This study was conducted using cluster random sampling of medical institutions within the urban area of Urumqi City. The participants were older adult individuals aged 65 years or older who underwent health examinations at three medical institutions within the urban area of Urumqi City between June 2023 and March 2024. Inclusion criteria: (1) Having resided in the urban area of Urumqi City for at least 6 months. (2) Aged 65 years or older. (3) Able to independently cooperate to complete the survey. Exclusion criteria: (1) Eligible individuals unwilling to participate in the study. (2) Individuals with psychiatric disorders or end-stage diseases. A total of 4,175 participants were initially enrolled. Seventeen participants who failed to complete all required examinations were excluded, and 251 participants with missing information (missing basic information, health status, or disease history) were excluded. Finally, 3,907 participants were included in the study. Among these, there were 1,766 males and 2,141 females. The flow chart is presented in Figure 1. This study was reviewed and approved by the Ethics Committee of the Urumqi Center for Disease Control and Prevention, with an ethics review approval number of 2024-C111.

Data were obtained through face-to-face questionnaires, laboratory tests, and physical examinations. All data collection and measurements were performed by experienced medical personnel who underwent standardized uniform training. The questionnaire covered basic demographic characteristics, lifestyle habits (such as smoking, drinking, exercise frequency, and dietary habits), laboratory tests (including fasting blood glucose, total cholesterol, triglycerides, high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, etc.). Laboratory tests were performed using a fully automated biochemical analyzer (Mindray BS-600M, Shenzhen, China). Physical examination items included height, weight, waist circumference, blood pressure, electrocardiogram (ECG), abdominal ultrasound, etc. Height was measured using an electronic stadiometer (CAMRY iHT721D, Zhongshan City, China). Weight was measured using an electronic weighing scale (CAMRY EF881H, Zhongshan City, China). Waist circumference was measured at the midpoint between the iliac crest and the lower rib margin using an electronic digital soft tape (SENSSUN iS620B, Zhongshan City, China), to the nearest 0.1 cm. The mean of two measurements was calculated. Blood pressure was measured using an electronic sphygmomanometer (OMRON HEM-7111, Kyoto, Japan). Systolic blood pressure (SBP) and diastolic blood pressure (DBP) were measured three times, and the average of the three readings was calculated. Electrocardiogram (ECG) was performed using a fully digital multi-channel ECG machine (Mindray BeneHeart R700, Shenzhen, China). Participants were placed in the supine position in a quiet environment during resting conditions, and a continuous recording for 10 s was obtained. Ultrasound examinations (liver, cardiovascular) were performed using a color Doppler ultrasound system (Mindray DC-80, Shenzhen, China) with its matching convex array probe. All equipment used in the study met the Chinese national standards.

Fatty liver disease definition: Based on abdominal ultrasound features including liver echogenicity, deep attenuation, and clarity of ductal structures, fatty liver was diagnosed according to the Chinese Expert Recommendations for the Standardized Diagnosis and Treatment of Fatty Liver Diseases (2019 Revision) criteria. Mild: Enhanced near-field echoes in the liver parenchyma (higher than kidney/spleen), deep-field echo attenuation ≤1/3, and clear intrahepatic ductal structures. Moderate: Deep-field echo attenuation between 1/3 and 2/3, and blurred ductal structures. Severe: Deep-field echo attenuation >2/3, non-visible ductal structures, accompanied by hepatomegaly and rounded edges (15). Fatty liver was diagnosed upon meeting any of the criteria for mild, moderate, or severe. Central obesity definition: Waist circumference was measured using an electronic digital soft tape at the midpoint between the iliac crest and the lower rib margin. Based on the Chinese Guidelines for the Diagnosis and Treatment of Obesity (2024 Edition), central obesity was defined as a mean waist circumference (from two measurements) ≥ 90 cm for males or ≥85 cm for females. BMI definition: BMI < 18.5 kg/m² was classified as underweight, 18.5 kg/m² ≤ BMI < 24 kg/m² as normal weight, 24 kg/m² ≤ BMI < 28 kg/m² as overweight, and BMI ≥ 28 kg/m² as obese (16). Hypertension definition: Defined as systolic blood pressure (SBP) ≥ 140 mmHg and/or diastolic blood pressure (DBP) ≥ 90 mmHg, a previous medical history of hypertension, or current antihypertensive medication use (17). Diabetes definition: Defined as fasting plasma glucose ≥7.0 mmol/L, previously diagnosed with diabetes, or using glucose-lowering medications (18). Dyslipidemia definition: Defined upon meeting any one of the following criteria: total cholesterol ≥6.22 mmol/L, triglycerides ≥2.26 mmol/L, low-density lipoprotein cholesterol ≥4.14 mmol/L, or high-density lipoprotein cholesterol <1.04 mmol/L (19). Electrocardiogram (ECG) definition: Based on ECG findings, an abnormal ECG was defined as the presence of any of the following: premature beats, arrhythmias, ST-segment changes, T-wave changes, or abnormal Q waves. Aortic sclerosis definition: Based on cardiovascular ultrasound findings, aortic sclerosis was defined as the presence of any one of the following: aortic wall thickening, increased echogenicity, detection of plaque (soft plaque, hard plaque, or mixed plaque), or luminal narrowing.

