Abstract
Background
Falls are among the most common safety concerns in people with visual impairment and can lead to serious consequences, including fractures, prolonged hospitalization, and even death. Patients with glaucoma are at increased risk of falls due to visual field loss, impaired motor coordination, and declines in cognitive function compared with the general population. Resting pulse rate is an easily obtainable measure in routine clinical practice; however, its contribution to fall risk prediction in patients with glaucoma has not been sufficiently investigated. To address this knowledge gap, we developed and compared multiple predictive approaches by incorporating a broad range of fall-related variables into prediction models, and we used explainable machine learning to quantify the contribution of resting pulse rate to fall risk prediction in glaucoma. In doing so, we aimed to explore the potential contribution of resting pulse rate as one of the model features in fall risk estimation, rather than as a standalone glaucoma-specific ophthalmic indicator.
Methods
Data were obtained from the China Health and Retirement Longitudinal Study (CHARLS). We included 249 participants with self-reported physician-diagnosed glaucoma who had no history of falls at the 2015 baseline survey and completed follow-up in 2018. The outcome was the occurrence of any fall between 2015 and 2018. To further characterize baseline differences, we also included 12,297 participants without glaucoma and without a history of falls at the 2015 baseline survey for comparative analyses.Candidate predictors comprised demographic characteristics, clinical comorbidities, medication use, self-reported vision status, and relevant laboratory measures. Self-reported near and distance vision were treated as limited visual functional information available in the database and were not considered equivalent to objective glaucoma-specific ophthalmic indicators. To compare machine learning models with a conventional statistical approach, we developed a logistic regression (LR) baseline model and trained six machine learning models: random forest, XGBoost, gradient boosting decision tree (GBDT), support vector machine (SVM), k-nearest neighbors (KNN), and AdaBoost. Feature selection was performed in the training set using recursive feature elimination with 5-fold cross-validation; within each fold, feature selection was conducted using only the fold-specific training subset and evaluated on the corresponding validation subset to reduce the risk of information leakage and overly optimistic performance estimates. After determining the final feature subset, hyperparameters were tuned and models were fitted using cross-validation within the training set. Model stability was assessed using 1,000 bootstrap resamples of the training set, and we reported the area under the receiver operating characteristic curve (AUC) with 95% confidence intervals, accuracy, and F1 score. Calibration curves and decision curve analysis were used to evaluate calibration and clinical net benefit. Finally, SHAP was applied to interpret the best-performing XGBoost model.
Results
A total of 249 eligible participants with glaucoma were included. During follow-up, 36 participants reported at least one fall, yielding a fall incidence of 14.46%. In contrast, among the 12,297 non-glaucoma participants included for baseline comparison, 873 reported at least one fall (7.1%; P < 0.001).In model development, the conventional logistic regression model showed the lowest discriminative performance, with an AUC of 0.676 (95% CI, 0.628–0.724). The XGBoost model achieved the best performance, with an AUC of 0.851 (95% CI, 0.812–0.886). Decision curve analysis indicated that, within a threshold probability range of 51.5% to 67.5%, the XGBoost model provided greater net benefit than the other machine learning models. SHAP-based feature importance further identified key predictors of falls in patients with glaucoma, with resting pulse rate ranking among the top contributing features in the XGBoost model.
Conclusion
In this study, the XGBoost model demonstrated the best performance for estimating fall risk among participants with self-reported glaucoma. SHAP analyses indicated that resting pulse rate, creatinine, age, blood urea nitrogen, frailty status, and height made relatively large contributions within the final model. Given the absence of objective ophthalmic parameters, these findings should be regarded as exploratory and interpreted cautiously. Resting pulse rate may provide supplementary information within model-based fall risk estimation, but it should not be interpreted as a standalone glaucoma-specific indicator or as evidence of causality.
Keywords: Glaucoma, Fall risk, Machine learning, Resting pulse rate, SHAP analysis
Introduction
With the global population aging at an accelerating pace, health issues among middle-aged and older adults have become a major public health challenge. Among these, falls are one of the most common and consequential types of unintentional injury. In this population, falls often lead to serious outcomes, including permanent disability and even death [1]. The causes of falls are typically multifactorial, involving age-related decline in physical function, increased burden of comorbidities, and poor living environments [2]. According to a 2018 report from the U.S. Centers for Disease Control and Prevention (CDC), approximately 27.5% of adults aged 65 and older experienced at least one fall in the past year, with 10.2% of them sustaining injuries such as fractures or head trauma that required medical attention or hospitalization [3].
Glaucoma is a chronic eye disease characterized by progressive optic nerve atrophy and irreversible visual field loss. It is one of the leading causes of blindness worldwide and significantly impairs patients’ visual function and ability to live independently [4]. Numerous studies have confirmed that individuals with glaucoma are at substantially higher risk of falling compared to the general population, primarily due to visual field constriction, impaired spatial awareness, and reduced sensitivity to environmental stimuli [5]. A large-scale epidemiological study further demonstrated that the fall risk among glaucoma patients exceeds that of individuals with other ocular diseases, including those with diabetic retinopathy and age-related macular degeneration [6]. Therefore, identifying fall risk predictors in middle-aged and older adults with glaucoma is of great importance for the prevention of fall-related events in this vulnerable population.
