Heterogeneous and nonlinear associations between depressive symptoms and functional disability in older Chinese adults

Abstract

Background

Existing studies on the association between depressive symptoms and functional disability in older adults have mainly focused on average effects. However, limited evidence is available on how this association varies across different levels of disability, and the potential nonlinear relationship between the two remains unclear.

Methods

This study used data from the 2015, 2018, and 2020 waves of the China Health and Retirement Longitudinal Study (CHARLS). A balanced panel of 1,189 older adults with disability was constructed. A two-way fixed-effects model was used to estimate the association between depressive symptoms and functional disability. Quantile regression (QR)was employed to examine heterogeneity across different quantiles of disability. Quantile random forest (QRF)was further used to explore the nonlinear relationship between depressive symptoms and functional disability.

Results

Depressive symptoms were significantly positively associated with functional disability (β = 0.171, p < 0.001). QR analyses showed that this association differed substantially across quantiles of disability and increased progressively from lower to higher quantiles (from 0.034 to 0.267). QRF analysis further revealed the effect became markedly stronger at higher levels of depressive symptoms. SHAP analysis at the individual level further supported these findings.

Conclusion

Depressive symptoms are an important factor affecting functional disability in older adults. Their effect shows significant distributional heterogeneity and nonlinear characteristics. Strengthening depression intervention among older adults with higher levels of disability may help delay the progression of functional decline.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40359-026-04984-7.

Introduction

With the acceleration of global population aging, disability has become a major public health issue affecting the quality of life of older adults. Disability is a dynamic process that unfolds over time [1]. Its progression not only undermines independent living among older adults, but also substantially increases medical and caregiving costs, thereby placing considerable burdens on individuals, families, and society [2]. Importantly, disability is graded by severity and exists along a continuum ranging from mild to severe [3, 4]. Therefore, identifying the key factors associated with different levels of disability is of great importance for developing targeted and effective intervention strategies. As the country with the largest older population in the world, China had approximately 35 million older adults with disabilities by 2024, accounting for 11.6% of its total older population [5]. At the same time, family-based care remains the dominant model of elder care in China [6]. Against the backdrop of rapid population mobility and shrinking family size, older adults face not only challenges associated with declining functional capacity but also increased vulnerability to psychological distress [7]. Examining the relationship between depression and functional disability among older adults in the Chinese context can therefore provide stronger empirical evidence to support targeted mental health interventions for disabled older adults.

Depression, a common mental disorder among older adults [8], has been widely recognized as an important risk factor for disability [9–12]. Previous studies have suggested that depression may accelerate functional decline by reducing physical activity and exacerbating the burden of chronic diseases [13]. At the same time, depression is the most disabling among various diseases [14]. However, the impact of depressive symptoms on functional disability may not be uniform across older adults. On the one hand, both the manifestation and severity of depressive symptoms vary considerably across individuals [15]. On the other hand, disability itself follows a progressive course from mild to severe levels [16]. Consequently, older adults with different levels of disability may experience different psychological effects. Focusing solely on the average effect of depressive symptoms on functional disability may obscure important differences across population subgroups, thereby limiting the identification of high-risk groups and the development of targeted interventions.

Building on previous research, several issues warrant further investigation. First, most studies have relied on mean-based regression approaches, such as ordinary least squares (OLS), to estimate the effect of depression on the average level of functional disability among older adults [17, 18]. Although these studies have documented a significant association between depression and functional disability, they provide limited insight into whether this relationship varies across different levels of disability. Moreover, late-life depression is inherently heterogeneous [19], and estimates derived from mean regression are susceptible to the influence of extreme values [20, 21], making it difficult to distinguish the effects of depression between older adults with mild disability and those with severe disability. Second, as depressive symptoms worsen and functional status deteriorates, the relationship between the two may not follow a simple linear pattern and may instead exhibit nonlinear acceleration effects. Previous research has suggested that the prediction of depression risk involves complex nonlinear interactions across different functional states [22]. However, traditional linear models have limited capacity to identify and characterize potential nonlinear relationships between depression and functional disability [23–25].