SPSS 26.0 statistical software was used, and data were presented as mean ± standard deviation, and composition ratio (%), with chi-square tests used for analysis between groups with different characteristics. Using R4.4.0 software, and leveraging the commonly used caret package, the original dataset was stratified by the target variable and partitioned into a training set (70%) and a test set (30%). The random forest classifier with default parameters (n_estimators = 100) and the Lasso model with default parameters (alpha = 1.0) were selected. The random forest classifier was implemented using the Boruta package, while the Lasso model was implemented using the caret package. Models were built on both the training set and the test set. The area under the receiver operating characteristic curve (AUC) scores were compared. This step is based on the pROC package (AUC confidence intervals are calculated by the bootstrap algorithm of the package). The intersection of significant features identified by both models (variables deemed important by both models) was used for feature selection. Following correlation analysis, these features were incorporated into the subsequent logistic regression model and restricted cubic spline (RCS) model. Categorical variables were encoded using ordinal encoding. Using R software version 4.4.0, adjusted logistic regression analyses were performed, incorporating different sets of factors. Based on the rms package within the software, and utilizing the Akaike Information Criterion (AIC) to select the knots for the restricted cubic spline (RCS) model, a dose–response relationship curve between waist circumference and fatty liver disease risk was established. The linearity assumption of the RCS model was tested using the likelihood ratio test.

A total of 3,907 older adult individuals were included in this study, with a fatty liver disease prevalence of 32.56%, and an average age of 72.23 ± 5.94 years. Among them, there were 1,766 males and 2,141 females, with the prevalence of fatty liver disease being 31.54% in males and 33.40% in females. A univariate chi-square test was conducted between different groups of older adult individuals, and the results showed that differences in age, BMI classification, central obesity, hypertension, diabetes, dyslipidemia, smoking status, drinking frequency, electrocardiogram (ECG), and aortic sclerosis were statistically significant (p < 0.05). Differences in gender, exercise frequency, and dietary habits were not statistically significant (p > 0.05), as shown in Supplementary Table 1.

Whether having fatty liver disease was used as the dependent variable. Variables showing statistically significant differences in univariate chi-square tests were incorporated into the random forest classifier model established using the Boruta algorithm. This algorithm constructs “shadow variables” (blue) as randomized reference benchmarks. For the majority of the 99 iterations (convergence number of feature selection rounds) in the random forest classifier, variables were confirmed as important features (green) with significant influence on fatty liver disease when their importance exceeded the maximum shadow variable importance. Variables with importance between the minimum and maximum shadow variable importance were considered tentative features (yellow) with potential influence on fatty liver disease. Variables with importance below the minimum shadow variable importance were regarded as rejected features (red), indicating either no impact or collinearity issues regarding fatty liver disease. Ranked from highest to lowest importance, the results identified seven variables as important features (green): BMI classification, central obesity, electrocardiogram, aortic sclerosis, dyslipidemia, diabetes, and age, Two variables: smoking status and drinking frequency were identified as uncertain features (yellow). Hypertension was identified as one rejected feature (red). The importance ranking is shown in Figure 2.

LASSO model was employed to identify predictors significantly associated with fatty liver disease from variables exhibiting statistical significance in univariate chi-square tests. To determine the optimal regularization strength, k-fold cross-validation (k = 5) was performed to compute the binomial deviance across varying λ values. The validation process partitioned the training set into 5 subsets. After iterative rotation and validation, the mean deviance was calculated, identifying λ yielding minimal deviance (lambda.min = 0.001344464), corresponding to log(λ) = −6.61176. The LASSO algorithm shrinks irrelevant variable coefficients exactly to zero, while retaining predictors with non-zero coefficients. This indicates that the contribution strength of these retained variables to predicting fatty liver disease is sufficient to overcome the regularization penalty. Leveraging this mechanism, nine key features with non-zero coefficients were selected: BMI classification, age classification, central obesity, drinking frequency, diabetes, electrocardiogram, dyslipidemia, aortic sclerosis, and smoking status, as visualized in Figure 3. This outcome reduced model dimensionality and mitigated overfitting risks. The model constructed using the cross-validation-selected lambda.min provides a reliable feature subset for subsequent analyses.