In recent years, the rapid advancement of artificial intelligence technologies—particularly machine learning—has brought significant innovation to clinical risk prediction modeling. This progress is largely attributed to the superior capacity of machine learning algorithms to process high-dimensional data and capture complex nonlinear relationships between variables [7]. Machine learning methods have been increasingly applied in disease screening and outcome prediction across a wide range of clinical conditions [8–10]. Compared to traditional statistical models, machine learning algorithms often deliver higher predictive accuracy and can identify key predictors from a large pool of variables, offering more personalized insights for clinical decision-making [11]. To date, a variety of machine learning models have demonstrated promising performance in predicting postoperative complications, cardiovascular and cerebrovascular outcomes, and cancer risk [12–14]. However, fall risk prediction models specifically targeting middle-aged and older adults with glaucoma—while integrating multiple relevant clinical and functional variables—remain limited. Moreover, despite the enhanced accuracy of machine learning models, their “black box” nature often limits transparency, making it difficult to determine the specific influence of each variable on the prediction outcome [15]. The SHapley Additive exPlanations (SHAP) method addresses this limitation by ranking variables based on their contribution to model output, offering a clear visualization of feature importance and enhancing interpretability [16]. Importantly, applying SHAP analysis after model construction enables a more systematic understanding of variable contributions, which may help generate hypotheses regarding the relative importance of candidate predictors in model-based fall risk estimation.
Using data from the China Health and Retirement Longitudinal Study (CHARLS), we included 249 middle-aged and older adults with self-reported glaucoma who had no history of falls at baseline and were followed from 2015 to 2018. We incorporated demographic characteristics, self-reported vision status, laboratory measurements, clinical comorbidities, and medication use to develop multiple machine learning models and compare their performance with a conventional logistic regression model. Because CHARLS does not provide objective ophthalmic parameters such as visual field loss, intraocular pressure, optic nerve imaging, or glaucoma severity grading, the visual variables available in this study should be interpreted as limited functional information rather than glaucoma-specific ophthalmic indicators. Model discrimination, calibration, clinical utility, and interpretability were evaluated using ROC curves, calibration plots, decision curve analysis, and SHAP, with the aim of identifying candidate variables that contribute to fall risk prediction in patients with glaucoma. The findings of this study are intended to be exploratory and hypothesis-generating rather than to support standalone clinical screening or causal inference.
Methods and materials
Data source and study population
This study was conducted using data from the China Health and Retirement Longitudinal Study (CHARLS), a nationally representative health information database for middle-aged and older adults established by the National School of Development at Peking University [17]. CHARLS initiated its baseline survey in 2011 and subsequently conducted follow-up waves in 2013, 2015, and 2018, enrolling approximately 17,700 participants [18]. The inclusion criteria were as follows: (1) glaucoma at the 2015 baseline survey. Glaucoma was defined based on participants’ self-reported response to the question, “Have a doctor, nurse, or paramedical professional ever treated you for glaucoma?” Participants answering “yes” were classified as having glaucoma. Because objective ophthalmic measurements were unavailable in CHARLS, this definition should be interpreted as self-reported physician-diagnosed glaucoma rather than a clinically adjudicated glaucoma phenotype; (2) no history of falls at baseline in 2015; (3) completion of follow-up between 2015 and 2018 with available fall outcome data; and (4) key study variables were complete or had missing values that could be imputed using multiple imputation with the mice package. The exclusion criteria were: (1) loss to follow-up, death during follow-up, or missing fall information; and (2) substantial missingness in key variables that could not be reasonably imputed using mice. Ultimately, 249 participants with glaucoma were included in the core predictive modeling analysis. For descriptive baseline comparison only, we also included 12,297 participants without glaucoma and without a history of falls at the 2015 baseline survey.The CHARLS project was approved by the Ethics Review Committee of Peking University (IRB00001052-11015), and all participants provided written informed consent. This study was reported in accordance with the TRIPOD guideline [19].
Data processing
In the CHARLS database, missing values in some variables are common. If participants with missing data were excluded outright or the missingness mechanism was ignored, the resulting reduction in sample size and potential selection bias could compromise the reliability of the findings. Therefore, we handled missing data using multiple imputation. To ensure feasibility and robustness, only variables with < 30% missingness were included in the model development. The missingness mechanism was assumed to be missing at random (MAR). Multiple imputation was performed using fully conditional specification (FCS) with the mice package in R (version 3.13.0; R version 4.1.0) [20].
