. CW and ZT provided the dataset, helped process the data, and reviewed and edited the manuscript. XS conceptualized the research question and design, reviewed the data analysis and result presentation, and revised the first manuscript draft. All authors contributed to the study finding impartation, edited the various versions of the manuscript, and agreed upon publication of the paper.