Title: Prediction of Functional Disability in Older Chinese Adults Using a Random Survival Forest Model

doi:10.21203/rs.3.rs-4935527/v1

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Research Article

Title: Prediction of Functional Disability in Older Chinese Adults Using a Random Survival Forest Model

https://doi.org/10.21203/rs.3.rs-4935527/v1

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Background

As life expectancy increases, so does the risk of age-related diseases and functional disability, which significantly raises the risk of all-cause mortality in older adults. Individuals with disabilities may die up to 20 years earlier than those who are non-disabled.

Objectives

To develop a prediction model for functional disability using random survival forest analysis (RSF).

Methods

Data were drawn from 2,364 older adults without functional disability from the China Health and Retirement Longitudinal Study (CHARLS), conducted from 2011 to 2020. Functional disability was the primary outcome. Univariable and multivariable Cox regression analyses were used to identify significant factors, which were then screened using variable importance (VIMP) and minimal depth to construct the RSF model. The model's performance was evaluated using calibration curves and the area under the receiver operating characteristic (AUC) curve. Multimorbidity trajectories were also identified as potential risk factors through group-based multi-trajectory modeling.

Results

Four multimorbidity trajectories were identified: no multimorbidity, newly-developing, moderate-developing, and severe-developing. The RSF model outperformed the Cox regression model in predicting functional disability, with key factors including age, education, walking time, grip strength, CES-D score, and multimorbidity trajectories. Significant factors identified were CES-D score, grip strength, multimorbidity trajectory, age, and the use of antihypertensive medications.

Conclusions

The RSF model, based on CHARLS data, effectively predicts functional disability in older adults, with depressive symptoms, handgrip strength, multimorbidity trajectories, age, and antihypertensive medication use emerging as key predictors.

functional disability

random survival forest

multimorbidity

older adults

People worldwide are living longer. With increasing life expectancy, the risk of developing age-related diseases and functional disability also increases [1]. Functional disability increases the risk of all-cause mortality in older adults [2, 3], with disabled individuals potentially dying up to 20 years earlier than their non-disabled counterparts [4].

Chronic diseases are a common issue and primary health challenge among older adults, leading to physical disability and even death [5]. Multimorbidity, the co-occurrence of multiple chronic conditions, is common [6]. Previous research indicates that 94.9% percent of adults aged 60 and older have at least one condition, while 78.7% have two or more [7]. Individuals with multimorbidity are more likely to experience physical decline, poor quality of life and early mortality [8]. Furthermore, more severe diseases and specific disease patterns are associated with a faster deterioration [9].

Despite numerous efforts have been made to predict functional disability in older populations [10], several limitations remain. First, most of prediction models select multimorbidity or chronic disease as a candidate predictors of functional disability, but most of them use a dichotomous multimorbidity status [11] or number of diseases [12], with little exploration of multimorbidity trajectory as a predictor. Additionally, previous studies often rely on linear models or linear mixtures, which have limitations in accounting for different developmental trajectories within a group [13]. Group-based trajectory modeling (GBTM), a finite mixture modeling technique, identifies distinct multimorbidity subgroups with varying trajectories, capturing the heterogeneity of individual trajectories [14]. This approach offers a more comprehensive understanding of long-term multimorbidity patterns in older adults. Moreover, potential risk factors included in models are often selected based on expert knowledge or prior literature [15]. The limitation of handling only a few variables might result in oversight of essential variables. Machine learning algorithms, which excel at selecting variables from a large pool without relying on prior hypotheses, can enhance the performance of prediction models [16]. Common machine learning algorithms, such as random forest, ridge regression, and gradient boosting, have been used to predict functional outcomes in community-dwelling older adults [17, 18]. However, these studies often overlook the time dimension, leading to imprecise predictions. Random survival forests (RSF), an ensemble tree method for analyzing right-censored survival data, can identify complex interactions among multiple variables and outperforms the traditional Cox proportional hazard model. However, only a few of the aforementioned studies have employed these methods [19].

In this study, we recruited the community-dwelling older adults without functional disability from the China Health and Retirement Longitudinal Study. We aimed to (1) analyze the diversity in multimorbidity trajectories using the GBTM, and (2) propose a prediction model of functional disability based on RSF analysis.