The ROC curves of the random forest classifier and the LASSO model for both the training and testing sets were above the ROC random guessing line, indicating that both models performed better than random guessing. The AUC value of the random forest model for the training set was 0.7555 (95% CI: 0.7356–0.7754), and the AUC value for the testing set was 0.6869 (95% CI: 0.6552–0.7185). The AUC value of the LASSO regression model for the training set was 0.7505 (95% CI: 0.7316–0.7695), and the AUC value for the testing set was 0.7221 (95% CI: 0.6921–0.7521). The AUC values of both models for the training set were greater than 0.7, indicating that both models have good predictive performance for the risk of fatty liver disease in the older adult population. The intersection of the screening results of the two models was used as a variable to be included in the subsequent model. The ROC curves of the two models are shown in Figure 4.

Correlation analysis was performed on the factors selected by the random forest classifier and lasso regression model, and no strong correlations were found between BMI classification, central obesity, electrocardiogram, aortic sclerosis, dyslipidemia, diabetes, and age classification. There was a positive correlation between BMI classification and central obesity with a correlation coefficient of 0.51, which did not reach the strong correlation threshold of 0.7, so no adjustments were made for these two factors. The correlation is shown in Figure 5.

The diagnostic criterion for central obesity is defined by waist circumference, so it is treated as a binary variable based on waist circumference. Therefore, a logistic regression model adjusting for different factors was used to explore the relationship between central obesity and fatty liver disease. BMI classification, central obesity, electrocardiogram, aortic sclerosis, dyslipidemia, diabetes, and age classification, which were selected by the random forest model from the training set data, were used as independent variables, and the presence of fatty liver disease (0 = no, 1 = yes) was used as the dependent variable to establish a multivariate logistic regression model. The results of univariate logistic regression in Model 1 showed that central obesity was significantly associated with fatty liver disease in the overall population, different gender subgroups (male group and female group), and different age subgroups (under 75 years old and 75 years and older) (p < 0.05). In Model 2, after adjusting for central obesity, age, and BMI classification, central obesity remained significantly associated with fatty liver disease in the overall population and different subgroups (p < 0.05). In Model 3, after further adjusting for central obesity, age, BMI classification, dyslipidemia, diabetes, electrocardiogram, and aortic sclerosis, central obesity remained significantly associated with fatty liver disease in both the overall population and different subgroups (p < 0.05), as shown in Table 1.

Waist circumference was used as the independent variable, and fatty liver disease was used as the dependent variable to establish a restricted cubic spline model using Akaike information criterion (AIC). The AIC values of restricted cubic spline models with different knot points were compared. In general, 3–7 knots are considered appropriate for restricted cubic spline models (20). In this study, when 3 knots were selected, the AIC values for the overall population model, the gender subgroup model, and the age subgroup model were the smallest (AIC _overall = 4,337.857, AIC _male = 1,910.379, AIC _female = 2,419.118, AIC _{under 75 years} = 3,102.407, and AIC _{75 years and older} = 1,202.374). Based on the importance ranking from the random forest model using the training set, six factors (age classification, BMI classification, diabetes, dyslipidemia, electrocardiogram, and aortic sclerosis) were included in the restricted cubic spline model.

The overall model results showed a nonlinear dose–response relationship between waist circumference and the presence of fatty liver disease (nonlinear test, χ² _overall = 6.08, p = 0.01). The risk of fatty liver disease in the older adult population increased with increasing waist circumference (OR < 1, decreased protective effect). Between 52 and 120 cm of waist circumference, the risk of fatty liver disease gradually increased, but the curve remained relatively flat, as shown in Figure 6. In the subgroup analysis by gender, the male model results showed a nonlinear dose–response relationship between waist circumference and the prevalence of fatty liver disease (nonlinear test, χ² _male = 10.17, p < 0.01). The curve change in the male model was similar to that of the overall population model. For males, the risk of fatty liver disease increased more rapidly between 62 and 100 cm of waist circumference and slowed down between 100.2 and 120 cm (OR < 1, decreased protective effect). The female model results showed a linear dose–response relationship between waist circumference and the prevalence of fatty liver disease (nonlinear test, χ² _female = 2.82, p = 0.09). The risk of fatty liver disease in the female group also increased with increasing waist circumference. Between 54 and 116 cm of waist circumference, the risk of fatty liver disease gradually increased (OR<1, decreased protective effect). The curve change in the male model was greater than that in the female model, as shown in Figure 7. In the subgroup analysis by age, both the model for the group under 75 years and the model for the group 75 years and older showed a linear dose–response relationship between waist circumference and the prevalence of fatty liver disease (nonlinear test, χ² _{under 75 years} = 2.77, p = 0.10; χ² _{75 years and older} = 1.89, p = 0.17). The curve change in both models was similar to the overall population model, with the risk of fatty liver disease gradually increasing with waist circumference in both age groups (OR < 1, decreased protective effect). The curve change in the model for the group under 75 years was greater than that for the group 75 years and older, as shown in Figure 8.