Against this background, the present study draws on longitudinal data from the 2015, 2018, and 2020 waves of the China Health and Retirement Longitudinal Study (CHARLS) to examine the impact of depressive symptoms on functional disability among Chinese older adults from the perspectives of distributional heterogeneity and nonlinearity. This study contributes to the literature in two ways. First, it applies quantile regression (QR) to assess how the effects of depressive symptoms differ across the distribution of functional disability, thereby identifying heterogeneous effects between older adults with lower and higher levels of disability. Second, it introduces quantile random forest (QRF) models to detect potential nonlinear relationships between depressive symptoms and functional disability and further complements the findings through SHapley Additive exPlanations (SHAP) analysis. By integrating these approaches, this study advances understanding of the relationship between depressive symptoms and functional disability and provides evidence to support targeted interventions for disabled older adults.

Methods

Study population

This study used data from the China Health and Retirement Longitudinal Study (CHARLS) to track the same cohort of older adults with disability. CHARLS is a nationally representative survey designed to collect high-quality microdata at both the household and individual levels among Chinese adults aged 45 years and older, with follow-up interviews conducted every 2–3 years [26]. The study protocol was approved by the Biomedical Ethics Review Committee of Peking University (IRB00001052-11015), and informed consent was obtained from all participants prior to data collection.

Following the conventional definition of older adults adopted in studies on population aging in China and previous research using CHARLS data [27–29], individuals aged 60 years and above were defined as older adults. This study used 2015 as the baseline year and selected older adults with functional disability at that time as the study population, constructing a balanced panel dataset covering three waves in 2015, 2018, and 2020. Given the relatively high attrition rate among disabled older adults during long-term follow-up, we retained only those who participated in all three survey waves to enhance sample continuity. Compared with an unbalanced panel, a balanced panel can, to some extent, reduce sample variation arising from attrition, mortality, and other factors, thereby providing a more stable representation of individual changes over time. The final balanced panel comprised 1,189 disabled older adults, yielding a total of 3,567 observations. Figure 1 presents the sample selection process.

Fig. 1.

Flowchart of the sample selection process. Note: ADL refers to Activities of Daily Living, and IADL refers to Instrumental Activities of Daily Living. The functional disability assessment includes 6 ADL items and 6 IADL items, yielding a total of 12 items

To address missing data, we applied multiple imputation by chained equations (MICE) and generated 20 imputed datasets (m = 20). Details of variables with missing values are provided in Supplementary Table S2. For the two-way fixed-effects model (FE-OLS), we combined parameter estimates across the imputed datasets using Rubin’s rules. For the quantile regression (QR) analysis, we estimated the model separately for each of the 20 imputed datasets and then pooled the regression coefficients and corresponding standard errors at each quantile to obtain the final results. For the Quantile Random Forest (QRF) and SHAP analyses, we conducted the analyses using the first completed imputed dataset. This approach reflects the primary purpose of these methods, namely identifying variable importance and potential nonlinear relationships, as well as the absence of a standardized procedure for pooling results from multiply imputed machine-learning models.

Variables

Functional disability

In all waves of CHARLS, respondents were asked about six activities of daily living (ADL), including dressing, bathing, eating, getting in and out of bed, using the toilet, and controlling urination and defecation, as well as six instrumental activities of daily living (IADL), including doing housework, preparing meals, shopping, taking medications, managing finances, and making telephone calls. Respondents were defined as having disability if they reported difficulty in at least one of these items [30]. Each item was coded on a three-point scale: 1 = having difficulty but still able to do it, 2 = having difficulty and needing help, and 3 = unable to do it. The total disability score ranged from 1 to 36, reflecting different levels of disability, with higher scores indicating more severe functional limitations.

Depression

Depressive symptoms were assessed in CHARLS using the 10-item Center for Epidemiologic Studies Depression Scale (CESD-10), which has been shown to have good reliability and validity among older Chinese adults [31, 32]. The scale consists of 10 items assessing respondents’ feelings and behaviors during the past week. Eight items are negatively worded and two are positively worded and reverse-coded. All items were rated on a four-point scale, which was recoded to range from 0 to 3. The total score ranged from 0 to 30, with higher scores indicating more severe depressive symptoms [33].

Covariates

Based on the study objectives and previous studies on depressive symptoms and functional disability among older adults [26, 34, 35], this study included 11 covariates covering demographic characteristics, health-related characteristics, and economic support. Supplementary Table S1 provides detailed definitions, variable types, and coding schemes for all variables.

