Hierarchical Structure in Activities of Daily Living and Long-Term Disability Trajectories in the Elderly Chinese Population: A 20-Year Cohort Study

4 Background: The global burden of disability is rising. Understanding the hierarchical structure 5 of activities of daily living (ADL) and the disability trajectory of elderly people is pivotal to 6 developing early interventions. Purpose: We aimed to determine the hierarchical structure of the 7 ability to perform ADL and further describe the disability trajectory of the elderly before death. 8 Methods: A longitudinal item response theory model (LIRT) was constructed from 28 345 elderly 9 participants in the Chinese Longitudinal Healthy Longevity Survey, in which ADL were measured 10 by the Katz scale for up to 20 years from 1998 to 2018, until the participants' death. The disability 11 values estimated from the LIRT were fitted to a mixed - effects model to examine how the disability 12 trajectories varied with different demographic characteristics. Results: The difficulty parameters 13 showed that ADL losses began with bathing - partial (  = - 1.396, SE=0.003), then toileting - partial , 14 bathing - total , dressing - partial , transferring - partial , dressing - total , feeding - partial , continence - partial , toileting - total , 15 feeding - total , transferring - total , and ended with continence - total (  =3.647, SE=0.013). Disability 16 trajectories varied with sex ( β =0.041, SE=0.001), place of residence ( β =0.010, SE=0.001), and 17 marital status ( β =0.144, SE=0.001). Females, people who lived in urban areas, and those who lived 18 without a spouse had poorer disability status. Conclusion: Losses in the ability to perform ADL 19 have a hierarchical structure. Demographic characteristics affect disability trajectories among the 20 elderly Chinese population.

Katz Scale, Disability Trajectories, Longitudinal Item Response Theory, Older adult 23 Introduction 24 The proportion of the global population older than 60 years of age will nearly double by 2050 25 as life expectancy increases and birth rates decline [1]. However, longer survival times do not 26 necessarily entail extended periods of good health. With advancing age, the elderly are prone to 27 contracting degenerative diseases, leading to a decline in their ability to live independently [2]. 28 Estimates predict 55 million elderly people will be living with a disability in China by 2025 [3]. As 29 such, disability causes a heavy burden on both the family and society [4]. Timely, research-based, 30 and effective interventions to improve the utilization of care services are urgently needed to mitigate 31 the burdens caused by disability. 32 Scientists generally interpret disability as the loss or limitation of a person's ability to perform 33 activities of daily living (ADL), which is an important indicator of individual health. Researchers 34 use the Katz Index, CARS scale, and Lawton scale for disability assessment [5,6]. However, the 35 total score of these scales may have low discrimination among people of varied disability status. 36 Moreover, the total score can also lead to a floor or ceiling effect. To minimize this deficiency, 37 American psychometrician Lord [7] and Danish statistician Georg Rasch [8] proposed a new test 38 method called Item Response Theory (IRT). In IRT, disability among the elderly can be regarded as 39 a potential continuum-avoiding floor and ceiling effects [9]. Among the different IRT models, 40 longitudinal item response theory (LIRT) is applied to data collected over prolonged periods. The 41 LIRT method reduces bias when estimating trajectory rates of decline [10]. For example, Marc et 42 al. [11] developed a LIRT model to characterize cognition over time, and it effectively captured the 43 multifaceted nature of cognition and its longitudinal trajectory. For disability, which is also a 44 progressive disease, LIRT is also applicable.

45
People found that ADL are hierarchical in nature [9,12]. Some researchers have applied LIRT 46 and linear mixed models to capture the hierarchical structure of ADL and changes in disability 47 trajectory over time by taking into account the correlation across multiple measurements in each 48 individual [9,13]. As a general consensus, older adults tend to lose the ability to perform activities 49 requiring lower extremity strength earlier than activities that require upper body strength [14][15][16].