Study design and participants

The study participants were recruited from the China health and retirement longitudinal study (CHARLS), an ongoing prospective cohort study that included 28 provinces across China. The details of the project have been described in detail elsewhere [20]. Briefly, participants were invited to undergo a comprehensive health check-up and complete a self-administrated questionnaire to provide comprehensive information on health status and related factors. The baseline survey began in 2011, and follow-up surveys were conducted in 2013, 2015, 2018, and 2020. The CHARLS study was approved by the Biomedical Ethics Review Committee of Peking University, and the participants provided informed consent.

Of the total participants who were enrolled in the project with informed consent at baseline, we excluded those aged < 65 years old at baseline. We further excluded the participants who lacked health status and functioning information form at more than two surveys, to ensure that each included participant had at least three completed surveys data on multimorbidity. In addition, participants with missing values for activities of daily living (ADL) in any survey were excluded. Finally, 2,364 older adults without functional disability at baseline were included in the study (Fig. 1).

Functional disability

Functional disability was assessed using the 6-item ADL scale, including dressing, bathing, eating, getting on and off the bed, going to the toilet, controlling urination and defecation. Participants with any difficulty with these items were assessed as having functional disabilities.

Candidate factors

The candidate factors were collected from self-administered questionnaires and health checkups conducted at baseline.

Sociodemographic variables included sex (male, female), educational background (less than lower secondary, upper secondary and vocational training, tertiary), marital status (married, other), and current working status (working or not). Health status and functioning variables included smoking now, ever smoking, ever drinking, body mass index (BMI) (calculated as the weight in kilograms divided by the height in meters squared, < 18.5 kg/m²; 18.5–25.0 kg/m²; > 25.0 kg/m²), receiving medication or treatment for chronic diseases, walking speed, and grip strength. Social activities were assessed by asking whether the respondent had participated in any social activities (play ma-jong, charity, community organization, club, interaction with friends) in the past month (yes or no). Balance tests were performed according to the semi-tandem, full-tandem and side-by-side tests (not completing the semi-tandem nor side-by-side test, not completing the semi-tandem but completing the side-by-side test, completing the semi-tandem but not completing the full-tandem test, and both completing the semi-tandem and full-tandem test). Depressive symptoms were assessed using the condensed version of the Center for Epidemiological Studies Depression Scale (CES-D), with high scores indicating greater depressive symptoms. Multimorbidity was assessed by asking the participants whether they had ever been diagnosed with two or more chronic diseases, including hypertension, dyslipidemia, diabetes, cancer, chronic lung diseases, liver diseases, heart diseases, stroke, kidney diseases, stomach or other digestive diseases, psychiatric problems, memory-related disease, arthritis or rheumatism and asthma.

Statistical analysis

Continuous variables are represented as means and standard deviations, while categorical variables are presented as counts (%). Baseline characteristics were compared using Pearson’s chi-squared test for categorical variables, and the t-test for continuous variables.

GBTM was used to analyzed multimorbidity at five different points to identify the potential trajectories of multimorbidity through the maximum likelihood estimation method and to identify subgroups with different trajectory types. This method allows for the handling of missing data for each individual and produces asymptotically unbiased parameter estimates. Age was employed as the timescale for the trajectories. The best-fitting trajectory models were selected based on the Bayesian Information Criterion (BIC), average posterior probability (> 0.7), and minimum sample size in each group that accounted for > 5.0% of the overall population.

The Cox and RSF models were used to assess the performance of multimorbidity trajectories in predicting functional disabilities. A univariate Cox proportional hazards model was used to identify significant risk factors, and the significant factors were included in the multivariate models. We used variable importance (VIMP) and minimal depth to screen for risk factors, including multimorbidity trajectories and covariates, and construct the RSF.

The dataset was randomly divided into training and testing sets in a 7:3 ratio. The testing set was used to evaluate the prediction performance of the RSF models. The accuracy of the predictive model was evaluated using calibration curves, and the area under the receiver operating characteristic (ROC) curve (AUC).

Statistical analyses were performed using SAS (version 9.4), and plots were created using R (version 4.1.0). All significance tests were two-tailed, with P < 0.05 indicating that the difference was statistically significant.