Demographic variables included gender, age, household registration, marital status, and educational level. Educational level was classified into three categories: primary school or below (Level 1), junior high school and senior high school (Level 2), and college education or above (Level 3). Given that disabled older adults often rely heavily on daily care and emotional support [6, 36], this study focused on the availability of practical support from a partner rather than legal marital status alone. Accordingly, marital status was categorized into two groups: living with a partner and not living with a partner. The former included individuals who were married and living with their spouse, married but temporarily living apart from their spouse due to work or other reasons, and those cohabiting with a partner. The latter included individuals who were never married, divorced, separated (no longer living as spouses), or widowed.

Health status variables included the number of chronic diseases, self-rated health, memory, and history of falls. Self-rated health and memory were originally assessed using a five-point Likert scale (1 = very good to 5 = poor). To ensure consistent directionality (where higher scores indicate better health), these variables were reverse-coded prior to analysis.

Economic support variables included pension income and financial support from children. Pension income was derived from multiple sources, including pensions from new rural resident pension, urban resident pension, urban and rural resident pension, commercial pension insurance, and old age pension allowances. Financial support from children encompassed both monetary and in-kind contributions. Monetary support included regular assistance (e.g., living expenses, utility bills, and communication costs) and irregular support for major life events (e.g., festivals, birthdays, weddings, and funerals), while in-kind support covered food, clothing, and other expenditures. Both pension income and financial support from children were natural log-transformed (ln(x + 1)) to reduce skewness and scale differences.

Analysis

This study developed an analytical framework integrating econometric and machine learning approaches to systematically examine the effects of depressive symptoms on functional disability in older adults from three perspectives: average effects, distributional heterogeneity, and nonlinear relationships. First, we use descriptive statistics to summarize the sample characteristics. Second, we apply a two-way fixed-effects (FE-OLS) model to estimate the average effect of depressive symptoms on functional disability. This model effectively controls for unobserved individual-specific factors that remain constant over time as well as common time trends, thereby identifying the association between within-individual changes in depressive symptoms and changes in disability.

To further examine the heterogeneous effects of depressive symptoms across the distribution of functional disability, we employed quantile regression (QR) and estimated regression coefficients at the 0.10, 0.25, 0.50, 0.75, and 0.90 quantiles. These quantiles represent older adults with low, moderately low, median, moderately high, and high levels of functional disability, respectively. Given the short panel structure of the data, consisting of three survey waves, estimating individual fixed-effects quantile regression models would require a large number of individual-specific parameters and may therefore suffer from the incidental parameters problem, potentially compromising estimation stability. To address this issue, we adopted pooled quantile regression models with year fixed effects to assess the heterogeneous effects of depressive symptoms across different levels of functional disability [37–39].

Building on the main analysis, we further applied Quantile Random Forests (QRF) to identify potential nonlinear relationships. Variable importance measures, partial dependence plots, and SHAP analyses helped interpret the predictive contribution of depressive symptoms across different levels of functional disability. It should be noted that QRF does not directly account for within-individual correlations in panel data. Therefore, we conducted the analysis using pooled panel data, with the primary aim of identifying variable importance and potential nonlinear relationships as a supplementary analysis to the main models. Finally, we performed robustness checks by introducing lagged variables and standardizing key variables to assess the reliability of the results. All statistical tests were two-sided, and p < 0.05 indicated statistical significance.

Results

Descriptive Statistics

This study included 1,189 disabled older adults and followed them across three survey waves over a six-year period. At baseline, participants had a mean age of 72.04 years, and women accounted for 66.19% of the sample. Descriptive statistics indicated that both depressive symptoms and functional disability increased over time during the follow-up period. Notably, the mean depression score increased substantially between 2018 and 2020, with an increase of 1.331 points. This change may be related to the COVID-19 pandemic. Previous studies have shown that social distancing and isolation during the pandemic exposed older adults to greater psychological stress [40], while experiences related to COVID-19 also contributed to higher levels of depressive symptoms among older adults [41]. As the 2020 survey was conducted during the COVID-19 outbreak, the marked increase in depression scores may reflect the adverse impact of the pandemic on the mental health of older adults. Table 1 and Supplementary Table S1 present detailed demographic characteristics and descriptive statistics of the study variables.

Table 1.