Primary outcome and covariates
The primary outcome was the occurrence of any fall between 2015 and 2018. Falls were defined using the 2018 CHARLS item asking whether the participant had fallen “since the last interview”; participants answering “yes” were classified as having experienced a fall event. Covariates were derived from the 2015 survey and included demographic characteristics, medication use, self-reported vision status, laboratory measurements from blood samples, and clinical comorbidities. These variables were selected because they were available in the CHARLS database and have been reported to be potentially relevant to falls in older adults. Self-reported near and distance vision were included as limited visual functional measures available in the database and were not intended to substitute for objective glaucoma-specific ophthalmic assessments.
Explainable machine learning tools
Using the follow-up data, we developed six machine learning models and a conventional logistic regression model to predict long-term fall risk in patients with glaucoma, including XGBoost, random forest, SVM, GBDT, KNN, AdaBoost, and logistic regression (LR). Feature selection was first conducted within the training set using recursive feature elimination (RFE) coupled with 5-fold cross-validation. The training set was partitioned into five mutually exclusive folds; in each iteration, four folds were used as the training subset and the remaining fold served as the validation subset. Feature selection was performed exclusively within the fold-specific training subset, and the performance of different feature subset sizes was compared using the AUC. The optimal feature subset was determined by aggregating results across the five folds, thereby minimizing the risk of information leakage and overly optimistic performance estimates. After the final feature subset was identified, hyperparameters were tuned via cross-validation within the training set to obtain the optimal parameter combinations and fit each model.To assess model stability and quantify performance uncertainty under a small-sample setting, we performed internal validation using 1,000 bootstrap resamples of the training set. Predictive performance was recorded for each resample, and we reported the AUC with 95% confidence intervals, along with accuracy and F1 score. Model calibration was evaluated using calibration plots, and clinical utility was assessed using decision curve analysis to compare net benefit across threshold probabilities. Finally, we applied SHAP (SHapley Additive exPlanations) to interpret the best-performing XGBoost model by quantifying and visualizing each feature’s contribution to the model output, thereby identifying key predictors with high contributions to fall risk prediction.
SHAP provides an approach to interpreting predictions from machine learning models by explicitly quantifying each feature’s contribution and direction of effect on the final prediction, helping to address the “black-box” nature of complex models [10]. The magnitude and sign of SHAP values intuitively indicate the extent to which a given variable increases or decreases the predicted risk. Moreover, each individual prediction can be explained by its corresponding set of SHAP values, which enhances model transparency and clinical interpretability [10].
Statistical analysis
Data preprocessing, model development, performance evaluation, and visualization were performed using R (version 4.1.0) and Python (version 3.8). Baseline characteristics were tabulated according to the following rules: for continuous variables with a normal distribution, groups were compared using the t test and results were reported as mean ± standard deviation; for non-normally distributed continuous variables, the Mann–Whitney U test was used and results were reported as medians. Categorical variables were summarized as counts and percentages. For categorical variables meeting the assumptions of the chi-square test, the chi-square test was applied; otherwise, Fisher’s exact test was used. A two-sided P value < 0.05 was considered statistically significant.
Result
Baseline characteristics
After screening, 249 participants with glaucoma and 12,297 participants without glaucoma were included for descriptive baseline comparisons. During follow-up, 36 participants with glaucoma reported at least one fall, corresponding to a fall incidence of 14.46%. In contrast, among the 12,297 non-glaucoma participants included for baseline comparison only, 873 reported at least one fall (7.1%; P < 0.001). These between-group comparisons were intended to describe differences in baseline characteristics and overall fall burden rather than to support causal inference.
Table 1 summarizes baseline differences between participants with and without glaucoma. Compared with the non-glaucoma group, participants with glaucoma were older (64 [56–70] vs. 57 [50–65] years; P < 0.001) and more frequently female (58% vs. 51%; P = 0.019). They also had a higher prevalence of comorbidities, including hypertension (43% vs. 24%; P < 0.001), diabetes (14% vs. 6%; P < 0.001), heart disease (33% vs. 12%; P < 0.001), and arthritis (56% vs. 29%; P < 0.001). Consistently, medication use was more common in the glaucoma group, including antihypertensive medications (33% vs. 18%; P < 0.001), diabetes medications (12% vs. 4%; P < 0.001), lipid-lowering medications (13% vs. 5%; P < 0.001), and cardiac medications (15% vs. 6%; P < 0.001). Importantly, poorer self-reported near vision (27% vs. 16%; P < 0.001) and distance vision (32% vs. 15%; P < 0.001) were more frequent among participants with glaucoma. However, these self-reported measures reflect limited visual functional information and should not be interpreted as equivalent to objective glaucoma-specific ophthalmic impairment.In addition, compared with the non-glaucoma group, the glaucoma group showed higher glucose and blood urea nitrogen levels, lower white blood cell and platelet counts, lower hemoglobin, shorter height and lower body weight, higher frailty scores, and a lower resting pulse rate.
Table 1.