Characteristics of participants

We included 2,364 older adults included in this study. The average age of the participants was 70.98 ± 5.14 years. Men (52.5%), married (72.9%), with less than a lower secondary education background (91.7%), not working (55.5%), never drinkers (61.5%), never smokers (57.8%), and not currently smoking (68.4%) accounted for the majority. Most older adults who were less likely to engage in social activities, took medication for chronic diseases, had good balance performance, and had higher CES-D scores. In addition, the average walking speed was 0.53m/s, the average grip strength was 28.24 kg, and the average CES-D was 7.70 (Table 1). The baseline characteristics between the training and test set were showed in Table S1. There is no significant differences between the training and testing set, except the social activities, grip strength, and CES-D score.

Table 1

Baseline characteristics of participants based on trajectories of multimorbidity
Variables ^a	Overall (n = 2364)	Group1 (n = 580)	Group2 (n = 1059)	Group3 (n = 578)	Group4 (n = 147)	P ^b
Age, years	70.98 ± 5.14	73.12 ± 6.27	71.28 ± 4.72	69.12 ± 3.76	67.69 ± 3.19	< 0.001
Sex, %
Male	1240 (52.5)	332 (57.2)	558 (52.7)	274 (47.4)	76 (51.7)	0.01
Female	1124 (47.5)	248 (42.8)	501 (47.3)	304 (52.6)	71 (48.3)	0.01
Educational background, %
Less than lower secondary	2167 (91.7)	547 (94.3)	964 (91.0)	525 (90.8)	131 (89.1)	0.058
Upper secondary & vocational training	134 (5.7)	25 (4.3)	60 (5.7)	40 (6.9)	9 (6.1)
Tertiary	63 (2.7)	8 (1.4)	35 (3.3)	13 (2.2)	7 (4.8)
Marital status, %
Married	1724 (72.9)	395 (68.1)	776 (73.3)	449 (77.7)	104 (70.7)	0.022
Others	640 (27.07)	185 (31.90)	283 (26.72)	129 (22.32)	43 (29.25)	0.022
Currently working, %
No	1311 (55.5)	299 (51.6)	583 (55.1)	340 (58.8)	89 (60.5)	0.244
Yes	1005 (42.5)	268 (46.2)	455 (43.0)	227 (39.3)	55 (37.4)
Missing	48 (2.0)	13 (2.2)	21 (2.0)	11 (1.9)	3 (2.0)
Ever drinks before, %
No	1455 (61.5)	350 (60.3)	660 (62.3)	361 (62.5)	84 (57.1)	0.522
Yes	908 (38.4)	230 (39.7)	399 (37.7)	216 (37.4)	63 (42.9)
Missing	1 (0.0)	0 (0.0)	0 (0.0)	1 (0.2)	0 (0.0)
Smoke ever, %
No	1367 (57.8)	312 (53.8)	628 (59.3)	341 (59.0)	86 (58.5)	0.16
Yes	997 (42.2)	268 (46.2)	431 (40.7)	237 (41.0)	61 (41.5)	0.16
Smoke now, %
No	1618 (68.4)	356 (61.4)	726 (68.6)	422 (73.0)	114 (77.6)	< 0.001
Yes	708 (29.9)	212 (36.6)	321 (30.3)	144 (24.9)	31 (21.1)
