Lagged effects of risk factors on the disability of older adults: A distributed lag non-linear model approach

Abstract

Objectives

This study aimed to explore the lagged and cumulative effects of risk factors on disability in older adults using distributed lag non-linear models (DLNMs).

Methods

We utilized data from the China Health and Retirement Longitudinal Study (CHARLS). After feature selection via Elastic Net Regularization, we applied DLNMs to evaluate the lagged effects of risk factors. Disability was defined as the presence of any difficulties in basic activities of daily living (BADL). The cumulative relative risk (CRR) was calculated by summing the lag-specific risk estimates, representing the cumulative disability risk over the specified lag period. Effect modifications and sensitivity analyses were also performed.

Results

This study included a total of 2,318 participants. Early-phase lag factors, such as the difficulty in stooping (CRR = 3.58; 95 %CI: 2.31–5.55; P < 0.001) and walking (CRR = 2.77; 95 %CI: 1.39–5.55; P < 0.001), exerted the strongest effects immediately upon occurrence. Mid-phase lag factors, such as arthritis (CRR = 1.51; 95 %CI: 1.10–2.06; P = 0.001), showed a resurgence in disability risk within 2–3 years. Late-phase lag factors, including depressive symptoms (CRR = 2.38; 95 %CI: 1.30–4.35; P < 0.001) and elevated systolic blood pressure (CRR = 1.64; 95 %CI: 1.06–2.79; P = 0.02), exhibited significant long-term cumulative risks. Conversely, grip strength (CRR = 0.80; 95 %CI: 0.54–0.95; P = 0.02) and social participation (CRR = 0.89; 95 %CI: 0.73–0.99; P = 0.04) were significant protective factors.

Conclusions

The findings underscore the importance of tailored interventions that account for various lag characteristics of different factors to effectively mitigate disability risk. Future studies should explore the underlying biological and sociological mechanisms of these lagged effects, identify intervention strategies that target risk factors with different lagged patterns, and evaluate their effectiveness.

What is known?

• •Along with ageing, the disability of older adults places a serious burden on individuals, families, and society.
• •Disability in ageing is a dynamic process, resulting from the long-term accumulation of multiple risk factors’ complex non-linear effects.
• •Previous studies primarily focused on the direct effects of risk factors at a single point in time, neglecting the time lag and cumulative effects across different time scales.

What is new?

• •Early-phase lag factors (e.g., functional limitations) reflected the direct impairment of fundamental physical functions essential for daily independence. Mid-phase lag factors (e.g., arthritis) suggested underlying processes such as changes in physiological reserve and self-management. Late-phase lag factors (e.g., higher systolic blood pressure) highlighted the long-term and cumulative burden.
• •The findings underscored the importance of tailored interventions that account for various lag characteristics of risk factors to effectively mitigate disability risk.

1. Introduction

Disability is commonly defined as limitations in basic activities of daily living (BADL) and/or instrumental activities of daily living (IADL) resulting from physiological, psychological, or social factors [1,2]. As people age, most individuals commonly experience a decline in their health or a gradual loss of the functional ability to perform basic yet valuable daily activities, such as bathing or housekeeping [3]. In China, the prevalence of disability among older adults is approximately 26.4 %, which is higher than in the US (15.6 %) and the UK (18.3 %) [4]. Disability is closely correlated with adverse outcomes, such as depression, reduced quality of life, increased hospitalization rates, and mortality risks [5,6]. Moreover, disability during ageing is a dynamic process, with its occurrence and development resulting from the long-term accumulation of multiple risk factors [7]. Therefore, accurately identifying disability risk and developing targeted interventions at an early stage are crucial.