Descriptive statistics by demographic characteristics

Variables	2015	2018	2020	Overall
Key variables
Depression	12.084 (7.150)	12.191 (7.076)	13.502 (6.839)	12.592 (7.050)
Functional disability	7.045(6.366)	8.616(7.226)	9.572(8.834)	8.411(7.615)
Demographic characteristics
Female(%)	66.19%	66.19%	66.19%	66.19%
Age	72.040 (6.310)	75.040 (6.310)	77.040 (6.310)	74.706 (6.635)
Rural household registration(%)	84.525%	84.525%	84.525%	84.525%
Without a partner(%)	30.614%	37.174%	42.052%	36.613%
Educational level	1.038(0.216)	1.038(0.216)	1.038(0.216)	1.038(0.216)
Health status
Number of chronic diseases	2.757(1.820)	3.366(2.020)	3.505(2.122)	3.209(2.017)
Self-rated health	1.679 (0.766)	2.366 (0.935)	2.325 (0.946)	2.123 (0.940)
Memory	1.511 (0.713)	1.634 (0.775)	1.518 (0.718)	1.554 (0.738)
History of falls(%)	30.95%	35.071%	35.576%	33.866%
Economic support
Pension income (ln)	4.622 (3.310)	5.326 (3.127)	6.431 (3.027)	5.460 (3.242)
Financial support from children (ln)	6.910 (2.794)	6.836 (2.739)	7.130 (2.670)	6.959 (2.737)
Sample size(N)	1189	1189	1189	3567

Note: Continuous variables are presented as mean (standard deviation), and categorical variables are presented as percentages. Statistics are based on the first imputed dataset

Fixed-effects and quantile regression results

Table 2 presents the results from the baseline regression and pooled quantile regression analyses. To further assess whether the estimated coefficients differed significantly across quantiles, we conducted cross-quantile tests. The results indicated significant differences in the estimated coefficients across quantiles (all p < 0.001; see Supplementary Table S3), supporting the presence of distributional heterogeneity.

Table 2.

Results of the baseline regression and pooled quantile regression analyses

	FE-OLS	QR_0.1	QR_0.25	QR_0.5	QR_0.75	QR_0.9
Depression	0.171***	0.034***	0.065***	0.149***	0.211***	0.267***
	(0.030)	(0.008)	(0.015)	(0.029)	(0.046)	(0.075)
Age		0.068***	0.116***	0.247***	0.397***	0.395***
		(0.009)	(0.014)	(0.024)	(0.041)	(0.063)
Number of chronic diseases	0.324*	0.006	0.017	0.092	-0.056	0.086
	(0.117)	(0.029)	(0.043)	(0.075)	(0.113)	(0.190)
Marital status	0.686	0.018	-0.157	-0.409	-1.042*	-0.836
	(0.638)	(0.108)	(0.159)	(0.288)	(0.485)	(1.017)
Self-rated health	-1.163***	-0.352***	-0.610***	-1.401***	-2.037***	-2.646***
	(0.173)	(0.071)	(0.097)	(0.166)	(0.245)	(0.382)
Memory	-0.292	-0.030	0.012	-0.074	0.308	1.014
	(0.193)	(0.078)	(0.096)	(0.195)	(0.425)	(0.533)
History of falls	1.276***	0.263*	0.674***	0.965***	1.699***	2.117**
	(0.263)	(0.120)	(0.166)	(0.287)	(0.496)	(0.796)
Pension income	-0.017	0.007	0.011	0.027	0.028	-0.133
	(0.036)	(0.014)	(0.024)	(0.049)	(0.078)	(0.130)
Financial support from children	0.031	-0.010	-0.030	-0.081	-0.147	-0.103
	(0.055)	(0.016)	(0.035)	(0.055)	(0.098)	(0.129)
Educational level		-0.252	-0.363	-0.318	0.097	3.686
		(0.169)	(0.403)	(0.684)	(2.050)	(2.191)
Gender		0.123	0.304*	0.101	-1.498*	-2.415**
		(0.097)	(0.150)	(0.282)	(0.590)	(0.782)
Household registration		0.022	-0.003	-0.379	-0.663	-0.817
		(0.144)	(0.198)	(0.466)	(0.782)	(0.986)
factor(year)2018		0.342*	0.733***	1.517***	2.099***	2.886***
		(0.140)	(0.209)	(0.301)	(0.564)	(0.785)
factor(year)2020		-0.083	0.104	0.978**	2.292**	5.672***
		(0.134)	(0.218)	(0.372)	(0.699)	(1.098)
(Intercept)		-3.064***	-5.311***	-10.965***	-15.876***	-14.096**
		(0.716)	(1.238)	(2.123)	(4.006)	(5.355)
Num.Obs.	3567	3567	3567	3567	3567	3567
Individual FE	Yes	No	No	No	No	No
Year FE	Yes	Yes	Yes	Yes	Yes	Yes

