This retrospective cross-sectional study was conducted in the Department of Endocrinology at Shenzhen Second People’s Hospital from July 2022 to March 2023. Patients with T2DM who received inpatient or outpatient care were identified according to the 2023 American Diabetes Association diagnostic criteria^[13]. Individuals with a history of osteoporosis or fracture, rheumatoid arthritis, severe liver or kidney disease, active malignancy, hormone replacement therapy, glucocorticoid use, or missing key physical or laboratory data were excluded [Supplementary Figure 1]. This study was approved by the Ethics Committee of Shenzhen Second People’s Hospital (Approval No. 2024-176-01PJ), ensuring compliance with the principles outlined in the Declaration of Helsinki. It was also granted permission to waive the need for patients to provide written informed consent.

The TyG index was combined with obesity-related anthropometric parameters to generate several TyG-based indices, including TyG-BMI, TyG-WC, TyG-WHtR, TyG-BRI, TyG-ABSI, TyG-WWI, TyG-LAP, TyG-CI, TyG-BSI, and TyG-RFM. The definitions and formulas are summarized in Supplementary Table 1.

Demographic and clinical data were collected, including age, sex, menopausal status, smoking and alcohol use, medical history, diabetes duration, diabetic complications, and medications. Body weight, waist circumference, hip circumference, and body mass index (BMI) were measured while patients were fasting and wearing light clothing. Fasting venous blood samples were analyzed for fasting plasma glucose, glycated hemoglobin (HbA1c), fasting C-peptide, lipids [total cholesterol (TC), triglycerides (TG), and low-density lipoprotein cholesterol (LDL-C)], renal and liver function markers [serum creatinine (SCr), blood urea nitrogen (BUN), uric acid (UA), total bilirubin (TBIL), albumin (ALB), alanine aminotransferase (ALT), and gamma-glutamyl transferase (γ-GGT)], calcium, phosphorus, 25-(OH)VitD, parathyroid hormone (PTH), N-terminal osteocalcin, procollagen type I N-terminal propeptide (P1NP), and beta-C-terminal telopeptide (β-CTX). Urinary albumin and urine albumin-creatinine ratio (UACR) were determined from 24-h urine collections. Lumbar spine BMD (T-score), femoral neck BMD (T-score), and total hip BMD (T-score) were measured using dual-energy X-ray absorptiometry with the GE Lunar iDXA system (GE Healthcare, Madison, WI, USA). Lumbar TBS values were then derived retrospectively using TBS iNsight software (version 3.0.0; Medimaps, Switzerland). TBS deterioration was defined as TBS < 1.23^[14].

The distribution of continuous variables was assessed using the Kolmogorov-Smirnov test. Normally distributed data were summarized as the mean ± SD, and nonnormally distributed data as the median and IQR. Categorical variables were summarized as frequencies and percentages. Differences between sexes were analyzed using the independent-samples t-test, Mann-Whitney U test, chi-square test, or Fisher’s exact test, as appropriate.

Spearman’s rank correlation was used to assess relationships among the TyG index and its derived indices. To permit comparisons across models, the TyG index and its derived indices were standardized as z-scores, so associations with TBS and lumbar spine BMD (T-score) were expressed per 1-standard deviation (SD) increase. We used three machine-learning algorithms, Boruta feature selection, random forest (RF), and XGBoost, to rank the feature importance of the TyG index and its derived indices for TBS and lumbar spine BMD (T-score) in patients with T2DM. For Boruta, the maximum number of iterations was 500, and tentative variables were resolved using the TentativeRoughFix function. For random forest, permutation-based importance was expressed as the percentage increase in mean squared error. The mtry parameter was tuned using repeated 5-fold cross-validation with 10 repeats, and 1,000 trees were fitted. For XGBoost, feature importance was quantified using gain, and the main hyperparameters were tuned using repeated 5-fold cross-validation with 10 repeats. To assess ranking stability, the feature-importance analysis was repeated 50 times using bootstrap resampling. Because the importance metrics differed across algorithms, values were standardized before comparison, and their mean was calculated as the consensus importance score. Each standardized TyG-related index was then entered separately into adjusted linear regression models for TBS and lumbar spine BMD (T-score) and into adjusted logistic regression models for TBS deterioration. False discovery rate (FDR) correction accounted for multiple testing in the regression analyses of TyG-derived indices. FDR-adjusted P values were reported as P_FDR, and P_FDR < 0.05 was considered statistically significant. Standardized β coefficients were used to compare variables. Model fit was assessed using R², adjusted R², and RMSE, where applicable. Receiver operating characteristic analysis evaluated discrimination of TBS deterioration by the TyG-derived indices. For each standardized index, predicted probabilities were generated from the corresponding logistic regression model, and area under the curve (AUC) values were calculated. TyG-WWI and each comparator were evaluated in the same analytic sample for each paired ROC comparison. TyG-WWI was the reference, and AUC differences were tested using the paired DeLong method. DeLong P values were adjusted using the Benjamini-Hochberg FDR procedure.