Previous studies [[8], [9], [10], [11], [12], [13]] have identified various factors associated with disability, including specific risk factors such as advanced age, slow gait speed, chronic diseases, depression symptoms, poor memory, and living without a spouse. Furthermore, a study employing multifactorial frameworks has revealed that the concurrent impact of conditions like multimorbidity, cognitive impairment, and depression significantly elevates disability risk [14]. The other study has established longitudinal associations, showing that metabolic syndrome and its components are associated with a higher risk of disability over time [15]. In terms of research design, previous studies have primarily focused on the direct effects of risk factors measured at a single time point, such as the effect of baseline variables on disability risk, while neglecting the time-lagged and cumulative impact of these factors across different time scales. In terms of data analysis methods, although traditional statistical methods (such as logistic regression analysis [15], Cox proportional hazards regression [8], and machine learning algorithms (e.g., Extreme Gradient Boosting) [11] have seen widespread application, these approaches exhibit certain limitations when capturing temporal correlations among risk factors, especially when dealing with complex multiple factors and nonlinear effects. It is particularly noteworthy that the impact of risk factors on disability is typically complex and nonlinear [16]. For instance, nonlinear relationships have been demonstrated between age, BMI [13], physical performance measures (such as the time required to complete five repeated chair standings) [11], and the risk of disability. Moreover, multiple factors (such as depression and comorbidity) may produce synergistic effects [10]. Therefore, existing methods may struggle to capture such complex patterns effectively. The limitations hinder a deeper understanding of the mechanisms underlying disability onset and may lead to interventions that lack precision and timeliness.

To overcome the limitations, this study proposes the following solutions. Firstly, using distributed lag non-linear models (DLNMs) as the statistical method. DLNMs provide a modeling framework for flexibly describing associations that exhibit potentially nonlinear and delayed effects in time series data [17]. Additionally, cumulative effects can be estimated by combining single effects across consecutive lag times [17], providing a reliable method for understanding the lagged impact of risk factors for disability. Secondly, a prospective cohort study design could overcome the limitations of single-time-point risk factor studies. Due to the extended follow-up period and substantial resource investment, nationally representative longitudinal cohort databases, such as the China Health and Retirement Longitudinal Study (CHARLS), offer a scientifically robust alternative [18]. CHARLS is a longitudinal survey of the middle-aged and elderly population in China, designed to provide a high-quality public micro-database with a wide range of information, serving the needs of scientific and policy research on ageing-related issues. The multidimensional data on socioeconomic, physical, and psychosocial variables provided by the CHARLS are critical for capturing the time effects of risk factors for disability. The CHARLS design aligns with international standards, and its rigorous protocols ensure data validity [18], as evidenced by peer-reviewed publications tracking disability progression [19]. Despite the limited time span of the CHARLS data, it is possible to dynamically track the temporal progression of elderly individuals from exposure to risk factors to the onset of disability.

Therefore, this study aimed to explore the effects of risk factors for disability under different time lags and their long-term accumulation effects by leveraging the DLNM. This approach is expected to provide more precise time window information for disability prevention in older adults, thereby providing a scientific foundation for timely interventions and personalized management strategies.

2. Methods

2.1. Study design and participants

This study was a prospective cohort study that utilized secondary data analysis from CHARLS. CHARLS was initiated in 2011 and involved 17,708 participants aged 45 years or older from 28 provinces across China, using a multistage, probability-proportional-to-size (PPS) sampling method [18]. CHARLS is an ongoing study, with follow-up surveys carried out every two to three years. The baseline national survey was conducted in 2011, followed by updates in 2013, 2015, 2018, and 2020. As the core physical measurement variables relevant to this study (e.g., grip strength [11] and gait speed [9]) were only reported in the first three waves of data, this analysis is restricted to three waves of CHARLS: 2011 (baseline), 2013 (first follow-up), and 2015 (second follow-up). Participants were included if they were aged 65 years or older in 2011, with no restrictions on other health conditions. Individuals with disability at baseline, those who did not participate in the 2013 and 2015 follow-ups, and those with missing data for age and BADL items were excluded. This study followed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) reporting guidelines [20].

2.2. Measures

Potential variables associated with functional decline and disability were identified based on existing literature [8,11,12,14] and expert knowledge in geriatrics. Variables with more than 30 % missing data were excluded, resulting in 71 variables retained for analysis. All data were collected through face-to-face household interviews using a structured questionnaire and Computer-Assisted Personal Interviewing (CAPI) technology.

2.2.1. Demographic and health characteristics

These variables included: 1) seven sociodemographic variables (age, gender, educational level, birthplace, widowed or not, household registration status, and health insurance); 2) five lifestyle variables (physical activity, drinking frequency, cigarettes per day, social activity participation, and life satisfaction); 3) 14 family and economic variables (total savings, total debt, fixed capital assets, total household income, annual household consumption, household size, living children number, co-residence status, children living near or not, contact with children, economic support received, death of children, public pension status and amount); 4) current employment status and category; 5) 16 comorbidity and hospitalization variables (diabetes, cancer, chronic lung disease, liver disease, kidney disease, digestive disease, mental disease, arthritis, dyslipidemia, asthma, hypertension, stroke, memory disease, heart disease, Charlson Comorbidity Index, and hospitalization); and 6) 14 health status variables (self-reported health status, self-rated memory, serial subtraction test, orientation, drawing test, word recall test, walking difficulty, chair standing up difficulty, stair climbing difficulty, stooping difficulty, heavy lifting difficulty, cion picking up difficulty, arm extension difficulty, and depression).