Note: FE-OLS standard errors are clustered at the individual level. Bootstrap standard errors for the QR models are based on 500 replications. Age was omitted from the FE-OLS model because of collinearity with individual and year fixed effects

* p < 0.05, ** p < 0.01, and *** p < 0.001

The two-way fixed-effects (FE-OLS) model showed a significant positive association between depressive symptoms and functional disability after controlling for both individual and time effects (β = 0.171, p < 0.001), suggesting that older adults with higher levels of depressive symptoms tended to exhibit higher levels of functional disability. The quantile regression results further revealed substantial variation in this association across the distribution of functional disability. As the quantile increased, the coefficient for depressive symptoms rose progressively from 0.034 to 0.267 (0.034 → 0.065 → 0.149 → 0.211 → 0.267; all p < 0.001). This upward trend indicates that depressive symptoms exerted a stronger effect among older adults with higher levels of functional disability.

Among the covariates, age was omitted from the FE-OLS model because of collinearity with the time fixed effects. In the QR model, age exhibited a significant positive association across all quantiles, with the coefficient increasing from 0.068 to 0.395 (all p < 0.001). This pattern suggests that advancing age was associated with higher levels of functional disability and that this association became more pronounced among older adults with greater disability. The number of chronic diseases showed a significant positive effect in the FE-OLS model (β = 0.324, p < 0.05) but did not reach statistical significance at any quantile. This finding suggests that the effect of chronic conditions may vary considerably across different levels of functional disability and does not exhibit a stable distributional pattern. Marital status was not statistically significant in the FE-OLS model. However, it showed a significant negative association at the 0.75 quantile (β = -1.042, p < 0.05), indicating that the presence of a partner has a smaller effect for high levels of functional disability.

Self-rated health showed a significant negative association with functional disability in the FE-OLS model (β = -1.163, p < 0.001). A similar pattern emerged across all quantiles, with the absolute value of the coefficient increasing from 0.352 to 2.646 (all p < 0.001). These results suggest that better self-rated health was associated with lower levels of functional disability and that this association became stronger among older adults with higher levels of disability. At the same time, potential reverse causality cannot be ruled out, as older adults with more severe functional disability may report poorer health status. To mitigate this concern, we re-estimated the models using a one-wave lagged measure of self-rated health in the subsequent robustness analyses.

A history of falls was significantly and positively associated with functional disability in the FE-OLS model (β = 1.276, p < 0.001). Positive associations also appeared across all quantiles, with the coefficients increasing from 0.263 to 2.117. These findings indicate that fall experiences were associated with higher levels of functional disability among older adults and that this association was more pronounced at higher levels of disability. Memory, pension income, and financial support from children did not reach statistical significance in either the FE-OLS or QR models.

Educational level, gender, and household registration are time-invariant variables; therefore, their coefficients were not reported in the FE-OLS model. In the QR model, neither educational level nor household registration reached statistical significance at any quantile. By contrast, gender exhibited distributional heterogeneity. The association between gender and functional disability remained inconsistent across the low- to middle-disability quantiles (0.10, 0.25, and 0.50), reaching statistical significance only at the 0.25 quantile (β = 0.304, p < 0.05). At the 0.75 and 0.90 quantiles, the coefficients for gender were − 1.498 (p < 0.05) and − 2.415 (p < 0.01), respectively, indicating that gender differences were concentrated among older adults with higher levels of functional disability. Women are less likely than men to reach high levels of disability, and this difference became more pronounced as the level of disability increased.

Figure 2 provides a more intuitive illustration of how the effect of depressive symptoms varies across the distribution of functional disability. The results show that the association between depressive symptoms and functional disability was not uniformly distributed and became more pronounced at higher quantiles. As the quantile increased, the coefficient for depressive symptoms rose steadily from 0.034 at the 0.10 quantile (p < 0.001) to 0.267 at the 0.90 quantile (p < 0.001). The FE-OLS model estimated an average effect of 0.171 (p < 0.001), which was lower than the corresponding estimates at the 0.75 and 0.90 quantiles (0.211 and 0.267, respectively; p < 0.001). This pattern further suggests that quantile regression can capture distributional differences that may not be apparent in mean-based regression models. It should be noted that the average effect estimated by the FE-OLS model is presented in Fig. 2 for reference only. The FE-OLS model captures the average within-person association, whereas pooled quantile regression characterizes conditional associations at different positions of the functional disability distribution and incorporates both within-person and between-person variation. Therefore, the estimates from the two approaches are not strictly comparable.