TyG-WWI was selected as the primary index based on the combined comparison of multiple machine-learning algorithms and regression models. Multivariable linear and logistic regression models were used to examine the relationships of TyG-WWI with TBS and BMD in patients with T2DM. TyG-WWI was treated as the primary exposure variable. Model 1 was unadjusted, Model 2 included age and sex, and Model 3 additionally included selected clinical and biochemical covariates. As shown in Supplementary Table 2, all candidate clinical and biochemical variables were entered into a random forest model, and variable importance was assessed using %IncMSE. Variables with %IncMSE > 1.0 were considered potentially informative. To reduce multicollinearity, variance inflation factors (VIFs) were assessed, and variables with VIF > 5 were excluded. ROC analysis evaluated the discrimination of TBS deterioration by logistic models incorporating TyG-WWI. AUCs and 95%CIs were calculated. The optimal cutoff was determined by maximizing the Youden index, defined as sensitivity + specificity - 1. For multivariable models, the cutoff represented a model-estimated probability threshold. Internal validation of Model 3 used 1,000 bootstrap resamples, and the optimism-corrected AUC and bootstrap-based cutoff estimates were reported. In each bootstrap resample, the model was refitted, and optimism was the difference between the AUC in the bootstrap sample and the AUC obtained when the bootstrap-fitted model was applied to the original dataset. The optimism-corrected AUC was calculated by subtracting mean optimism across all valid resamples from the apparent AUC. The optimal model-estimated probability cutoff was recalculated in each resample by maximizing the Youden index. The median represented the bootstrap cutoff, and its 95%CI was estimated using the 2.5th and 97.5th percentiles of the bootstrap distribution.

To evaluate the robustness of the main findings, a sensitivity analysis additionally adjusted Model 3 for overall antidiabetic drug use. The sensitivity model therefore included TyG-WWI, age, sex, RF-selected covariates, and antidiabetic drug use. Linear regression was used for continuous TBS, while logistic regression and ROC analysis were used for TBS deterioration.

Given the role of menopausal status in bone metabolism, we performed analyses stratified by menopausal status among women. The association between TyG-WWI and TBS deterioration in postmenopausal women was assessed using logistic regression. Three models were fitted. Interaction analyses assessed whether menopausal status, sex, or age modified the association between TyG-WWI and TBS deterioration. The nonlinear relationship between TyG-WWI and TBS was further assessed using restricted cubic spline (RCS) regression. Four knots were placed at the 5th, 35th, 65th, and 95th percentiles, and the model included the same covariates as Model 3. Overall and nonlinear associations were tested using analysis of variance, and adjusted TBS values with 95%CIs were plotted. Participants with missing values for the corresponding TyG-related index or outcome were excluded from the relevant analysis, and exposure and outcome variables were not imputed. Missing continuous covariates were handled using multiple imputation by chained equations, whereas missing categorical covariates were retained as a separate “Unknown” category. Women with missing menopausal-status information were excluded from the menopause-stratified and menopause-interaction analyses.

Statistical analyses were performed using R version 4.3.0. Baseline comparisons, correlation analyses, and regression models used the stats package. Machine-learning analyses were performed with Boruta, randomForest, xgboost, and caret packages. The car, pROC, boot, rms, mice, and ggplot2 packages were used for VIF assessment, ROC analysis, bootstrap validation, restricted cubic splines, multiple imputation, and figure generation, respectively. Statistical significance was defined as a two-sided P < 0.05.

Among the 309 patients with T2DM, 158 were women. Baseline characteristics are shown in Table 1. Women were older than men (62.63 ± 9.87 vs. 58.87 ± 11.43, P = 0.002). Renal function and blood biochemical indicators showed that SCr and UA were significantly lower in women than in men (P < 0.001), as were TBIL and γ-GGT (P < 0.01). Serum phosphorus was significantly higher in women than in men (P = 0.002), whereas serum calcium did not differ significantly between the sexes (P = 0.354). Regarding bone-related measures, N-terminal osteocalcin levels were slightly higher in women than in men (P = 0.046), whereas T-scores at the femoral neck, total hip, and lumbar spine were significantly lower in women than in men (femoral neck T-score: -1.79 vs. -1.19; total hip T-score: -1.11 vs. -0.51; lumbar spine T-score: -1.32 vs. -0.39; all P < 0.001). Lumbar spine TBS was also significantly lower in women than in men (1.26 vs. 1.34, P < 0.001), consistent with poorer trabecular microarchitecture in women. TyG-WC was significantly higher in men than in women (825.32 ± 128.20 vs. 773.82 ± 123.07, P < 0.001). TyG-WWI was slightly higher in women than in men, although the difference was not statistically significant (100.44 ± 12.70 vs. 97.84 ± 11.20, P = 0.057). Smoking and alcohol use were less common among women (both P < 0.001), whereas diabetes duration, complications, antidiabetic therapy, lipid levels, and glucose-related measures did not differ significantly between the sexes.