Missing	38 (1.6)	12 (2.1)	12 (1.1)	12 (2.1)	2 (1.4)
Social activities, %
No	1198 (50.7)	301 (51.9)	533 (50.3)	293 (50.7)	71 (48.3)	0.554
Yes	1084 (45.9)	253 (43.6)	496 (46.8)	263 (45.5)	72 (49.0)
Missing	82 (3.5)	26 (4.5)	30 (2.8)	22 (3.8)	4 (2.7)
Any medication for hypertension, %
No	1768 (74.8)	558 (96.2)	809 (76.4)	325 (56.2)	76 (51.7)	< 0.001
Yes	595 (25.2)	22 (3.8)	250 (23.6)	252 (43.6)	71 (48.3)
Missing	1 (0.0)	0 (0.0)	0 (0.0)	1 (0.2)	0 (0.0)
Any medications for lung condition, %
No	2179 (92.2)	575 (99.1)	992 (93.7)	500 (86.5)	112 (76.2)	< 0.001
Yes	184 (7.8)	5 (0.9)	67 (6.3)	77 (13.3)	35 (23.8)
Missing	1 (0.0)	0 (0.0)	0 (0.0)	1 (0.2)	0 (0.0)
Any medications for heart problems, %
No	2121 (89.7)	575 (99.1)	973 (91.9)	471 (81.5)	102 (69.4)	< 0.001
Yes	242 (10.2)	5 (0.9)	85 (8.0)	107 (18.5)	45 (30.6)
Missing	1 (0.0)	0 (0.0)	1 (0.1)	0 (0.0)	0 (0.0)
Any medications for arthritis, %
No	2062 (87.2)	554 (95.5)	920 (86.9)	473 (81.8)	115 (78.2)	< 0.001
Yes	301 (12.7)	26 (4.5)	138 (13.0)	105 (18.2)	32 (21.8)
Missing	1 (0.0)	0 (0.0)	1 (0.1)	0 (0.0)	0 (0.0)
Any medications for digestive disease, %
No	2098 (88.7)	563 (97.1)	955 (90.2)	474 (82.0)	106 (72.1)	< 0.001
Yes	265 (11.2)	17 (2.9)	104 (9.8)	103 (17.8)	41 (27.9)
Missing	1 (0.0)	0 (0.0)	0 (0.0)	1 (0.2)	0 (0.0)
BMI, %
≤ 18.5	236 (10.0)	80 (13.8)	109 (10.3)	40 (6.9)	7 (4.8)	< 0.001
18.5–23.9	939 (39.7)	259 (44.7)	435 (41.1)	199 (34.4)	46 (31.3)
≥ 24	830 (35.1)	153 (26.4)	362 (34.2)	241 (41.7)	74 (50.3)
Missing	359 (15.2)	88 (15.2)	153 (14.4)	98 (17.0)	20 (13.6)
Balance test summary score, %
No semi/no s-b-s	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0 (0.0)	0.459
No semi/yes s-b-s	32 (1.4)	12 (2.1)	9 (0.8)	10 (1.7)	1 (0.7)
Yes semi/no full	484 (20.5)	117 (20.2)	224 (21.2)	116 (20.1)	27 (18.4)
Yes semi/yes full	1380 (58.4)	337 (58.1)	629 (59.4)	330 (57.1)	84 (57.1)
Missing	468 (19.8)	114 (19.7)	197 (18.6)	122 (21.1)	35 (23.8)
Walking speed test, sec	4.68 ± 2.33	4.67 ± 2.23	4.64 ± 2.21	4.70 ± 2.53	4.96 ± 2.71	0.556
Grip strength, kg	28.24 ± 9.74	27.96 ± 9.59	27.98 ± 9.79	28.95 ± 9.90	28.60 ± 9.41	0.29
CES-D	7.70 ± 5.90	6.58 ± 5.49	7.32 ± 5.67	8.52 ± 6.05	11.52 ± 6.49	< 0.001
Notes: a. Mean values (SD) for continuous variables and n (%) for categorical variables. b. Categorical data were compared using the Pearson’s chi-squared test. Continuous variables were compared using the t-test.