Fig. 2.

Heterogeneous effects of depression across the disability distribution. Note: The black solid line shows the quantile regression coefficients of depression on disability score. The shaded area represents the 95% confidence interval. The red dashed line represents the average within-person association estimated from the two-way fixed-effects model and is shown for reference only

Quantile random forest and SHAP results

To further evaluate the predictive contributions of individual variables to functional disability and to examine potential nonlinear relationships, this study introduced quantile random forest (QRF) as a supplementary analytical approach (Fig. 3).

Fig. 3.

Variable importance ranking and partial dependence plots based on QRF. Note: Panel A shows the variable importance from quantile random forest, Panel B shows the partial dependence of depression on disability. The solid purple line represents the median prediction generated by the QRF model, the shaded area indicates the 25th–75th percentile interval (reflecting individual differences), and the red dashed line shows the smoothed trend to facilitate visualization of the overall pattern

The variable importance results (Fig. 3A) revealed substantial differences in the predictive contributions of individual variables to functional disability among older adults. Age emerged as the most important predictor, followed by financial support from children and depressive symptoms. Pension income, the number of chronic conditions, self-rated health, and memory also contributed to the prediction of functional disability to varying degrees. By contrast, marital status and history of falls showed relatively low importance. Overall, depressive symptoms ranked among the top three predictors, highlighting their important role in explaining variations in functional disability among older adults. Partial dependence analysis (Fig. 3B) further revealed the relationship between depressive symptoms and functional disability. The results indicated a nonlinear increasing trend, with higher levels of depressive symptoms associated with higher predicted levels of functional disability. At lower levels of depressive symptoms, the association remained relatively modest. As depressive symptoms increased to moderate and high levels, the predicted level of functional disability rose more rapidly. In particular, when depressive symptoms exceeded 20 points, the predictive effect of depressive symptoms on functional disability accelerated markedly. In addition, the quantile range of the predicted values widened as depressive symptoms increased, indicating greater variability across individuals at higher levels of depressive symptoms. This pattern further reflects the heterogeneous nature of functional disability.

On this basis, SHAP analysis was further applied to interpret the model (Fig. 4) and to reveal the contribution patterns of variables at the individual level. Unlike variable importance, which reflects overall predictive contribution, SHAP values characterize the marginal contribution of each variable to the prediction for a specific observation.As shown in Fig. 4A, age, self-rated health, and depressive symptoms emerged as the three most important predictors. Overall, depressive symptoms remained a key predictor of functional disability. The wide distribution of SHAP values associated with depressive symptoms indicates substantial variation in their contribution to individual predictions. In addition, financial support from adult children, history of falls, and pension income demonstrated moderate explanatory power, whereas marital status and memory contributed relatively little to the prediction of functional disability.

Fig. 4.

SHAP plots. Note: Panel A shows the SHAP summary plot, in which the horizontal spread reflects variable importance. Panel B shows the SHAP dependence plot for depressive symptoms. A SHAP value greater than 0 indicates an increased predicted level of disability, whereas a SHAP value less than 0 indicates a decreased predicted level

The SHAP dependence plot (Fig. 4B) further revealed the nonlinear effect of depressive symptoms on disability. At lower levels of depressive symptoms (CESD-10 scores of approximately 0–12), SHAP values remained negative and changed relatively gradually, indicating that depressive symptoms contributed to lower predicted levels of functional disability within this range. As depressive symptoms increased further (approximately 12–20 points), SHAP values became positive and continued to rise, suggesting an increasingly positive contribution of depressive symptoms to the prediction of functional disability. At higher levels of depressive symptoms (above 20 points), SHAP values increased further, indicating a stronger predictive contribution. Meanwhile, the distribution of SHAP values became more dispersed at higher levels of depressive symptoms, suggesting greater heterogeneity in predicted outcomes across older adults. These findings provide individual-level evidence that complements the results of the QR and QRF analyses.