50
Scientists have observed a pattern in the loss of ADL: females experienced an initial loss of their 51 ability to walk independently outside the home, followed by the inability to independently groom, 52 bathe, dress, toilet, and feed themselves, while males experienced a similar pattern, except that the 53 inability to dress occurred second [17]. In addition, disability trajectories change dynamically over 54 time. Although controversial, some research reports that disability change is sex-specific and 55 influenced by education level.

56
This study aimed to use LIRT and mixed-effects model to study the hierarchical structure of 57 ADL losses and the disability trajectories of people over 60 years of age in China. The outcomes of 58 this study will provide a reference to develop effective interventions for older people living with a 59 disability.  Our study used the Katz scale to assess daily living ability. The Katz scale precisely evaluates 74 the ability to perform specific ADL, including bathing, dressing, transferring, feeding, toileting, and 75 continence, using a three-point scale (no limitation, partial limitation, or total limitation) of task 76 performance. The Chinese version, which has been extensively tested in pilot interviews, yields 77 reliable and valid responses [19]. Participants who refused or declined to answer a question were 78 handled as missing cases. proposed by Samejima [20], was chosen as a generic IRT building block to relate each test item to 82 the potential trait. In the GRM model for hierarchical reactions, every item has three parameters: (1) 83 Two difficulty parameters (κpartial and κtotal) which define the thresholds for change (from no 84 limitation to partial limitation and from partial to full limitation, corresponding with κpartial and κtotal, 85 respectively). In the disability severity continuum, items with a small κ indicate that older people 86 are more likely to lose this ability. In this study, the difficulty parameters revealed the hierarchical 87 structure of the ADL. (2) An item with a higher discrimination parameter (α) means that it is more 88 capable of positioning individuals at the closest disability level.

89
To achieve the dual goals of identifying the difficulty and discrimination parameters of the Katz 90 scale and assessing declines in the ability to perform ADL, we chose a LIRT model for data 91 analysis [11]. Each individuals(s) response score to a specific item (i) at a given time (t) was 92 recorded as ,, s t i Y , and the corresponding disability status of the individual was θ s,t (every six items 93 correspond to the same θ, and a larger θ indicated a more serious disability status). In this study, the 94 response category of every item was K = 3, and its cumulative probability was expressed as i. k corresponds to the selected category of the individual. For the longitudinal aspect of the model: To determine disability trajectories, the time between interview and death was taken as the 112 independent variable (t) and the disability level (θ) of the elderly, obtained in the aforementioned 113 LIRT, was taken as the dependent variable (scale to [-3,3]). We used a mixed-effects model to 114 analyze changes in function over time. The model is shown below:  The hierarchical structure of declining ability to perform ADL, provided by the estimated 141 difficulty parameters, is presented in Table 3. Firstly, with a range between -1.396 and 3.647, we 142 confirmed that ADL loss began with bathing-partial and ended with continence-total. Regarding some   strategies for health problems, and as such, geriatric medicine must evolve to intervene at an earlier 177 stage of the disability process to be more effective. To date, some research has demonstrated a 178 positive effect of primary prevention on dependence morbidity [23][24][25]. For the elderly, disability is 179 a primary dimension of health and function, and it acts as an indicator or guideline for developing 180 health policies for this age group [26]. The study provides foundational evidence upon which to 181 formulate early intervention policies for preventing disability in the elderly.

183
According to Baker's [27] guidelines for a normal ogive model, the discrimination value of 184 continence was moderate, and all other items were very high. Poor discrimination refers to a task or 185 activity (i.e., scale items) that prove unresponsive to changes in a particular person's disability level.