To evaluate associations of the TyG index and its derived indices with bone microarchitecture, we combined machine-learning feature selection with multivariable linear and logistic regression. Across Boruta, RF, and XGBoost, TyG-WWI ranked first among the TyG index and its derived indices [Figure 1], indicating the highest consensus feature importance for TBS.

To permit direct comparisons across measurement scales, all TyG-derived indices were standardized as z-scores. The β coefficients and odds ratios (ORs) for these indices are therefore expressed per 1-SD increase. In the multiple linear regression model, TBS was specified as the outcome variable, and all standardized TyG-derived indices were inversely associated with TBS, with standardized TyG-WWI having the largest absolute regression coefficient. In Model 3, each 1-SD increase in TyG-WWI was associated with a 0.0217-unit decrease in TBS (β = -0.0217, standardized β = -0.1983, 95%CI: -0.0326 to -0.0108, P = 1.09 × 10^-4, P_FDR = 0.000511), representing the largest adjusted association with lower TBS among the evaluated indices [Figure 2].

In logistic regression with TBS deterioration (TBS < 1.23) as the outcome, standardized TyG-WWI had the strongest association among the evaluated indices. In Model 3, each 1-SD increase in TyG-WWI was associated with 47.9% higher odds of TBS deterioration (OR = 1.479, 95%CI: 1.072 to 2.039, P = 0.017, P_FDR = 0.0341, AUC = 0.83) [Supplementary Figure 2]. Other indices showed nominal or FDR-adjusted associations, including standardized TyG-ABSI (Model 3: OR = 1.390, 95%CI: 1.004 to 1.924, P = 0.0473, P_FDR = 0.0592, AUC = 0.826) and standardized TyG-CI and TyG-BSI (Model 3: OR = 1.450, 95%CI: 1.049 to 2.005, P = 0.0245, P_FDR = 0.0350, AUC = 0.828). Standardized TyG-BRI and TyG-RFM were also positively associated with TBS deterioration across all models, whereas standardized TyG-BMI was not statistically significant in any model. Paired DeLong tests compared discrimination across TyG-derived indices using TyG-WWI as the reference. In Model 1, TyG-WWI had a significantly higher AUC than TyG-BMI, TyG-WC, TyG-LAP, TyG-CI, and TyG-BSI after FDR correction. The DeLong test results are shown in Supplementary Figure 3. Comprehensive machine-learning and regression analyses indicated that TyG-WWI had the strongest overall combination of feature importance, association magnitude, and discrimination among the TyG-derived indices in patients with T2DM. This finding was consistent for both continuous TBS and TBS deterioration outcomes.

TyG-WWI was entered into the regression models on its original scale; therefore, the β coefficients are expressed per 1-unit increase in TyG-WWI. In the linear regression analysis (Model 1), TyG-WWI was inversely associated with TBS (β = -0.0025, standardized β = -0.2701, 95%CI: -0.0034 to -0.0015, P < 0.001) [Supplementary Figure 4]. After adjustment for age and sex (Model 2), the inverse association between TyG-WWI and TBS remained significant (β = -0.0018, standardized β = -0.2022, 95%CI: -0.0027 to -0.0010, P < 0.001); age (β = -0.0033, P < 0.001) and female sex (β = -0.0669, P < 0.001) were also inversely associated with TBS. In the multivariable Model 3, which additionally included selected renal function, bone metabolism, vitamin D, and other covariates, the inverse association with TyG-WWI remained significant. Each 1-unit increase in TyG-WWI was associated with a 0.0018-unit decrease in TBS (β = -0.0018, standardized β = -0.1983, P < 0.001), whereas the other selected covariates were not statistically significant [Table 2].

Interaction analyses showed no significant effect modification by sex or age for the association between TyG-WWI and TBS (sex: P = 0.485; age: P = 0.575; Supplementary Table 3), indicating that there was no statistical evidence that the association varied by sex or age. Restricted cubic spline analysis then assessed potential nonlinearity between TyG-WWI and TBS. With knots at the 5th, 35th, 65th, and 95th percentiles, no significant nonlinear association was observed (P for nonlinearity = 0.425). The spline showed no clear threshold or U-shaped pattern, supporting an approximately linear association in the adjusted model [Supplementary Table 4 and Supplementary Figure 5].