Comparison of baseline characteristics between participants with and without glaucoma
| Variables | Total (n = 12546) | Glaucoma (n = 249) | Non- Glaucoma (n = 12297) | p |
|---|---|---|---|---|
| age, Median (Q1,Q3) | 57 (50, 65) | 64 (56, 70) | 57 (50, 65) | < 0.001 |
| sex, n (%) | 0.019 | |||
| male | 6189 (49) | 104 (42) | 6085 (49) | |
| female | 6357 (51) | 145 (58) | 6212 (51) | |
| BMI, Median (Q1,Q3) | 23.82 (21.78, 25.96) | 23.96 (21.67, 26.06) | 23.81 (21.78, 25.95) | 0.828 |
| smoked, n (%) | 0.746 | |||
| 0 | 7104 (57) | 144 (58) | 6960 (57) | |
| 1 | 5442 (43) | 105 (42) | 5337 (43) | |
| drank, n (%) | 0.077 | |||
| 0 | 6788 (54) | 149 (60) | 6639 (54) | |
| 1 | 5758 (46) | 100 (40) | 5658 (46) | |
| height, Median (Q1,Q3) | 1.59 (1.53, 1.65) | 1.56 (1.52, 1.61) | 1.59 (1.53, 1.65) | < 0.001 |
| weight, Median (Q1,Q3) | 60.3 (53.9, 67.33) | 59.5 (52.5, 65.98) | 60.3 (53.9, 67.4) | 0.037 |
| waist, Median (Q1,Q3) | 86.1 (80, 92.4) | 86 (80.6, 94.5) | 86.1 (80, 92.38) | 0.366 |
| hypertension, n (%) | < 0.001 | |||
| 0 | 9524 (76) | 143 (57) | 9381 (76) | |
| 1 | 3022 (24) | 106 (43) | 2916 (24) | |
| diabetes, n (%) | < 0.001 | |||
| 0 | 11,715 (93) | 214 (86) | 11,501 (94) | |
| 1 | 831 (7) | 35 (14) | 796 (6) | |
| lung disease, n (%) | < 0.001 | |||
| 0 | 11,379 (91) | 199 (80) | 11,180 (91) | |
| 1 | 1167 (9) | 50 (20) | 1117 (9) | |
| stroke, n (%) | 0.008 | |||
| 0 | 12,271 (98) | 237 (95) | 12,034 (98) | |
| 1 | 275 (2) | 12 (5) | 263 (2) | |
| psychiatric disorders, n (%) | < 0.001 | |||
| 0 | 12,369 (99) | 235 (94) | 12,134 (99) | |
| 1 | 177 (1) | 14 (6) | 163 (1) | |
| arthritis, n (%) | < 0.001 | |||
| 0 | 8781 (70) | 109 (44) | 8672 (71) | |
| 1 | 3765 (30) | 140 (56) | 3625 (29) | |
| liver disease, n (%) | 0.018 | |||
| 0 | 12,032 (96) | 231 (93) | 11,801 (96) | |
| 1 | 514 (4) | 18 (7) | 496 (4) | |
| kidney disease, n (%) | 0.013 | |||
| 0 | 11,741 (94) | 223 (90) | 11,518 (94) | |
| 1 | 805 (6) | 26 (10) | 779 (6) | |
| gastric disease, n (%) | < 0.001 | |||
| 0 | 9751 (78) | 151 (61) | 9600 (78) | |
| 1 | 2795 (22) | 98 (39) | 2697 (22) | |
| asthma, n (%) | < 0.001 | |||
| 0 | 12,082 (96) | 223 (90) | 11,859 (96) | |
| 1 | 464 (4) | 26 (10) | 438 (4) | |
| heart disease, n (%) | < 0.001 | |||
| 0 | 11,020 (88) | 168 (67) | 10,852 (88) | |
| 1 | 1526 (12) | 81 (33) | 1445 (12) | |
| hip, n (%) | 0.817 | |||
| 0 | 12,302 (98) | 244 (98) | 12,058 (98) | |
| 1 | 244 (2) | 5 (2) | 239 (2) | |
| eyesight distance, n (%) | < 0.001 | |||
| 0 | 1925 (15) | 80 (32) | 1845 (15) | |
| 1 | 10,621 (85) | 169 (68) | 10,452 (85) | |
| eyesight close, n (%) | < 0.001 | |||
| 0 | 2037 (16) | 67 (27) | 1970 (16) | |
| 1 | 10,509 (84) | 182 (73) | 10,327 (84) | |
| frailtyb, Median (Q1,Q3) | 12.18 (7.82, 19.2) | 20.06 (13.33, 30.66) | 12.04 (7.79, 19.08) | < 0.001 |
| Diabetes meds, n (%) | < 0.001 | |||
| 0 | 12,020 (96) | 220 (88) | 11,800 (96) | |
| 1 | 526 (4) | 29 (12) | 497 (4) | |
| Lipid-lowering meds, n (%) | < 0.001 | |||
| 0 | 11,925 (95) | 217 (87) | 11,708 (95) | |
| 1 | 621 (5) | 32 (13) | 589 (5) | |
| Cardiac meds, n (%) | < 0.001 | |||
| 0 | 11,799 (94) | 212 (85) | 11,587 (94) | |
| 1 | 747 (6) | 37 (15) | 710 (6) | |
| Antihypertensive meds, n (%) | < 0.001 | |||
| 0 | 10,303 (82) | 168 (67) | 10,135 (82) | |
| 1 | 2243 (18) | 81 (33) | 2162 (18) | |
| Kidney meds, n (%) | 0.032 | |||
| 0 | 12,360 (99) | 241 (97) | 12,119 (99) | |
| 1 | 186 (1) | 8 (3) | 178 (1) | |
| UA, Median (Q1,Q3) | 4.82 (4.1, 5.6) | 4.7 (4, 5.4) | 4.82 (4.1, 5.6) | 0.102 |