Social activity participation was assessed by asking, “Did you participate in any of the following activities last month?” Examples include socializing with friends, playing cards or board games, joining community clubs, doing volunteer work, and attending educational or training courses. Physical activity was defined as whether respondents engage in any intensity of physical activity for more than 10 min per week. Chronic conditions were determined based on a definitive diagnosis from a doctor. The score of the Charlson Comorbidity Index was calculated using the method previously reported by Charlson et al. [21]. Participants reported self-reported health/memory through the question “Would you say your health/memory is very good, good, fair, poor, or very poor?” In the serial subtraction test, participants must subtract seven from 100 five times in a row. Their score was the number of correct responses. Orientation was assessed by asking participants about their current year, month, day, day of the week, and season. The drawing test was a binary variable that assessed participants’ ability to copy complex shapes (such as an intersecting pentagon or cube). The word recall test utilized 10 Chinese words for assessment, with the score representing the average number of words correctly recalled in both the immediate and delayed tests. Functional limitations were assessed by inquiring whether participants experienced difficulty with the following activities: walking 100 m, standing up from a chair, climbing stairs, stooping, extending their arms, lifting heavy objects, and picking up coins from a table. Depressive symptoms were assessed using the 10-item Centre for Epidemiologic Studies Depression (CESD-10) Scale [22]. Participants were required to rate the frequency of each symptom over the past week on a 4-point scale (zero indicates ‘rarely or never,’ three indicates ‘most or all of the time’). It is recommended that a score of 10 or higher be adopted as the criterion for identifying depressive symptoms.

2.2.2. Physical examination

Thirteen physical examination variables (walking speed, chair stand time, balance test, peak expiratory flow, systolic blood pressure, diastolic blood pressure, pulse, dominant hand, grip strength, waist, abdominal obesity, BMI, and BMI category) were collected by trained interviewers using standardized devices and protocols.

Walking speed was measured by completing two return trips over a distance of 2.5 m. Chair stand performance was assessed by recording the time taken to complete five sit-to-stand repetitions from a 47-cm-high stool without using arms. Balance was tested using semi-tandem, full-tandem, and side-by-side stands. If the participant could complete the semi-tandem test for 10 s without stepping out of place or grabbing hold of anything, they were allowed to stand in complete tandem. The balance test was categorized into a 4-level ordinal score based on performance: 1) unable to complete either the semi-tandem or side-by-side stand for the maximum time; 2) unable to complete the semi-tandem stand but able to complete the side-by-side stand; 3) able to complete the semi-tandem stand but unable to complete the full-tandem stand; and 4) able to complete both the semi-tandem and full-tandem stands for the maximum time. A higher score indicates better balance function [23]. Peak expiratory flow was measured three times using an AiPu peak flow meter, and the highest reading was used. Grip strength was measured twice for each hand using a Yuejian WL-1,000 dynamometer, and the highest value for the participants’ dominant hand was recorded. Anthropometric measurements included height (Seca 213 height gauge), weight (Omron HN-286 scale), and waist circumference (soft tape). Abdominal obesity is defined as a waist circumference of 85 cm or greater in women and 90 cm or greater in men.

2.2.3. Disability status

The BADL measures the respondent’s ability to perform daily tasks, including dressing, bathing, eating, getting out of bed, using the toilet, and controlling urination and defecation. The participants’ responses to every task were categorized into four responses: 1) “No, I have no difficulty,” 2) “I have difficulty but can still do it,” 3) “Yes, I need some help,” and 4) “I cannot do it.” A respondent with any level of difficulty (e.g., a response of 2, 3, or 4) on any BADL item was considered to have a disability [24].

2.3. Data analysis

All the data analyses were performed with R software, version 4.4.3. A descriptive analysis was performed to characterize the study populations. Continuous variables following a normal distribution were described using means and standard deviations (SD); those not normally distributed were described as median and interquartile range (IQR). Categorical variables were described using frequencies and percentages (%). Multiple interpolation was used to address missing values. An Elastic Net Regularization (ENR) approach was used to select risk factors closely related to disability, which is effective in avoiding overfitting [25]. Based on this, the variables for subsequent DLNM construction were determined.