After a 10-year follow-up period, 451 (19.13%) older adults developed functional disabilities (Table 2). The individuals with disabilities were more likely to be older, female, have a lower educational background and marital status, and were not working or participating in social activities. They were also more likely to take medications for chronic diseases, had poor balance performance, lower grip strength, and higher CES-D scores. Additionally, they were more likely to fall into the moderate-developing and severe-developing multimorbidity trajectories.

Table 2

Baseline characteristics of participants with and without disability after ten years follow-up
Variables^a	Overall (n = 2364)	Participants without disability (n = 1913)	Participants with disability (n = 451)	P^b
Age, year	70.98 (5.14)	70.73 (5.02)	72.04 (5.50)	< 0.001
Gender, %
Male	1240 (52.5)	1032 (53.9)	208 (46.1)	0.003
Female	1124 (47.5)	881 (46.1)	243 (53.9)	0.003
Harmonized education levels, %
Less than lower secondary	2167 (91.7)	1734 (90.6)	433 (96.0)	0.001
Upper secondary & vocational training	134 (5.7)	123 (6.4)	11 (2.4)
Tertiary	63 (2.7)	56 (2.9)	7 (1.6)
Marital status, %
Married	1724 (72.9)	1424 (74.4)	300 (66.5)	0.001
others	640 (27.2)	489 (25.7)	151 (33.5)	0.001
Currently working, %
No	1311 (55.5)	1028 (53.7)	283 (62.7)	< 0.001
Yes	1005 (42.5)	850 (44.4)	155 (34.4)
Missing	48 (2.0)	35 (1.8)	13 (2.9)
Ever drinks before, %
No	1455 (61.5)	1176 (61.5)	279 (61.9)	0.117
Yes	908 (38.4)	737 (38.5)	171 (37.9)
Missing	1 (0.0)	0 (0.0)	1 (0.2)
Smoke ever, %
No	1367 (57.8)	1098 (57.4)	269 (59.6)	0.414
Yes	997 (42.2)	815 (42.6)	182 (40.4)	0.414
Smoke now, %
No	1618 (68.4)	1297 (67.8)	321 (71.2)	0.322
Yes	708 (29.9)	586 (30.6)	122 (27.1)
Missing	38 (1.6)	30 (1.6)	8 (1.8)
Social activities, %
No	1198 (50.7)	947 (49.5)	251 (55.7)	0.063
Yes	1084 (45.9)	898 (46.9)	186 (41.2)
Missing	82 (3.5)	68 (3.6)	14 (3.1)
Any med for hypertention, %
No	1768 (74.8)	1456 (76.1)	312 (69.2)	0.001
Yes	595 (25.2)	457 (23.9)	138 (30.6)
Missing	1 (0.0)	0 (0.0)	1 (0.2)
Any meds for lung condition, %
No	2179 (92.2)	1779 (93.0)	400 (88.7)	0.002
Yes	184 (7.8)	134 (7.0)	50 (11.1)
Missing	1 (0.0)	0 (0.0)	1 (0.2)
Any meds for heart problems, %				0.629
No	2121 (89.7)	1721 (90.0)	400 (88.7)
Yes	242 (10.2)	191 (10.0)	51 (11.3)
Missing	1 (0.0)	1 (0.1)	0 (0.0)
Any meds for arthritis, %
No	2062 (87.2)	1694 (88.6)	368 (81.6)	< 0.001
Yes	301 (12.7)	218 (11.4)	83 (18.4)
Missing	1 (0.0)	1 (0.1)	0 (0.0)
Any meds for digestive disease, %
No	2098 (88.7)	1709 (89.3)	389 (86.3)	0.148
Yes	265 (11.2)	203 (10.6)	62 (13.7)
Missing	1 (0.0)	1 (0.1)	0 (0.0)
BMI, %
≤ 18.5	236 (10.0)	185 (9.7)	51 (11.3)	0.444
18.5–23.9	939 (39.7)	766 (40.0)	173 (38.4)
≥ 24	830 (35.1)	679 (35.5)	151 (33.5)
Missing	359 (15.2)	283 (14.8)	76 (16.9)
Balance test summary score, %
No semi/yes s-b-s	32 (1.4)	24 (1.3)	8 (1.8)	< 0.001
Yes semi/no full	484 (20.5)	378 (19.8)	106 (23.5)
Yes semi/yes full	1380 (58.4)	1168 (61.1)	212 (47.0)
Missing	468 (19.8)	343 (17.9)	125 (27.7)
Walking speed test, sec	4.68 ± 2.33	4.58 ± 2.26	5.15 ± 2.57	< 0.001
Grip strength, kg	28.24 ± 9.74	28.88 ± 9.68	25.41 ± 9.54	< 0.001
CESD	7.70 ± 5.90	7.20 ± 5.69	9.82 ± 6.27	< 0.001
Trajectory of multimorbidity, %
No multimorbidity	580 (24.5)	499 (26.1)	81 (18.0)	< 0.001
Newly-developing-decline	1059 (44.8)	871 (45.5)	188 (41.7)
Moderate-developing	578 (24.5)	447 (23.4)	131 (29.0)
Severe-developing	147 (6.2)	96 (5.0)	51 (11.3)
Notes: a. Mean values (SD) for continuous variables and n (%) for categorical variables. b. Categorical data were compared using the Pearson’s chi-squared test. Continuous variables were compared using the t-test.
Abbreviations: BMI, body mass index; semi, semi-tandem test; full, full-tandem test, s-b-s: side-by-side test; CES-D, Center for Epidemiological Studies Depression

Trajectories of multimorbidity

Combined with the BIC (-13647.16), Avepp (all > 0.7), and the number of participants in each group (> 5%) (Table S2), the best-fitting model identified four multimorbidity trajectories (Fig. 2).