| BUN, Median (Q1,Q3) | 14.85 (12.89, 17.09) | 15.69 (13.17, 17.93) | 14.85 (12.89, 17.09) | 0.004 |
| pulse, Median (Q1,Q3) | 73.5 (68, 79.5) | 71.5 (66, 78.5) | 73.5 (68, 79.5) | 0.008 |
| creatinine, Median (Q1,Q3) | 0.77 (0.69, 0.88) | 0.74 (0.66, 0.84) | 0.77 (0.69, 0.88) | 0.002 |
| WBC, Median (Q1,Q3) | 5.85 (5.08, 6.7) | 5.7 (4.7, 6.4) | 5.85 (5.1, 6.7) | 0.002 |
| MCV, Median (Q1,Q3) | 91.7 (88.43, 94.7) | 92.3 (88.54, 96.4) | 91.7 (88.42, 94.7) | 0.036 |
| PLT, Median (Q1,Q3) | 204 (172.42, 237) | 188 (152.8, 218) | 204 (173, 237) | < 0.001 |
| glucose, Median (Q1,Q3) | 95.5 (90.09, 105.23) | 96.22 (90.09, 115.32) | 95.5 (90.09, 105.23) | 0.023 |
| HDL, Median (Q1,Q3) | 50.19 (44.79, 55.98) | 50.58 (45.17, 57.92) | 50.19 (44.79, 55.91) | 0.318 |
| LDL, Median (Q1,Q3) | 100.54 (86.87, 114.67) | 101.93 (87.64, 117.68) | 100.54 (86.87, 114.67) | 0.476 |
| Hb, Median (Q1,Q3) | 13.74 (12.8, 14.72) | 13.24 (12.36, 14) | 13.76 (12.8, 14.74) | < 0.001 |
| Cycs, Median (Q1,Q3) | 0.81 (0.73, 0.91) | 0.87 (0.77, 0.96) | 0.81 (0.73, 0.91) | < 0.001 |
| CRP, Median (Q1,Q3) | 1.6 (0.9, 2.64) | 1.4 (0.8, 2.5) | 1.6 (0.9, 2.64) | 0.27 |
| fall down, n (%) | < 0.001 | |||
| 0 | 11,637 (93) | 213 (86) | 11,424 (93) | |
| 1 | 909 (7) | 36 (14) | 873 (7) |
Feature selection
We first performed feature selection within the training set using recursive feature elimination (RFE) coupled with 5-fold cross-validation. The training set was partitioned into five mutually exclusive folds; in each iteration, four folds were used as the training subset and the remaining fold served as the validation subset. Feature selection was conducted exclusively within the fold-specific training subset, and the predictive performance of different feature subset sizes was compared using the AUC as the primary metric. The optimal feature subset was determined by aggregating results across the five folds, thereby minimizing the risk of information leakage and overly optimistic performance estimates.As shown in Fig. 1, the cross-validated AUC increased rapidly when a small number of features were included and achieved the best performance when 12 features were retained. Accordingly, we selected these 12 features for subsequent model development: resting pulse rate, creatinine, age, blood urea nitrogen, frailty score, height, white blood cell count, C-reactive protein, mean corpuscular volume, platelet count, high-density lipoprotein, and uric acid.
Fig. 1.
Relationship Between Feature Numbers and Model AUC Based on XGBoost
Comparison of predictive model performance
We developed six machine learning models and a conventional logistic regression model to predict the occurrence of falls during follow-up among participants with glaucoma. Figures 2 and 3 present ROC curves for all models. Overall, all six machine learning models achieved higher AUCs than the logistic regression baseline (AUC = 0.676; 95% CI, 0.628–0.724). Among the machine learning approaches, the XGBoost model demonstrated the best discriminative performance, with an AUC of 0.851 (95% CI, 0.812–0.886). The AdaBoost model ranked second, with an AUC of 0.821 (95% CI, 0.777–0.859). Figure 4 further summarizes model performance during training, internal validation, and cross-validation. The XGBoost model showed the most favorable overall performance, achieving an AUC of 0.851 (95% CI, 0.812–0.886), with an accuracy of 0.786, F1 score of 0.783, recall of 0.786, precision of 0.811, and specificity of 0.724. To further examine generalization across different training sample sizes, we plotted the learning curve for the XGBoost model (Fig. 5).