2.3.1. Distributed lag non-linear model construction

The DLNM was employed to assess the relationships between each risk factor and disability. The factors at each time point were independently incorporated into the construction of cross-basis functions to estimate their effects on disability within different lag intervals. The main model is as follows:

Logit [P (Disability_it = 1)] = α + cb (Factor_it, lag = 4) + ns (Age_it, df = 5) + β₁ Gender_i + β₂ Education_i + β₃ Birthplace_i + ns (Time_t, df = 2).

Where P (Disability_it = 1) is the disability status for individual i at time t; α is the intercept; cb (Factor_it, lag = 4) is a cross-basis matrix, where a linear function and a natural cubic spline function with five degrees of freedom (df) are applied to estimate the linear and lagged effects of each risk factors, respectively; ${\text{Factor}}_{\text{it}}$ is the specific risk factor observed in year t; ns (Age_it, df = 5) is a natural cubic spline for age with 5 degrees of freedom to control for nonlinear Age effects; ${\text{Gender}}_{\mathrm{i}}$, ${\text{Education}}_{\mathrm{i}}$, and ${\text{Birthplace}}_{\mathrm{i}}$ are time-invariant covariates; ns (Time_t, df = 2) is a natural cubic spline for the time trend with 2 degrees of freedom to control for long-term trends. The selection of all model parameters was guided by the Akaike information criterion (AIC). The cumulative relative risk (CRR) was derived by pooling the effect estimates across each lagged year to reflect the cumulative risk of disability over time.

2.3.2. Effect modification

To explore potential effect modification and determine whether the associations between risk factors and disability differed across key population subgroups, stratification analyses were performed by gender and age (the age stratification uses 75 years as the threshold, aligning with the critical age point for functional decline as defined in the Global Ageing Report) [26]. At the 95 %CI level, the statistical significance of the differences between all subgroups was determined using the following method: first, the effect estimates (β) and their standard errors (SE) were calculated for each subgroup; subsequently, Z-value was derived based on the ratio of the difference between the two groups’ effect estimates to the square root of the sum of the squares of their corresponding standard errors. The P-value was subsequently calculated using the standard normal distribution based on the Z-value.

2.3.3. Sensitivity analysis

Several sensitivity analyses were performed to assess the robustness of the results. First, we adjusted the degrees of freedom to 4 and 3. Second, we attempted to include people with disability at baseline. Third, we used a B-spline curve for the lag dimension, and the other curves remained unchanged. Fourth, we excluded extreme values of numerical variables in this study. Statistical significance is defined as a two-tailed P < 0.05. And if the 95 %CI for RR value does not include the null effect value (i.e., 1), the effect is considered statistically significant (at a significance level of α = 0.05).

2.4. Ethical considerations

The Biomedical Ethics Review Committee of Beijing University approved the CHARLS study (IRB00001052-11015), and participants in the CHARLS study provided consent for the secondary use of their data. CHARLS data are publicly available and can be obtained by submitting a formal request at the CHARLS home page at http://charls.pku.edu.cn.

3. Results

3.1. Demographics of the participants

A total of 2,318 participants were included in the study. The detailed sample selection process is shown in Appendix A. The baseline average age was 71.08 ± 5.18 years. Among all the participants, 52.3 % were male, 92.5 % participants had an education level of lower secondary school, and 49.6 % were born and raised locally. In terms of health conditions, 32.1 % reported arthritis, 32.1 % had hypertension, and 15.1 % had heart disease. Regarding physical function, 42.5 % had difficulty climbing stairs, 25.8 % had difficulty stooping, and 24.2 % had difficulty standing up from a chair. Economically, 36.7 % reported receiving a public pension, and the median annual total household income was 8,350.00 yuan. In terms of work status, 43.8 % were currently working. The detailed characteristics of the participants are presented in Appendix B.

3.2. Predictors’ selection via Elastic Net Regression

We employed ENR with an α of 0.5, balancing between Lasso (L1) and Ridge (L2) regularization. The optimal penalty parameter (λ) was determined through 10-fold cross-validation. At this λ value, the ENR model selected 34 non-zero coefficients from the initial pool of 71 variables. Key protective factors included stronger grip strength, receipt of a public pension, active social participation, and better word recall performance. Prominent risk factors encompassed various functional limitations (e.g., walking, stooping difficulty) and adverse health conditions (e.g., depression, arthritis, and poor self-rated health) (Appendix C).