Robustness analysis

To assess the robustness of the baseline findings, we conducted a series of robustness checks from three perspectives: model dynamics, variable scaling, and potential endogeneity. First, we introduced a one-wave lagged measure of functional disability into the model to account for the persistence of disability over time and to examine whether the association between depressive symptoms and current functional disability remained stable under a dynamic specification. This approach also helps mitigate the potential influence of reverse causality to some extent. Second, we standardized both the depressive symptom scores and functional disability scores to evaluate the sensitivity of the results to variable scaling. Finally, we re-estimated the models using a one-wave lagged measure of self-rated health to address the potential reverse causality between self-rated health and functional disability, as older adults with more severe disability may be more likely to report poorer health status. This approach also helps reduce potential endogeneity bias. The robustness checks yielded results consistent with the baseline findings (Table 3). Across all alternative specifications, the estimated coefficients for depressive symptoms remained stable in both direction and statistical significance, supporting the robustness of the main results. In addition, the quantile regression coefficients continued to increase across higher quantiles, further supporting the conclusion that depressive symptoms exert a stronger influence among older adults with higher levels of functional disability.

Table 3.

Robustness Checks of Depression Effects on Disability

Model	FE-OLS	QR(0.1)	QR(0.25)	QR(0.5)	QR(0.75)	QR(0.9)
Baseline	0.171*** (0.030)	0.034*** (0.008)	0.065*** (0.015)	0.149*** (0.030)	0.211*** (0.046)	0.267** (0.075)
Lagged disability	0.149** (0.041)	0.029* (0.012)	0.055* (0.020)	0.076** (0.023)	0.132** (0.035)	0.151. (0.072)
Standardized depression	1.216*** (0.214)	0.238*** (0.060)	0.459*** (0.104)	1.058*** (0.207)	1.501*** (0.328)	1.897** (0.534)
Standardized disability	0.023*** (0.004)	0.004*** (0.001)	0.008*** (0.002)	0.020*** (0.004)	0.028*** (0.006)	0.035** (0.010)
Lagged self-rated health	0.188*** (0.040)	0.035** (0.012)	0.066** (0.018)	0.186*** (0.037)	0.243*** (0.060)	0.269* (0.105)

Note: Results are pooled across 20 multiply imputed datasets using Rubin’ s rules. Standard errors are reported in parentheses

p < 0.1, * p < 0.05, ** p < 0.01, and *** p < 0.001

Discussion

This study used longitudinal data to systematically examine the effects of depressive symptoms on disability in older adults from the perspectives of average effects, distributional heterogeneity, and nonlinear relationships. The findings showed that depressive symptoms were significantly and positively associated with disability. More importantly, this association varied substantially across different levels of disability and exhibited clear nonlinear characteristics.

Consistent with previous research, depressive symptoms are an important factor influencing functional disability among older adults [42, 43]. Existing studies have shown that higher levels of depressive symptoms are not only associated with a greater risk of disability [34], but may also exacerbate the severity of disability [44]. In recent years, studies examining the bidirectional relationship between depressive symptoms and disability have gradually emerged [45]; however, most of this research has been based on mean effects, making it difficult to capture differences across populations with varying levels of functional status. In contrast, the present study further finds that the effect of depressive symptoms on disability varies significantly across different points of the distribution, which is consistent with previous findings that the impact of mental health-related factors is more pronounced among individuals with higher levels of disability [46].

The QR results show that, as the quantiles of disability increase, the effect of depressive symptoms gradually strengthens, with a significantly stronger impact observed among individuals with higher levels of disability compared to those with lower levels. This increasing trend suggests that the negative effects of depressive symptoms are more concentrated among older adults with poorer functional status. Previous studies have suggested that individuals with higher levels of disability are often characterized by reduced functional capacity, a greater burden of chronic conditions, and lower levels of social support, factors that may amplify the adverse impact of depressive symptoms on disability [47–49]. In addition, prior research has proposed that depressive symptoms may indirectly exacerbate functional decline through mechanisms such as impulsivity and emotional intelligence [50, 51].

The QRF results further indicate the nonlinear and heterogeneous nature of this association. The effect of depressive symptoms on functional disability remains relatively modest at lower levels, but exhibits an accelerated increasing trend at higher levels. This suggests that the impact of depressive symptoms on functional ability is not linear [52], but rather increases rapidly after reaching a certain level. A possible explanation is that when depressive symptoms are mild, their impact on individual functioning is relatively limited; however, as depressive symptoms worsen, individuals are more likely to experience social isolation, and living alone among older adults may further exacerbate the deterioration of functional status [53, 54]. In addition, the partial dependence plot shows that inter-individual variability increases substantially at higher levels of depressive symptoms, indicating that the effect of depression is not evenly distributed across populations with different functional statuses, and is more likely to accelerate the progression of disability among those with poorer functional conditions [55, 56]. This finding underscores the importance of implementing targeted psychological interventions among high-risk populations.