As shown in Fig. 2, the number of chronic diseases increased with age, and Groups1 to 4 showed a stratified distribution from low to high. Group 1 (580 individuals, 24.53%) had the lowest chronic disease counts, with a slow increase from 0.1 to 0.3 diseases, and was defined as “no multimorbidity” group. Group 2 (1,059, 44.52%) had 1.9 chronic diseases at baseline, gradually increasing to 2.1 and then decreasing to 0.8, and was defined as the “newly-developing” group. Group 3 (578, 24.62%) had multimorbidity at baseline, which increased to 4.1, and was defined as “moderate-developing” group. Group 4 (416, 6.34%) had the lowest number of individuals, with the highest number of chronic conditions, progressing from 4.2 at baseline to 6.4. This group was defined as the “severe-developing” group.

Basic characteristics of trajectory grouping

The basic characteristics of the different developmental tracks of multimorbidity are shown in Table 1. Older adults in the no multimorbidity group were older, man, current smoker, with a lower marriage rate. While in the severe developing group, they were more likely to have a history of using medication for the chronic disease, an abnormal BMI, and higher score of CES-D score.

Cox regression model

Univariate Cox regression analysis identified predictors of functional disability (Table 3). These included higher age, female sex, not married, taking medication for a lung condition, arthritis and digestive disorders, a higher walking time, a higher CES-D score and newly-developing, moderate-developing and severe-developing multimorbidity. Older adults who were current workers, with a higher educational background and higher grip strength were less likely to have a functional disability. The multivariate Cox regression predictors of functional disability were also identified, and the significant predictive factors were age, higher educational background, grip strength, CES-D score, and multimorbidity trajectory.

Table 3

Cox regression analysis results
Variables	Univariate analysis HRs, 95% CI	Multivariate analysis HRs, 95% CI
Age, years	1.033 (1.014, 1.052)	1.030 (1.001, 1.059)
Sex
Male	ref	ref
Female	1.275 (1.032, 1.575)	0.875 (0.644, 1.188)
Educational background
Less than lower secondary	ref	ref
Upper secondary & vocational training	0.314 (0.149, 0.664)	0.334 (0.123, 0.908)
Tertiary	0.642 (0.304, 1.358)	0.683 (0.250, 1.867)
Marital status
Married	ref	ref
Others	1.41(1.16, 1.71)	0.363 (0.090, 1.467)
Currently working
No	ref	ref
Yes	0.743 (0.595, 0.928)	0.812 (0.618, 1.066)
Drink ever
No	ref
Yes	0.955 (0.768, 1.188)
Smoke ever
No	ref
Yes	0.899 (0.724, 1.116)
Smoke now
No	ref
Yes	0.808 (0.634, 1.031)
Social activities
No	ref
Yes	0.861 (0.694, 1.067)
Any med for hypertension
No	ref	ref
Yes	1.415 (1.128, 1.775)	1.098 (0.816, 1.476)
Any meds for lung condition
No	ref	ref
Yes	1.487 (1.053, 2.100)	1.257 (0.833, 1.894)
Any meds for heart problems
No	ref
Yes	1.059 (0.756, 1.484)
Any meds for arthritis
No	ref	ref
Yes	1.582 (1.204, 2.079)	1.020 (0.721, 1.442)
Any meds for digestive disease
No	ref	ref
Yes	1.368 (1.018, 1.837)	0.938 (0.648, 1.358)
BMI
≤ 18.5	ref
18.5–23.9	0.926 (0.644, 1.331)
≥ 24	0.872 (0.601, 1.263)
Balance test summary score
No semi/yes s-b-s	ref
Yes semi/no full	0.943 (0.383, 2.322)
Yes semi/yes full	0.623 (0.256, 1.517)
Walking speed test, sec	1.063 (1.023, 1.105)	1.024 (0.976, 1.075)
Grip strength, kg	0.969 (0.957, 0.982)	0.981 (0.965, 0.997)
CES-D score	1.059 (1.042, 1.076)	1.035 (1.014, 1.056)
Trajectory of multimorbidity
No multimorbidity	ref	ref
Newly-developing	1.490 (1.101, 2.017)	1.790 (1.219, 2.630)
Moderate-developing	1.818 (1.313, 2.517)	2.095 (1.323, 3.318)
Severe-developing	3.006 (2.003, 4.512)	3.285 (1.841, 5.861)
Abbreviations: HRs: hazard ratios; CI: confidence interval; BMI, body mass index; semi, semi-tandem test; full, full-tandem test, s-b-s: side-by-side test; CES-D, Center for Epidemiological Studies Depression