3.3. Distributed lag nonlinear model of risk factors on disability

3.3.1. Characteristics of the time-lagged effects of risk factors

In the DLNM, a total of 21 factors showed statistically significant effects at one or more time lags. The lagged effects varied considerably according to specific factors and changed over time. The lagged effect of some factors was greatest in the year of occurrence (lagged by 0 years). Although there was some fluctuation in the lagged effects, the majority of factors exhibited significant effects primarily within a lag of 0–2 years. As the time lag increased to 3–4 years, the effects tended to diminish or become statistically insignificant. Some risk factors, such as stroke, hospitalization, systolic blood pressure, and depression, exhibited lower effects at the beginning of occurrence but tended to rebound within 2–3 years or longer. Among all the risk factors, grip strength, public pension status, social participation, and word recall were identified as the protective factors against disability among older adults. Appendix C displays the lagged effects of 34 risk factors on disability over a lag of 0–4 years. The diverse temporal dynamics of the lagged effects prompted us to classify the risk factors according to the time of their peak or persistent effects.

3.3.2. Classification of lagged effect pattern of risk factors

Based on the lag effect characteristics identified, risk factors were categorized into three primary time-lagged effect patterns: early-phase, mid-phase, and late-phase lags. Early-phase lag factors (peak effect at lags of 0–1 years): these factors exerted their strongest effects immediately or within the first year (lag of 0–1), with effects often diminishing rapidly thereafter. Key factors included walking difficulty, chair standing up difficulty, stair climbing difficulty, stooping difficulty, arm extension difficulty, heavy lifting difficulty, coin picking up difficulty, and total debt. Mid-phase lag factors (a delayed peak/rebound at lags of 2–3 years): The highest risk (or a significant rebound) for these factors emerged later, specifically at lags of 2–3 years. While some showed an initial effect, the most pronounced peak in risk or protection effects was delayed. Notable examples were social participation, arthritis, stroke, grip strength, self- reported health, mental disease, economic support received, and word recall. Late-phase lag factors (persistent effects up to lags of 3–4 years): the effects of this group persisted over a longer duration, typically reaching their maximum or maintaining significance at lags of 3–4 years. Unlike factors with diminishing effects, they exhibited cumulative or progressively worsening risks over the lag period. The key factors included hospitalization, systolic blood pressure, public pension status, depression, and dyslipidemia. Detailed lag-response curves are provided in Appendix D.

3.3.3. Cumulative effects of risk factors

Fig. 1 presents the CRR of all risk factors within lags of 0–4 years. It could be observed that grip strength (CRR = 0.80; 95 %CI: 0.54–0.95; P = 0.02) and social participation (CRR = 0.89; 95 %CI: 0.73–0.99; P = 0.04) were protective factors against disability. For hazard factors, arthritis (CRR = 1.51; 95 %CI: 1.10–2.06; P = 0.001), depression (CRR = 2.38; 95 %CI: 1.30–4.35; P < 0.001), chair standing up difficulty (CRR = 2.33; 95 %CI: 1.47–3.68; P < 0.001), stair climbing difficulty (CRR = 1.59; 95 %CI: 1.04–2.43; P = 0.01), hospitalization (CRR = 1.37; 95 %CI: 1.01–1.87; P = 0.02), heavy lifting difficulty (CRR = 2.23; 95 %CI: 1.36–3.67; P < 0.001), self-reported health (CRR = 1.45; 95 %CI: 1.19–2.21; P = 0.04), stooping difficulty (CRR = 3.58; 95 %CI: 2.31–5.55; P < 0.001), systolic blood pressure (CRR = 1.64; 95 %CI: 1.06–2.79; P = 0.02), walking difficulty (CRR = 2.77; 95 %CI: 1.39–5.55; P < 0.001), and economic support received (CRR = 2.20; 95 %CI: 1.29–3.38; P < 0.001) have a statistically significant cumulative lagged effects on disability.

Fig. 1.

The cumulative relative risk of factors with lags of 0–4 years.

3.4. Effect modification

Table 1 presents the results of the subgroup analyses by gender and age. The cumulative effects of risk factors varied across subgroups. Males showed stronger cumulative effects in difficulties in chair standing, heavy lifting, and walking. In contrast, females were more vulnerable to the cumulative effects of depression, difficulty in stooping, and coin picking up. Regarding age, adults older than 75 years were more susceptible to the cumulative impacts of difficulty in coin picking up and poor self-reported health.