Fig. 2.
ROC Curves of Machine Learning Models for Fall Risk
Fig. 3.
ROC curve of the traditional logistic regression model
Fig. 4.
Comparison of predictive performance across different models
Fig. 5.
Learning curve of the XGBoost model
Calibration curves for all models are shown in Fig. 6. Across models, some degree of miscalibration was observed across predicted probability ranges; in general, closer alignment of the calibration curve to the 45-degree reference line indicated better agreement between predicted and observed event probabilities. Decision curve analysis is shown in Fig. 7. With the exception of KNN, all models demonstrated positive net benefit over a broad range of threshold probabilities. Notably, the XGBoost model yielded the highest net benefit between threshold probabilities of 0.515 and 0.675 and outperformed both “treat-all” and “treat-none” strategies within this range.To further characterize the clinical trade-offs of applying different risk thresholds to the XGBoost model, we plotted a threshold risk analysis curve (Fig. 8). The x-axis represents the risk threshold, whereas the y-axis shows the number of individuals classified as high risk (blue line) and the number of fall events captured among those classified as high risk (red line); the green dashed line indicates the total number of fall events in the sample. As the threshold increased, fewer individuals were classified as high risk, and the number of captured events also decreased. Specifically, when the threshold was below 0.6, more participants were labeled as high risk, improving event capture but potentially increasing the false-positive burden. When the threshold approached 0.7, the number of individuals classified as high risk declined sharply, with a corresponding reduction in captured events, suggesting a higher risk of missed true high-risk individuals. Balancing the decision curve results with the threshold risk analysis, we selected 0.6 as the optimal threshold for defining high fall risk, aiming to reduce excessive false-positive identification at lower thresholds while avoiding missed identification of truly high-risk individuals at higher thresholds.
Fig. 6.
Calibration curves of the models
Fig. 7.
Decision curve analysis of the models
Fig. 8.
Risk Threshold Analysis of the XGBoost
Interpretation of the XGBoost model using SHAP
We applied SHAP to interpret the best-performing XGBoost model. Figure 9 illustrates the overall contribution of each feature to the model output, quantified by the mean absolute SHAP value. Resting pulse rate showed the largest contribution, followed by creatinine, age, blood urea nitrogen, frailty score, and height. Figure 10 presents a SHAP summary (beeswarm) plot to further depict the relationship between feature values and prediction direction. The x-axis represents SHAP values, where SHAP > 0 indicates that the feature pushes the prediction toward a higher fall risk, whereas SHAP < 0 pushes the prediction toward a lower risk. Point colors reflect feature values, with red indicating higher values and blue indicating lower values. Overall, higher values of resting pulse rate, creatinine, and age tended to increase the predicted fall risk, whereas higher values of WBC and PLT tended to decrease the predicted risk. These findings indicate that resting pulse rate had a relatively large contribution within the final model; however, this should not be interpreted as evidence of causality or as implying that its clinical effect necessarily exceeds that of other established factors. The relationship between resting pulse rate and fall risk therefore requires further investigation.
Fig. 9.
SHAP-Based Feature Importance of XGBoost
Fig. 10.
SHAP beeswarm plot of the XGBoost model
To illustrate the model’s decision-making process at the individual level, we generated SHAP force plots for two representative participants (Figs. 11A–B). Figure 11A shows an individual without a fall event, whereas Fig. 11B shows an individual who experienced a fall. In the force plots, the base value represents the model’s baseline output without incorporating individual feature information, and f(x) denotes the final model output after incorporating all features for that individual. Red features push the prediction toward a higher fall risk, whereas blue features push the prediction toward a lower risk. The arrow length reflects the magnitude of each feature’s impact, with longer arrows indicating larger contributions.
Fig. 11.
A. SHAP force plot for an individual without a fall event. B. SHAP force plot for an individual with a fall event
Taken together, the global SHAP importance ranking (Fig. 9) and the individual force plots (Fig. 11) suggest that resting pulse rate not only has the highest overall contribution, but also frequently shows substantial “push–pull” effects at the individual level, indicating a pronounced influence on the final prediction. Given that resting pulse rate is easily obtainable and can be monitored longitudinally, these findings suggest that it had a relatively large contribution within the final model. However, this should be interpreted as a model-based contribution rather than as evidence of causality or as support for standalone clinical screening, particularly given the absence of objective ophthalmic parameters in the database.