RFS model

We ranked the importance of factors containing multimorbidity trajectories and covariates using VIMP (Fig. S1) and minimal depth (Figure. S2), respectively. By combining VIMP and minimal depth (Fig. 3), the RFS model selected 10 variables were selected: CES-D score, grip strength, multimorbidity trajectory, age, 2.5-meters walking times, marital status, BMI, balance test summary score, educational background, and medications for hypertension.

Model performance

For model differentiation, the AUC of the Cox and RSF models for predicting functional disability in five years were 0.685 (95% CI: 0.650–0.720) and 0.823 (95% CI: 0.794–0.851) for the training set (Fig. S3), 0.748(95% CI: 0.691–0.805) and 0.775 (95% CI: 0.720–0.829) for the test set (Fig. S4). The calibration curve is shown in Fig. S5 and Fig.S6. The RFS model showed better calibration compared to the Cox model, with a closer fit to the diagonal dashed line, which represents an ideal evaluation by a perfect model.

This study constructed models to predict functional disability over five years in community-dwelling older adults, using the RSF and Cox regression analyses. This is the first that using multimorbidity trajectory as a risk factor in a functional disability prediction model for older adults. A comparison of the AUC scores and calibration curves showed that RSF model had better predictive performance for the onset of functional disability in older adults than the Cox regression model.

Studies have shown that predictive models based solely on survival status do not provide sufficient information for clinicians to determine the optimal timing of intervention in older adults. The dependent variables of traditional Cox regression included survival time and a binary variable indicating the survival outcome. Although this accounts for patient survival time, it performs poorly with high-dimensional clinical data because the assumption of proportional hazards constrains the predictive effect. Thus, it cannot provide clinicians with timely decision-making guidance within a limited time and with scarce medical resources. The RSF model does not depend on predefined assumptions like proportional hazards, or linearity and reduces the computation time by replacing cross-validation with out-of-bag data estimation [21]. A systematic review found that the median C-statistics ranging from 0.65 to 0.76 for existing development models, and from 0.60 to 0.68 for validation models when using linear or Cox models predict the functional status in community-dwelling older adults [10]. The C-statistics for another Cox model for predicting functional disability among older adults was 0.804 [22], while it was 0.818 for a machine learning model [17]. The C-statistics of the RSF model in this study is 0.823, which indicated higher efficacy than the Cox regression model in predicting functional disability in older adults. Although a random forest model in predicting the functional disability showed a 0.821 and 0.793 of C-statistics in training and testing set, they only follow up for 3 years and did not consider the time dimension [18].

Both the RSF and Cox regression models were able to screen for variables of high importance. The important variables that were common to both models included multimorbidity trajectories, depressive symptoms, grip strength, age, and taking medication for hypertension. To the best of our knowledge, this is the first study to include multimorbidity trajectory as a risk factors for the onset of functional disability. We identified four types of multimorbidity trajectories: no multimorbidity, new development, moderate development, and severe development. These findings are consistent with previous research [23–25], as more than half of the participants (69.3%) did not have multimorbidity or had a newly developing trajectory during the follow-up period, indicating that most older adults were aging healthily. Additionally, moderately and severely developing trajectories increased the risk of disability, especially in older adults with more diseases. In line with prior findings [23–25]. we also identified subgroups with moderately and severely developing trajectories that showed no improvement over time (i.e., no decrease in multimorbidity with time). However, there was a decrease of the chronic diseases number in the “no multimorbidity” and “newly-developing” groups and missing value appeared in the moderate and severe-developing groups after their 77.5 years. It may suggested that the older adults was keeping with more severe multimorbidity live shorter [26]. Still need more research to demonstrate.