Table 1.

The cumulative effects of factors over 0–4 lag years modified by gender, and age.

Subgroups	Male	Female	P	<75 (years)	≥75 (years)	P
Factor	CRR (95 %CI)	CRR (95 %CI)		CRR (95 % CI)	CRR (95 %CI)
Arm extension difficulty	1.86 (0.58–5.97)	2.14 (0.95–4.83)	0.700	1.61 (0.79–3.31)	1.68 (0.86–3.89)	0.910
Arthritis	1.78 (1.06–3.01)	1.61 (1.00–2.58)	0.620	1.67 (1.16–2.43)	1.53 (1.02–2.62)	0.680
Depression	2.06 (1.06–3.25)	3.31 (1.78–4.68)	<0.001	2.28 (1.09–4.78)	1.91 (1.06–5.20)	0.560
Chair standing up difficulty	4.77 (2.16–6.50)	1.85 (0.93–3.67)	<0.001	2.16 (1.24–3.76)	2.35 (1.42–6.49)	0.750
Stair climbing difficulty	1.27 (0.88–2.35)	1.39 (0.92–2.46)	0.780	1.52 (1.04–2.81)	2.79 (1.22–7.25)	0.030
Coin picking up difficulty	2.35 (0.48–4.58)	3.41 (0.92–6.65)	0.030	2.11 (0.71–6.27)	4.65 (1.13–7.58)	<0.001
Grip strength	0.81 (0.29–1.03)	0.68 (0.24–1.27)	0.690	0.64 (0.32–1.28)	0.85 (0.63–1.25)	0.610
Total debt	1.02 (0.98–1.07)	0.96 (0.91–1.01)	0.110	1.00 (0.97–1.04)	1.02 (0.89–1.16)	0.810
Hospitalization	2.32 (1.37–3.93)	1.68 (0.87–2.86)	0.090	1.39 (0.95–2.05)	1.76 (0.89–3.21)	0.320
Heavy lifting difficulty	3.91 (1.27–6.08)	2.03 (1.05–3.93)	<0.001	3.05 (1.63–5.70)	3.85 (1.23–6.58)	0.060
Mental disease	4.15 (1.36–6.22)	3.98 (1.42–5.38)	0.500	2.55 (1.60–4.71)	2.03 (1.32–3.89)	0.260
Public pension status	0.76 (0.42–1.36)	0.82 (0.51–1.46)	0.880	0.99 (0.65–1.53)	1.00 (0.71–1.45)	0.970
Self-reported health	1.66 (0.81–3.41)	1.50 (0.77–2.94)	0.750	1.21 (0.72–2.02)	3.90 (1.96–5.87)	<0.001
Social participation	0.85 (0.72–0.98)	0.77 (0.64–0.86)	0.380	0.86 (0.72–1.07)	0.75 (0.68–1.00)	0.550
Stooping difficulty	3.65 (2.26–5.55)	4.30 (3.22–6.31)	0.020	4.22 (3.08–6.84)	5.08 (2.75–8.59)	0.020
Stroke	1.04 (0.72–1.70)	1.03 (0.87–2.28)	0.980	0.92 (0.58–1.84)	0.93 (0.65–1.56)	0.980
Systolic blood pressure	1.90 (1.03–3.94)	1.94 (0.93–4.07)	0.940	1.39 (0.72–2.67)	1.62 (0.89–4.06)	0.690
Word recall	0.92 (0.85–1.01)	1.05 (0.97–1.14)	0.050	0.96 (0.90–1.02)	0.93 (0.85–1.11)	0.770
Walking difficulty	3.59 (1.36–5.33)	2.32 (1.27–5.21)	<0.001	2.54 (1.28–4.82)	2.58 (1.05–5.28)	0.930
Dyslipidemia	1.24 (0.85–2.79)	1.65 (0.88–3.10)	0.430	1.28 (0.86–2.98)	2.21 (1.15–4.07)	0.080
Economic support received	2.60 (1.25–5.39)	2.67 (1.29–5.41)	0.880	2.86 (1.71–4.80)	2.25 (1.28–4.98)	0.200

Note: CRR = cumulative relative risk.

3.5. Sensitivity analysis

The associations between disability and risk factors remained largely stable in the sensitivity analyses (Appendix E). Although there are slight differences among the groups, the overall direction remains stable.

