This cross-sectional study utilized data from the 2009–2010 National Health and Nutrition Examination Survey (NHANES), available on the NHANES website.¹ Details of NHANES’ continuous design are provided on the platform. Since responses related to chronic CLBP in the NHANES dataset are only available within the inflammatory arthritis questionnaire, which targets individuals aged 20 to 69 years, we included participants who completed this specific questionnaire for the assessment of CLBP. Exclusion criteria were: (1) missing CLBP data; (2) missing BMI values; (3) absent WC or weight measurements; and (4) pregnancy.

CLBP was identified based on NHANES criteria, defined as persistent pain in the region between the lower thoracic border and horizontal gluteal fold, lasting nearly daily for at least three consecutive months. Assessment required “yes” responses to the following questions: “Was there one time when you had pain, aching, or stiffness in your low back on almost every day for 3 or more months in a row?” and “Do you still have low back pain, aching, or stiffness?”

The primary outcome was CLBP, while BMI and WWI served as independent variables. BMI was calculated as weight divided by the square of height (kg/m²), while WWI (cm/√kg) was derived by dividing WC (cm) by the square root of weight (kg).

Demographic and clinical factors potentially influencing CLBP, BMI, and WWI were included as covariates: age, gender, education level, smoking status, alcohol consumption, poverty income ratio (PIR), sedentary time, diabetes status, and lumbar bone mineral density (BMD). Education was categorized into below high school, high school, or above high school. We referred to previous studies and categorized PIR into three groups: PIR < 1.5,1.5 ≤ PIR < 3.5, or PIR ≥ 3.5 (26). Alcohol consumption was defined as drinking more than 12 beverages in the past year, and smoking status as having smoked over 100 cigarettes in a lifetime. BMI was classified into three categories: <25 kg/m², 25–30 kg/m², and >30 kg/m². Diabetes was based on a physician’s diagnosis, sedentary time (minutes/day) was self-reported, and lumbar BMD was measured via dual-energy X-ray absorptiometry (DXA).

Statistical analyses were conducted using R software (RStudio: Integrated Development for R. RStudio, PBC, Boston, MA, USA) (27, 28), with p < 0.05 considered statistically significant. Importing and visualizing datasets using the tidyverse package (29) in R, multiple imputation was performed using random forest methods via the mice package (30) to address missing data, generating five imputed datasets that incorporated all variables in the analysis. Results from the imputed datasets were combined for analysis. Characteristics of complete, missing, and imputed datasets were compared to ensure robustness. CDC-recommended sampling weights (“wtmec2yr”) were applied to reflect the U.S. population, following NHANES guidelines. Weighted means (± standard deviation) were used for continuous variables, and weighted percentages for categorical variables. Weighted logistic regression models were fitted using the survey package (31), and data manipulation was conducted using dplyr (32). T-tests assessed the relationships between BMI, WWI, and CLBP, and weighted logistic regression models were applied. Model 1 was unadjusted, Model 2 adjusted for gender, age, and education, and Model 3 adjusted for all covariates. Sensitivity analyses were performed to validate findings, including subgroup analyses, threshold effect analyses, smooth curve fitting by using the mgcv package (33). Log-likelihood ratio tests compared single-line and segmented models to identify thresholds. If nonlinear associations were observed, segmented regression models estimated effects and determined thresholds.

We conducted correlation tests for WWI and CLBP, demonstrating the high correlation between WWI and CLBP. However, we aim to accurately predict CLBP with the assistance of machine learning techniques, which has significant implications for the diagnosis and prevention of CLBP. To enhance the reliability of machine learning model training outcomes, we incorporated additional variables correlated with the previously included covariates, all derived from the 2009–2010 NHANES cycle dataset. These variables encompassed WWI-related measures (waist circumference and weight), BMD-related parameters (ward’s triangle BMD, femoral neck BMD, and lumbar spine BMD at L1-L4 vertebrae), Demographics-related factors (race, income level and marital status), and health status indicators (sleep quality, hypertension, healthy dietary patterns, and analgesic medication use), totaling 26 variables.

Python version 3.8 (Python Software Foundation, Wilmington, DE, USA) (34) is utilized for machine learning. The pandas (35) package was utilized for data analysis and processing. To conduct effective feature selection and enhance the interpretability of machine learning models, we employed permutation feature importance (PFI) (36) using the scikit-learn package (37). PFI quantifies feature importance by evaluating the increase in model prediction error following the permutation of feature values, thereby disrupting their relationship with the target variable. This severe imbalance may cause the model to be biased toward the majority class (no CLBP symptoms), thereby reducing its effectiveness in predicting CLBP. To mitigate this issue, we reduced the sample size of the majority class (no CLBP) to match the sample size in the minority class (CLBP). By employing the imblearn package (38) to implement random undersampling, we ensured balanced class representation during model training. This approach was selected due to its simplicity and effectiveness in improving model performance when handling imbalanced data.