Multiple longitudinal studies have established a significant relationship between depressive symptoms and the onset of functional disability in the general aging population [27]. A 6-year follow-up study in community-dwelling older adults found that the incidence of functional disability increases by about 14% with each additional symptom of depression [28]. In line with these findings, we found a 1.04-fold increase in the CES-D score in the risk of incident functional disability in older adults. Therefore, it is necessary to establish a program to lower the incidence of depression among older adults and guiding targeted intervention while emphasizing the importance of multi-morbidity management. Handgrip strength is often used as an indicator of overall muscle strength in aging adults, and low grip strength is associated with functional disabilities and all-cause mortality [29, 30]. Hand grip strength is highly predictive of functional disability 25 years later and hence could be used for early screening of individuals at an increased risk of physical disability in old age [31]. Additionally, older adults with hypertension have a significantly higher likelihood of functional disability, and this association is not dependent on the number and severity of concomitant diseases [32]. Further, the use of anti-hypertensive medications is also associated with functional disability, but older adults may have a lower adherence to taking medication [33]. However, the questionnaire in the present study did not include medication adherence variables as variable. Further studies are required to explore this issue.

This study had several strengths. We not only compared the predictive efficacy of the RSF and Cox regression models but also identified variables that strongly influenced the onset of functional disability and ranked them for significance, which may guide timely interventions and facilitate personalized care plans. Also, this study uses group-based trajectory modeling to identify potential categories of multimorbidity developmental trajectories, effectively identifies population subgroups with similar chronic disease developmental histories, and further investigates their impact on new-onset functional disability, to provide a basis for interventions for functional disability risk in China's older adults.

However, despite the strengths, this study has some limitations. First, a type I error may have occurred because the diagnosis of chronic disease and the assessment of functional disability are based on self-reported questions. Although studies have demonstrated the validity of using self-reported diseases as medical records [34], this approach may still underestimate the prevalence in the population. Future studies could use wearable devices to measure gait performance, muscle mass, and strength. Secondly, owing data limitations, we did not consider the effects of other confounding factors, such as disease severity, medication adherence, and nutrient supplement intake, on the results of the study. In addition, there are a number of confounding factors that are not included due to the high level of missing data. Future studies should also consider exploring the integration of additional risk factors. Finally, older adults with multiple chronic diseases may have dropped out of the survey because of poor health or death, thus affecting the extrapolation of the results to a certain extent. More representative samples could be included in the subsequent analysis.

The RSF model is a better predictor of functional disability than the Cox regression model. Depressive symptoms, grip strength, trajectories of multimorbidity, and age ranked as important variables in both models. Therefore, the RSF analysis can provide new insights for predicting functional disability in older adults.

Ethics approval and consent to participate

This study involves no data collected from human subjects. We only used publicly available de-identified samples. This paper performed secondary data analysis on survey data that had obtained ethical approval before being collected and are publicly available.

Consent for publication

Not applicable.

Availability of data and materials

The datasets generated and/or analysed during the current study are available in the CHARLS repository, https://charls.charlsdata.com/index/zh-cn.html.

Competing interests

The authors declare that they have no competing interests.

Funding

This work was supported by the Key R&D and promotion special project of Henan Province (scientific and technological research) (Grant No.242102310316), the National Support Program for Postdoctoral Researchers of China (Grant No.GZC20232414).

Authors' contributions

Yifan Shan, Shuai Jiang, Hang Fu, Chengzeng Wang: study design. Yifan Shan, Shaui Jiang, Wei Fan, Jing Hong Gao, Wei Lu: data analysis and manuscript preparation. Yanran Duan, Yafeng Zhang, Sufan Wang: analysis double-check. Yifan Shan, Shuai Jiang, We Fan, Jinghong Gao, Wei Lu, Yanran Duan, Yafeng Zhang, Hang Fu, Chengzeng Wang: review and editing.

Acknowledgements

We would like to acknowledge the China Health and Retirement Longitudinal Study (CHARLS) team for providing data. We are grateful to all subjects who participated in the survey.

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Title: Prediction of Functional Disability in Older Chinese Adults Using a Random Survival Forest Model

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Abstract

Background

Objectives

Methods

Results

Conclusions

Figures

Introduction

Methods

Study design and participants

Functional disability

Candidate factors

Statistical analysis

Results

Characteristics of participants

Trajectories of multimorbidity

Basic characteristics of trajectory grouping

Cox regression model

RFS model

Model performance

Discussion

Conclusions

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1