4. Discussion

To our knowledge, this is the first study in China to apply the DLNM to explore the time-lagged and cumulative effects of diverse risk factors for disability among older adults. Our study identified three distinct lagged effects patterns, which likely reflect different underlying biological and psychosocial processes. Early-phase lag factors (e.g., difficulty in walking) exerted their strongest impact shortly or within the first year, underscoring the direct impairment of fundamental physical functions essential for daily independence. Mid-phase lag factors (e.g., arthritis) exhibited delayed peaks or rebounds in effects at lags of 2–3 years. This pattern suggests gradual processes such as changes in physiological reserve and self-management. Finally, late-phase lag factors demonstrated persistent effects over 3–4 years, highlighting the long-term, cumulative burden imposed by conditions like hospitalizations and chronic psychological distress (e.g., depression). Collectively, these findings provide a novel perspective and substantive evidence for understanding the dynamic progression of disability and developing precise intervention strategies.

In terms of hazard factors, self-reported health is regarded as an accurate indicator of overall functional capacity, with studies consistently linking it to various health and functional outcomes [27]. Additionally, our results corroborate the role of depression as a significant predictor of difficulties in activities of daily living [28]. Similarly, the association between hospitalization and increased risk of functional dependence and long-term disability, a widely acknowledged adverse outcome [29], is strongly supported by our findings. Furthermore, our study reinforces that stroke is a major contributor to disability, which is typically associated with its complications and the protracted rehabilitation process [13]. At the same time, higher systolic blood pressure ( ≥140 mmHg) likely contributes indirectly by increasing the risk of stroke [30]. Functional limitations, such as difficulty in standing up, are confirmed to increase the risk of mobility issues and disability significantly [31]. Consistently, joint diseases like arthritis are known to impair self-care, transfers, and mobility, leading to poorer performance in both BADL and IADL [32]. In terms of protection factors, our findings are consistent with evidence that greater grip strength [33] and active social participation [34] help preserve physical function and promote mobility.

Our findings suggest that there are three main lag patterns of risk factors. Among the early-phase factors, functional limitations, such as difficulties with walking, stooping, or climbing stairs, were the most significant predictors of subsequent disability. This pattern indicates that compromised basic physical functions pose an acute, direct risk to daily independence. A sudden decline in lower-body mobility [31] can profoundly impair an older adult’s independence. On the one hand, these limitations are intrinsically linked to underlying musculoskeletal and neurological decline, manifesting as muscle atrophy [35], joint degeneration, and neurological deterioration [36]. These pathophysiological changes typically result from the cumulative impact of chronic conditions (e.g., arthritis [36]) or the ageing process itself. On the other hand, a newly occurring functional limitation may itself be the result of a serious acute event. Falls, fractures, and early strokes can all lead to a sudden and rapid reduction in mobility that can affect an individual’s independence [37,38]. Consequently, the risk of disability arising from these factors associated with functional limitations’ rises sharply, typically peaking within the first year of onset.

The mid-phase lag pattern was primarily associated with self-rated health, grip strength, stroke, and arthritis. This lag pattern may be attributable to two underlying mechanisms: the decline of physiological reserve and challenges in long-term self-management. Physiological reserve is defined as the potential capacity of cells, tissues, or systems in response to changes in physiological demand [39]. It’s essential for coping with health stressors and determining the level of disturbance an individual can tolerate [40]. Self-reported health and grip strength are both indicators of quantitative evaluation of physiologic reserve [41]. Individuals’ physiological reserves may decline gradually due to natural ageing and underlying diseases [42]. Therefore, the impact of Self-reported health and grip strength on the risk for disablity may not be immediately apparent, but instead becomes statistically significant over time, thereby exhibiting lag effects in the mid-phase. Conversely, for factors like arthritis and stroke, self-management is crucial for symptom control and functional recovery [43]. However, self-efficacy and adherence often wane over time due to insufficient support or waning motivation [39], potentially leading to suboptimal rehabilitation, treatment failure, and disease progression [44].

The late-phase lag factors, including more frequent hospitalizations, higher depression scores, and higher systolic blood pressure, exhibited persistent effects on disability risk over 3–4 years. This pattern highlights the long-term and cumulative effects on the risk for disability, making it more difficult to perform BADL or IADL [45] independently. A disability associated with hospitalization is often a sentinel event with profound effects on patients long after discharge [45]. It has long-term adverse effects on the functional status of older adults [46]. Up to two-thirds of patients may take as long as 12 months or longer to recover to baseline function after discharge [47].