All participants were randomly allocated into training and testing sets using a 7:3 ratio. We employed six machine learning algorithms implemented using the scikit-learn, LightGBM (39), and XGBoost (40) packages, including Random Forest, Gradient Boosting, Light Gradient Boosting Machine (LightGBM), Naive Bayes, Support Vector Machine (SVM), and Extreme Gradient Boosting (XGBoost).

The hyperparameter optimization process involves systematic adjustment of key parameters for each machine learning model. This study employs a grid search-based hyperparameter tuning approach combined with five-fold cross-validation to evaluate different parameter combinations, ensuring model stability and minimizing the influence of random variables. The objective is to identify optimal configurations that maximize model performance, with particular attention to metrics such as accuracy and area under the curve (AUC). The optimal model for depression prediction was determined by comparing performance metrics on the test set.

Out of 10,537 participants from the 2009–2010 NHANES dataset, 4,687 participants were included after excluding individuals with missing CLBP data (n = 3), BMI data (n = 3), waist and weight data (n = 349), and pregnant women (n = 67). The screening process is shown in Figure 1.

Table 1 compares the characteristics of participants with CLBP (n = 566) and those without CLBP (n = 4,121). Significant differences were observed in age, with CLBP individuals being older (47.35 years vs. 43.54 years, p < 0.001). The prevalence of diabetes was significantly higher in the CLBP group (15.91% vs. 8.66%, p < 0.001). Smokers were more prevalent among CLBP participants (62.37%) compared to the non-CLBP group (42.88%, p < 0.001). Both BMI and WWI were higher in the CLBP group (BMI: p < 0.001; WWI: 11.13 ± 0.80 vs. 10.88 ± 0.80, p < 0.001). Education level also differed significantly, with more participants having less than high school education in the CLBP group (p = 0.014). No significant differences were observed in sedentary time, total spine BMD, drinking status, or sex distribution.

Table 2 displays the associations between WWI, BMI, and CLBP across three models. For WWI, each unit increase was consistently associated with higher odds of CLBP, even after full adjustment for all covariates (Model 3: OR = 1.31, 95% CI: 1.08–1.60, p = 0.006). Quartiles of WWI also showed a significant trend, with participants in Quartile 4 having the highest odds of CLBP compared to Quartile 1 (Model 3: OR = 1.62, 95% CI: 1.12–2.34, p = 0.010).

For BMI, each unit increase was associated with a smaller, yet significant, increase in CLBP risk (Model 3: OR = 1.03, 95% CI: 1.01–1.05, p = 0.006). While Quartile 3 showed significant associations across models, Quartile 4 results were less consistent. Overall, WWI demonstrated a stronger and more consistent relationship with CLBP than BMI, suggesting its potential as a better predictor of CLBP.

Subgroup analyses (Table 3) revealed positive associations between WWI, BMI, and CLBP across various demographic and health-related groups, including age, sex, education, smoking, and diabetes. WWI had a stronger effect size in individuals aged 40–60 years, males, and those with lower education levels. BMI associations were notable among individuals with diabetes or lower BMD. No significant interaction effects were observed, confirming the robustness of the findings.

Smooth curve fitting and threshold effect analysis (Figure 2; Table 4) identified nonlinear relationships between WWI, BMI, and CLBP. For BMI, a threshold was identified at 20.17, where BMI had a negative association with CLBP below this value (β = 0.84, 95% CI: 0.76–0.93) and a positive association above it (β = 1.03, 95% CI: 1.03–1.04). For WWI, the threshold was 11.6, with a significant positive association below the threshold (β = 1.31, 95% CI: 1.21–1.42), while no significant relationship was observed above the threshold.

Compared to BMI, WWI demonstrates slightly higher diagnostic performance, with an AUC of 0.589 versus 0.573 for BMI (Figure 3). However, both indicators exhibit limited discriminative ability, as their ROC curves lie relatively close to the diagonal. Nevertheless, WWI appears to be a marginally more promising indicator for CLBP, offering slightly better predictive value than BMI. Therefore, we applied machine learning methods to further evaluate the predictive capability of WWI for CLBP.