In logistic regression, Model 1 showed that the odds of TBS deterioration were 4.4% higher for each 1-unit increase in TyG-WWI (OR = 1.044, 95%CI: 1.021 to 1.067; P < 0.001). After adjustment for age and sex in Model 2, the association remained statistically significant (OR = 1.034, 95%CI: 1.008 to 1.060, P = 0.010). In the fully adjusted Model 3, each 1-unit increase in TyG-WWI was associated with 3.3% higher odds of TBS deterioration (OR = 1.033, 95%CI: 1.006 to 1.061, P = 0.017) [Supplementary Table 5]. These findings indicated that TyG-WWI remained independently associated with deterioration of trabecular bone microarchitecture. ROC curve analysis showed that the discriminatory ability of models incorporating TyG-WWI was higher after covariate adjustment. The AUC was 0.636 (95%CI: 0.563 to 0.708) for Model 1, 0.819 (95%CI: 0.765 to 0.874) for Model 2, and 0.830 (95%CI: 0.778 to 0.883) for Model 3 [Supplementary Figure 6], with higher discrimination in the adjusted models. In Model 3, the optimal model-estimated probability threshold was 0.361 [Figure 3], with a sensitivity of 0.667, specificity of 0.868, and Youden index of 0.535. These findings suggest that Model 3 showed acceptable discrimination of TBS deterioration after internal validation. However, the optimal model-estimated probability threshold showed noticeable variability in bootstrap analysis; therefore, this threshold should be considered exploratory and requires external validation before clinical application.

Given the established influence of menopausal status on bone metabolism, we performed a stratified analysis among postmenopausal women. As shown in Supplementary Table 6, among 139 postmenopausal women, 63 had TBS deterioration and 76 did not. In Model 1, TyG-WWI was associated with higher odds of TBS deterioration (OR = 1.035, 95%CI: 1.007 to 1.065, P = 0.015; AUC = 0.619, 95%CI: 0.524 to 0.715). After adjustment for age (Model 2), the association between TyG-WWI and TBS deterioration was attenuated and no longer statistically significant (OR = 1.026, 95%CI: 0.994 to 1.058, P = 0.110; AUC = 0.758, 95%CI: 0.676 to 0.839). Results were similar in the fully adjusted Model 3 (OR = 1.025, 95%CI: 0.992 to 1.059, P = 0.136; AUC = 0.784, 95%CI: 0.707 to 0.860). The interaction between TyG-WWI and menopausal status was not statistically significant (P for interaction = 0.904; Supplementary Figure 7). Thus, there was no statistical evidence that menopausal status modified the association between TyG-WWI and TBS deterioration. However, the interaction analysis may have been underpowered and should be interpreted cautiously.

After further adjustment for antidiabetic drugs, the association between TyG-WWI and continuous TBS remained essentially unchanged. The regression coefficient was -0.0018 in both Model 3 and the sensitivity model, and the standardized β changed minimally from -0.1983 to -0.1981 [Supplementary Table 7]. For TBS deterioration, the AUC was 0.830 in Model 3 and 0.840 in the sensitivity model, with largely overlapping 95% confidence intervals [Supplementary Figure 8]. These results suggest that additional adjustment for antidiabetic drugs did not materially change the association between TyG-WWI and TBS-related outcomes.

TyG-WWI was not significantly associated with lumbar spine BMD (T-score) in linear regression (Model 1) (β = -0.0048, 95%CI: -0.0193 to 0.0096, P = 0.509). The association remained nonsignificant after adjustment for age and sex in Model 2 (β = 0.0010, 95%CI: -0.0128 to 0.0148, P = 0.883). In multivariable Model 3, which included the RF-selected covariates, the association between TyG-WWI and lumbar spine BMD (T-score) remained nonsignificant (β = 0.0007, 95%CI: -0.0137 to 0.0150, P = 0.926) [Supplementary Table 8], indicating that TyG-WWI was not independently associated with lumbar spine BMD (T-score). In multivariable Model 3, age (β = -0.0251, P = 0.0036), female sex (β = -1.001, P < 0.001), and P1NP (β = -0.0105, P = 0.0376) were inversely associated with lumbar spine BMD (T-score), whereas the other covariates were not statistically significant. Interaction analyses [Supplementary Table 9] showed that neither the TyG-WWI-by-age interaction (β = -0.00022, 95%CI: -0.00141 to 0.00097, P = 0.714) nor the TyG-WWI-by-sex interaction (P = 0.243) was statistically significant. These findings indicated that the association between TyG-WWI and lumbar spine BMD (T-score) did not vary significantly by age or sex. Overall, TyG-WWI was not associated with lumbar spine BMD (T-score), and neither age nor sex significantly modified this association.