According to Beck’s [48] cognitive theory of depression, individuals with depressive tendencies adopt dysfunctional attitudes when faced with stress. These attitudes can lead to decreased personal motivation, depressed mood, and clinical somatic disorders (e.g., disability). This is also corroborated by longitudinal evidence showing that older adults with depression experience accelerated physical decline over extended periods [49]. The persistent presence of higher systolic blood pressure has been linked to subsequent cognitive decline [50], which can be attributed to insidious cerebrovascular and neurodegenerative processes, including cerebral amyloid angiopathy, tau pathology, and hippocampal atrophy [51]. These pathological progressions commonly take years, so these factors do not show an immediate impact on disability and tend to show a gradual cumulative burden.

Based on the lag characteristics of risk factors, more tailored management strategies can be developed for the older groups. The Short Physical Performance Battery (SPPB), the Timed Up and Go Test (TUG), and gait speed all provide an objective and quantitative reflection of an individual’s physical performance [52]. There’s an urgent need to incorporate standardized physical mobility assessments into routine health evaluations for older adults to identify those at risk of disability effectively [53].

For mid-phase lag factors, emphasis should be placed on physiologic reserve and chronic disease management. Intrinsic capacity (IC) is a determinant of physiological reserves [54], and it’s possible to enhance reserves by improving IC—the Integrated Care for Older People (ICOPE) plan [55]. Concurrently, it is essential to establish an effective self-management education program, such as the Chronic Disease Self-Management Program (CDSMP) [56], which helps regularly assess the effectiveness of self-management in older adults in controlling disease progression. Additionally, controlling blood pressure levels and monitoring mental health are crucial for maintaining the individual’s long-term health. Guideline recommends home blood pressure monitoring as the best way to understand the effectiveness of antihypertensive treatment in hypertensive patients [57], while regular mental health screening can facilitate the early detection and management of chronic psychological distress.

5. Strengths and limitations

This study had several strengths. First, this study was based on a nationally representative cohort with a large set of predictors. Second, we used the DLNM for the first time to explore the time lag characteristics of risk factors associated with disability. Third, we performed a series of sensitivity analyses to show that the results were considerably robust. Nevertheless, it is important to acknowledge several limitations. First, due to the inclusion of objective physical measurements and database constraints, the analysis was restricted to data from the CHARLS 2011–2015 waves. Consequently, caution is necessary when interpreting the findings to assess disability risks at this stage. Second, the study examined the association between individual risk factors and disability, but did not analyze the potential interactions between them. Third, some of the participants’ information was self-reported, which may introduce some information bias. Lastly, our study was conducted in China, which may limit the generalizability of our findings to other regions.

6. Conclusions

This study employed DLNM to investigate the impact of risk factors for disablity on older adults at various time lags and their cumulative effects over time. We identified three distinct effect patterns: early-phase lag factors had an immediate impact, reflecting direct functional impairments; mid-phase lag factors showed delayed peaks, suggesting roles for declining physiological reserve and self-management; and late-phase lag factors exerted persistent and cumulative effects. These findings provide a temporal framework for developing targeted interventions to reduce the risk of disability and improve health during ageing. Future studies should explore the underlying biological and sociological mechanisms of these lag effects in depth, identify intervention strategies that target risk factors with different lag patterns, and evaluate their effectiveness.

CRediT authorship contribution statement

Yitong Mao: Conceptualization, Methodology, Formal analysis, Validation, Data curation, Writing - original draft, Writing - review & editing. Zhiting Guo: Conceptualization, Methodology, Formal analysis, Validation, Writing - review & editing, Project administration. Wen Gao: Methodology, Writing - review & editing, Supervision, Project administration. Yuping Zhang: Writing - review & editing, Supervision, Project administration. Jingfen Jin: Writing - review & editing, Supervision, Funding acquisition, Project administration.

Data availability statement

The datasets used and analysed during the current study are available from the corresponding author on reasonable request.

Funding

This study was supported by Scientific Research Fund of National Health Commission of the People’s Republic of China - Major Science and Technology Program for Medicine and Health in Zhejiang Province (WKJ-ZJ-2406).

Declaration of competing interest

The authors have declared no conflict of interest.

Appendices. Supplementary data

The following are the supplementary data to this article.