Notably, unlike previous studies that have primarily focused on health-related determinants of disability, the QRF analysis identified depressive symptoms as a more important predictor of functional disability than several traditional health indicators, including self-rated health and the number of chronic diseases. This finding highlights the important role of psychological factors in functional outcomes among older adults and is consistent with previous evidence emphasizing the contribution of mental health to functional status in later life [57, 58]. It is also important to note that, although the main analysis relied on fixed-effects models, the QRF analysis did not account for the repeated-measures structure of the panel data. As a result, observations from the same respondent at different time points may not be fully independent. Therefore, the variable importance rankings and partial dependence patterns should be interpreted with caution, as repeated observations may lead to an overestimation of the effective sample size. Nevertheless, the QRF and SHAP analyses primarily served to identify variable importance and potential nonlinear relationships as supplementary analyses. The main conclusions of this study are based on the FE-OLS and QR results, both of which account for individual heterogeneity. Therefore, this limitation is unlikely to materially affect the overall conclusions.

The above findings suggest that the association between depressive symptoms and functional disability exhibits substantial distributional heterogeneity, with a stronger association observed among individuals with moderate to high levels of disability. Therefore, strengthening early identification and intervention for older adults at moderate to high risk [59–61] may play a more substantial role in mitigating the progression of disability. In the context of healthy aging, traditional intervention strategies that primarily target physiological function may be insufficient to effectively address functional decline, whereas enhancing interventions targeting depressive symptoms may yield greater health benefits [62]. Incorporating mental health–related indicators into comprehensive intervention frameworks for older adults with disability may therefore have important practical implications.

This study also has several limitations. First, this study included only older adults who already had functional disability in 2015, focusing on changes in disability over time rather than the onset of disability. Therefore, the findings are limited to already disabled older adults. Second, this study employed a balanced panel including only individuals who were successfully followed across all three waves. Since older adults with higher levels of disability were more likely to die or be lost to follow-up, the final sample may not fully represent those with severe disability, potentially leading to selective attrition bias and affecting the representativeness of the results. Third, both depressive symptoms and functional ability were measured through self-report, which may introduce potential bias and affect the accuracy of the results. Fourth, although this study employed longitudinal data and further controlled for prior functional disability in the robustness analyses, the possibility of reverse causality cannot be completely ruled out. For example, while depressive symptoms may contribute to functional disability, functional disability itself may also worsen negative emotions and depressive symptoms. If reverse causality exists, the estimated effect of depressive symptoms on functional disability may be overstated. Therefore, the association observed in this study may reflect both the influence of depressive symptoms on functional disability and the influence of functional disability on depressive symptoms. It is worth noting that the coefficient for depressive symptoms decreased after controlling for prior functional disability but remained statistically significant in both the FE-OLS and QR models. This finding suggests that prior disability status explains part of the observed association but does not fully account for it. The relationship may also be shaped by multiple factors, including health status, chronic conditions, and social support. Therefore, future research should draw on longer-term longitudinal data and causal inference approaches to further examine the complex relationship between depressive symptoms and functional disability.

Conclusions

Depressive symptoms play an important role in functional decline among older adults. Their effects are not evenly distributed, but instead show clear heterogeneity and are more pronounced among individuals with higher levels of disability. Future interventions should consider depressive symptoms an important target for functional recovery in older adults, particularly among those with more severe disability, in order to delay the progression of disability and promote healthy aging [63].

Authors’ contributions

C.W. contributed to writing the original draft, reviewing and editing the manuscript, as well as visualization, methodology development, software implementation, formal analysis, and data curation. Y.L. contributed to writing the original draft and reviewing and editing the manuscript, and was also responsible for validation, supervision, project administration, and methodology development. All the authors approved this submission to BMC Psychology.

Funding

No funding support.

Data availability

The datasets used and analysed in this study are available in the CHARLS repository, https://charls.pku.edu.cn/en. Additionally, the data can be requested from the corresponding author upon reasonable request.

Declarations

Ethics approval and consent to participate

The study was conducted in accordance with the Declaration of Helsinki. Ethical approval was granted by the Biomedical Ethics Committee of Peking University (IRB 00001052–11015), and all participants provided written informed consent prior to data collection.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.