Discussion
In this retrospective cohort study based on a large public database, we first described baseline differences between participants with and without glaucoma. The incidence of falls was 14.46% in the glaucoma group, which was significantly higher than the 7.1% observed in the non-glaucoma group (P < 0.001). However, these between-group comparisons were descriptive in nature and should not be interpreted as indicating an independent effect of glaucoma itself, given the substantial differences in age, frailty, and comorbidity burden between the two groups. We then developed and internally validated six machine learning algorithms and one conventional logistic regression approach to estimate the probability of falls specifically within the cohort of middle-aged and older adults with self-reported glaucoma. Among these models, XGBoost achieved the best predictive performance. We also examined threshold-dependent trade-offs using calibration plots and decision curve analysis. Based on the balance between false-positive identification and missed high-risk individuals within this dataset, we selected a threshold probability of 0.6 as a working threshold for model interpretation. However, this threshold should be understood as an analytical choice within the present study rather than a clinically established intervention threshold. XGBoost has been widely used in clinical event prediction to estimate outcome risk, although its findings still require cautious interpretation in modest-sized cohorts such as ours [21–23].Although machine learning models often show strong predictive ability in clinical settings, their “black-box” nature can limit interpretability, which remains an important barrier to broader clinical adoption [24]. SHAP, grounded in Shapley value theory from cooperative game theory, assigns an exact contribution value to each feature and thereby reveals the relative importance of predictors in model prediction [25].In our study, we applied SHAP to interpret the XGBoost model and enhance clinical interpretability. Resting pulse rate showed the highest contribution within the final model. This model-based contribution should be distinguished from the descriptive between-group comparison, in which the non-glaucoma group had a slightly higher median resting pulse rate but a lower overall fall rate.However, this finding should be interpreted as indicating relative importance within a multivariable prediction model, rather than establishing resting pulse rate as a causal determinant or a standalone clinical marker of falls in older adults with glaucoma.
Resting pulse rate is an easily obtainable marker of autonomic function in routine clinical practice, and prior studies have shown that an elevated resting pulse rate is associated with increased risks of multiple diseases [26–28]. Evidence also suggests that autonomic dysregulation reflected by a higher resting pulse rate is linked to worse functional status in middle-aged and older adults and to an increased risk of subsequent functional decline [29].In older populations, this dysregulated state may impair blood pressure regulation and contribute to orthostatic hypotension and insufficient cerebral perfusion, thereby increasing the risk of falls [30]. From a biological perspective, it is therefore plausible that a higher resting pulse rate may be associated with an elevated risk of falls in older adults, given that falls are typically multifactorial events involving muscle weakness, impaired balance, and the burden of chronic comorbidities [31, 32].Older patients with glaucoma often experience reduced motor function due to visual field defects [33],and may therefore be more prone to a heightened susceptibility to falls. Notably, the association between binocular visual field loss and fall-related behavioral outcomes appears relatively consistent.As binocular visual field impairment worsens, visual input during everyday activities such as walking, turning, and obstacle avoidance is reduced, limiting visually guided postural control and gait adjustment. This can increase fear of falling and promote activity avoidance [34]. Such behavioral changes may further reduce physical activity and functional capacity, thereby increasing subsequent fall risk and contributing to greater fall susceptibility in patients with glaucoma [35]. Recent studies have also linked visual field loss to severe falls requiring hospitalization, suggesting that visual impairment may not only increase the likelihood of minor falls but may also be associated with more consequential fall outcomes, such as fractures and traumatic brain injury requiring inpatient care [36]. Against this background, if patients with glaucoma concurrently exhibit the dysregulated functional state suggested by an elevated resting pulse rate, their risk of severe falls may be further increased.Accordingly, our study provides additional evidence from an explainable machine learning perspective: even after incorporating a broad range of fall-related variables, resting pulse rate remained the top contributing feature in the XGBoost model and showed a clear positive influence on the model output in both SHAP beeswarm plots and individual force plots. These findings suggest that resting pulse rate may provide incremental information for fall risk stratification in patients with glaucoma beyond basic characteristics and routine laboratory measures.Nevertheless, because objective ophthalmic parameters were unavailable and visual status was based on self-reported measures, these pathophysiological interpretations remain speculative and should not be overinterpreted.