186
In our research, toileting, transferring, and dressing all showed high degrees of discrimination, but 187 bathing and continence were not discriminative. Similarly, other scholars have found the same 188 parameter order (toileting>transferring >dressing) in a two-parameter IRT model [28,29]. In 189 previous calculations of the parameters between ADL items, it was generally believed that the 190 discrimination of toileting, dressing, and bathing was higher [30,31]. However, in this study, bathing The continuum of declining ability to perform ADL began with bathing-partial and ended with 197 continence-total. As noted in previous publications [17,[32][33][34], bathing was the first ADL to 198 deteriorate, which was defined by Katz et al. as the threshold of disability. In this study, the local 199 parameter between bathing-partial and bathing-total was only 1.022, confirming that bathing was the 200 first ADL to be lost among the elderly. Scientists report that bathing was the first ADL that both 201 older Americans and Chinese have difficulty performing [14]. However, the bathing task was 202 informative only in the low ability range, so partial and total bathing limitation occurred when the 203 elderly were slightly disabled.

204
The second ADL to be lost was toileting-partial. Among the six items explored here, the behavior 205 of the toileting item was peculiar. The distance on the continuum between its partial and total 206 limitation thresholds was much higher (4.252) than the other activities (ranging from 0.759 207 (dressing) to 3.507 (transferring)). Furthermore, its discriminative ability was very high, showing 208 that the item correctly discriminates between individuals at the two levels of disability.

210
The Bayesian methodology allowed the longitudinal slope estimates to remain vague for 211 subjects with little (or no) floe-up time. We fitted our model on all participants and concluded that 212 males, greater age, fewer years of education, living in rural areas, and without a spouse were 213 associated with a faster deterioration in the ability to perform ADL. We discovered that older 214 females had a higher level of disability, but their function deteriorated at a slower rate. As a result, 215 there is a larger proportion of dependent women among the elderly population in China. Education 216 has always been considered a factor that slows aging and ability decline [35][36][37]. The probable 217 reason may be that people with lower education levels might pay less attention to their physical 218 health, not to mention the prevention of chronic disease. In addition, this phenomenon is more 219 common in rural areas. Marital status, as a defining feature of the social environment, has long been 220 argued to affect an individual's risk of disability [38]. Marital status has been significantly associated 221 with physical disability [39,40], and marital closeness moderates the negative psychological effects 222 of high levels of disability on depression, anxiety, and self-esteem [41]. variable [42,43]. In the mixed-effects model, females, living in urban areas, and living without a 227 spouse had worse ADL status. Interestingly, disability status was better in rural areas. It may be that 228 rural medical services are relatively inaccessible, and older adults become frailer at a younger age 229 and die earlier, so the remaining elderly are in better condition [44]. Overall, differentiating among 230 the expected trajectories and related needs would help to tailor strategies and programs to improve 231 elder care prior to death.

233
The innovative feature of our study was that it relied on a longitudinal analysis of 20-year 234 follow-up data from a substantial sample of the general elderly population. Moreover, the LIRT and 235 mixed-effects model allowed us to capture the multifaceted nature of disability. The LIRT also 236 allowed us to estimate item and disability distribution parameters, as the data were from a 237 longitudinal cohort study. In addition, the correlation between the subject-specific covariates and the 238 slope of deterioration was embedded in the same model.  Table 1 Baseline characteristics of the CLHLS study population Table 2 Posterior means and 95% credible intervals of the discrimination parameters for items in Katz scale Table 3 Posterior means and 95% credible intervals of the Local parameters for items in Katz scale

Figure 2
Twenty-year mean trajectories of disability preceding death grouped by gender*marital status.
Note: MY means males living with a spouse, FY means females living with a spouse, MN means males living without spouse, FN means females living without spouse. Adjusted for age, place of residence and years of education. Figure 1 Twenty-year mean trajectories of disability preceding death grouped by gender*place of residence. Note: MU means males living in urban, FU means females living in urban, MR means males living in rural, FR means females living in rural. Adjusted for age, marital status and years of education.

Figure 2
Twenty-year mean trajectories of disability preceding death grouped by gender*marital status. Note: MY means males living with a spouse, FY means females living with a spouse, MN means males living without spouse, FN means females living without spouse. Adjusted for age, place of residence and years of education.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. TableS1.doc