Using a large nationwide cohort, we developed and compared multiple prediction models for fall risk among middle-aged and older adults with glaucoma, and ultimately selected the XGBoost model as the best-performing approach. SHAP analyses further showed that resting pulse rate had the highest contribution among candidate predictors.Given the absence of objective ophthalmic parameters and the modest sample size of the glaucoma cohort, this finding should be regarded as exploratory and hypothesis-generating. It suggests that resting pulse rate may provide supplementary information in model-based fall risk estimation, but it does not support standalone clinical screening, glaucoma-specific mechanistic inference, or individual-level causal interpretation.Several limitations should be acknowledged. First, glaucoma status was based on participants’ self-reported physician diagnosis, and objective ophthalmic assessments (e.g., intraocular pressure measurements and optic nerve imaging) were unavailable; therefore, we were unable to perform stratified analyses by glaucoma subtype, disease severity, or the extent of visual field loss. Accordingly, self-reported near and distance vision in the present study should be interpreted only as limited visual functional information and not as substitutes for visual field assessment or other objective glaucoma-specific indicators.Nevertheless, previous studies have reported a certain degree of agreement between self-reported eye diseases, including glaucoma, and clinical records, and the reliability of self-reports is generally acceptable in epidemiological research [37, 38]. Second, although we included multiple medication-related variables (for example, antihypertensive, cardiac, glucose-lowering, and lipid-lowering medications) as candidate predictors, CHARLS does not provide detailed information on specific drug names or dosages for glaucoma participants, limiting our ability to evaluate the effects of particular medications on resting pulse rate and its contribution to the model. Third, fall events were self-reported using follow-up questionnaires and may be subject to recall bias and misclassification. Fourth, because an independent external validation cohort is not currently available, the generalizability of our XGBoost model across different clinical settings remains to be established. In addition, the modest size of the glaucoma cohort and the limited number of fall events may affect model stability and increase the risk of statistical uncertainty despite internal validation procedures. Accordingly, the relative contribution ranking produced by SHAP should also be interpreted cautiously, as it may be sensitive to sample size and model structure in a modest-sized cohort. We are currently attempting to collect data from patients with glaucoma at Zhujiang Hospital, Southern Medical University for external validation. Although preliminary data have been obtained, prospective external validation is not yet feasible due to limited sample size and incomplete follow-up information. Finally, the study population consisted primarily of middle-aged and older adults in China (predominantly Asian), and thus the applicability of the model to other racial or regional populations is uncertain and warrants further validation in diverse settings.Despite these limitations, the potential value of resting pulse rate for fall risk prediction remains clinically meaningful. In the context of the present model, it may provide supplementary information for estimating fall risk among older adults with self-reported glaucoma. However, its role should be interpreted cautiously and should not be viewed as sufficient for standalone clinical screening or decision-making. Further prospective studies with more comprehensive ophthalmic assessments are needed to confirm and refine these findings.
Conclusion
We developed an explainable XGBoost prediction model, which showed the best performance for estimating fall risk among patients with glaucoma. In addition, explainable machine learning enabled a more precise exploration of fall-related predictors in this population. SHAP analyses indicated that resting pulse rate had the highest contribution to fall risk prediction and also exerted a pronounced influence in individual-level explanations. In the absence of objective ophthalmic parameters, these findings should be regarded as exploratory and interpreted cautiously. Resting pulse rate may provide supplementary information in model-based fall risk estimation, but it should not be interpreted as a standalone glaucoma-specific indicator, a basis for clinical screening, or evidence of causality. Further prospective studies with more comprehensive ophthalmic assessments are needed to validate these findings. Nevertheless, further validation in independent cohorts with more comprehensive ophthalmic parameters and detailed medication information is warranted.
Acknowledgements
We thank the China Health and Retirement Longitudinal Study (CHARLS) team for providing access to the data used in this study, and we are grateful to all participants and investigators involved in the CHARLS project.
Abbreviations
- CHARLS
China health and retirement longitudinal study
- LR
Logistic regression
- RF
Random forest
- XGBoost
Extreme gradient boosting
- GBDT
Gradient boosting decision tree
- SVM
Support vector machine
- KNN
k-Nearest Neighbors
- AdaBoost
Adaptive boosting
- SHAP
SHapley additive exPlanations
- RFE
Recursive feature elimination
- ROC
Receiver operating characteristic
- AUC
Area under the curve
- CDC
Centers for disease control and prevention
- BMI
Body mass index
- WBC
White blood cell count
- MCV
Mean corpuscular volume
- PLT
Platelet count
- CRP
C-reactive protein
- BUN
Blood urea nitrogen
- HDL
High-Density lipoprotein
- LDL
Low-Density lipoprotein
- UA
Uric acid
- Hb
Hemoglobin
- Cycs
Cystatin C
- FCS
Fully conditional specification
- MAR
Missing at random
- IRB
Institutional review board
- TRIPOD
Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis
Author contributions
ZRZ and JWW were responsible for the conception and design of the study, data analysis, and drafting of the manuscript. JH, as the corresponding author, supervised the study design, interpreted the findings, and revised the manuscript. SZT, GLP, HRJ, WLN, and CZJ contributed to data curation, literature review, and discussion of the results, and provided important revisions to the manuscript. All authors have read and approved the final version of the manuscript and take full responsibility for the accuracy and integrity of the work.
Funding
This study did not receive any funding support.
Data availability
The datasets used and analyzed in this study are available from the China Health and Retirement Longitudinal Study (CHARLS) database: https://charls.pku.edu.cn.
Declarations
Ethics approval and consent to participate
The CHARLS project was approved by the Institutional Review Board of Peking University (IRB00001052-11015). All participants provided written informed consent prior to participation.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Zhenrong Zhang and Junwei Wang contributed equally to this work.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The datasets used and analyzed in this study are available from the China Health and Retirement Longitudinal Study (CHARLS) database: https://charls.pku.edu.cn.