Preoperative distal radius CT hounsfield unit and other imaging predictors of postoperative radiocarpal traumatic arthritis after distal radius fracture

Abstract

Purpose

Postoperative radiocarpal traumatic arthritis (TA) after distal radius fracture (DRF) may cause persistent pain and functional impairment. Early risk stratification may help identify patients at increased risk. This study aims to identify independent predictors of radiocarpal TA after DRF and develop multifactorial predictive models.

Methods

We retrospectively analyzed 226 DRF patients grouped by radiocarpal TA status. Variables were screened using univariate and correlation analyses. Logistic regression (LR) and support vector machine (SVM) models were developed using a 70/30 stratified train–test split (seed = 42); 10-fold stratified cross-validation was performed within the training set, and final performance was evaluated on the test set.

Results

Independent predictors included preoperative step-off > 2 mm (OR = 6.12, 95% CI: 1.79–20.94), radial shortening > 3 mm (OR = 8.02, 95% CI: 2.55–25.21), low distal radius CT Hounsfield Unit (OR = 0.99, 95% CI: 0.99–1.00). The LR model achieved an AUC of 90.71%, and the SVM model an AUC of 91.34%.

Conclusion

Both LR and SVM models showed promising internal performance for predicting radiocarpal TA after DRF. These findings may support preoperative risk stratification, but external validation is required before clinical application.

Introduction

Distal radius fracture (DRF) is among the most common fractures in adults, accounting for approximately 16%–18% of all fractures, with a particularly high incidence in elderly patients with osteoporosis [1]. Post-traumatic arthritis (TA) of the radiocarpal joint is a common complication of DRF, potentially causing chronic pain, joint stiffness, limited range of motion, and functional impairment, thereby significantly affecting patients’ quality of life [2]. Previous studies have identified postoperative radiographic parameters—such as articular step-off, radial shortening, and changes in volar tilt—as closely associated with the development of radiocarpal TA after DRF [3–5]. In particular, postoperative articular step-off > 2 mm is recognized as a key predictor of radiocarpal joint degeneration [3, 6].

Moreover, increasing evidence suggests that inflammatory markers such as neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), and systemic inflammation response index (SIRI) are closely associated with osteoarthritis and post-traumatic arthritis in joints other than the wrist [7, 8]. However, studies incorporating these indices into predictive models for radiocarpal TA after DRF remain scarce.

To the best of our knowledge, studies specifically establishing predictive models for postoperative radiocarpal TA following DRF remain limited. Existing research has either focused on functional outcomes or single-factor imaging associations, without systematically exploring the combined predictive potential of preoperative imaging parameters and systemic inflammatory markers within a unified framework. Moreover, direct comparisons between traditional statistical approaches and machine learning algorithms in this context are lacking. Therefore, this study aimed to develop and internally evaluate predictive models for radiocarpal TA after DRF by integrating imaging and inflammatory parameters using logistic regression (LR) and support vector machine (SVM) methods.

Materials and methods

Study subjects

This retrospective study, conducted in accordance with the STROCSS criteria [9], screened consecutive patients with distal radius fracture (DRF) who underwent surgical treatment at the Bone Center of Beijing Luhe Hospital, Capital Medical University, between January 2019 and March 2024. A total of 980 surgically treated DRF patients were screened. After application of the predefined inclusion and exclusion criteria, 754 patients were excluded, primarily because of ineligibility or incomplete imaging/follow-up data, leaving 226 patients with complete clinical and imaging follow-up for analysis. These patients were classified into a non-TA group (n = 133) or a TA group (n = 93) based on imaging and clinical evaluations at the final follow-up. The patient selection process is summarized in Fig. 1.

Fig. 1.

Flowchart of patient selection and study enrollment. A total of 980 surgically treated distal radius fracture patients were initially screened, of whom 754 were excluded according to the predefined criteria. The final analysis included 226 patients, comprising 133 patients in the non-traumatic arthritis group and 93 patients in the traumatic arthritis group

This study was approved by the Ethical Committee NAC of Beijing Luhe Hospital affiliated to Capital Medical University (Ethical Committee N° 2025-LHYK-071-01). The requirement for informed consent was waived by the committee due to the retrospective design and anonymization of patient data.

Inclusion criteria

1. Radiographically confirmed DRF, defined as a fracture line located within 3 cm proximal to the distal radial articular surface on X-ray and/or computed tomography (CT).

2. Age ≥ 18 years at the time of surgery.

3. Surgical treatment was performed via volar locking plate fixation using the standard flexor carpi radialis approach (volar approach open reduction and internal fixation). Anatomic or near-anatomic reduction was targeted intraoperatively. Intraoperative fluoroscopy was used to assess restoration of radial inclination, volar tilt, and articular congruity, aiming for an articular step-off ≤ 2 mm.

4. Complete preoperative imaging data, including standard anteroposterior and lateral wrist X-rays and CT scans.

5. Patients underwent postoperative clinical and radiographic follow-up. Follow-up duration was defined as the interval from surgery to the last clinical and radiographic assessment. The minimum follow-up was 12 months, and the maximum follow-up was 3 years. Evaluations were performed as part of routine follow-up rather than at fully standardized prespecified time points.

Exclusion criteria

1. Open fractures or concurrent traumatic injuries, such as craniocerebral or thoracoabdominal trauma.

2. Pathological fractures, including those caused by bone tumors or bone tuberculosis.

3. Follow-up duration < 12 months, incomplete postoperative follow-up data, or loss to follow-up.

4. Severe systemic diseases (e.g., malignancy, severe cardiovascular or cerebrovascular disease, liver or renal insufficiency) that could affect outcome evaluation.

5. History of ipsilateral wrist surgery or severe pre-existing degenerative arthritis.

Data collection

The following variables were collected:

• General information: sex, age, history of diabetes mellitus.

• Preoperative imaging parameters: AO fracture classification, presence of articular step-off > 2 mm, presence of radial shortening > 3 mm, radial inclination (°), volar tilt (°), distal radius CT Hounsfield Unit (HU), and presence of ulnar styloid fracture. All imaging parameters were independently measured by three orthopedic surgeons (attending or higher) under blinded conditions. Interobserver agreement was quantified using Cohen’s kappa statistic. Final values were determined by averaging three measurements. In the event of significant discrepancy between two measurements, the third surgeon re-evaluated the images and the consensus value was adopted.

• Preoperative hematologic parameters: white blood cell (WBC) count, neutrophil count, lymphocyte count, monocyte count, platelet count, NLR, PLR, and SIRI. Blood samples for these hematologic indices were collected on the first day of hospital admission before surgery.

Preoperative variable measurement methods

Follow-up duration: defined as the interval from surgery to the last clinical and radiographic assessment.

TA within 12 months: defined as radiocarpal TA diagnosed within 12 months after surgery.

Time to TA: defined, for patients who developed radiocarpal TA, as the interval from surgery to the first radiographic and clinical diagnosis of TA.

Radiocarpal TA: Diagnosed from postoperative anteroposterior and lateral wrist X-rays obtained ≥ 12 months after surgery, showing joint space narrowing, osteophyte formation, and subchondral sclerosis. Clinical confirmation included persistent wrist pain, stiffness, or functional limitation [3]. Because of the retrospective design and variability in available follow-up imaging, a standardized radiographic grading system for wrist arthritis was not uniformly applied; therefore, radiocarpal TA was analyzed as a binary outcome (present/absent).

Preoperative distal radius CT HU: Because distal radius fractures are often accompanied by articular surface collapse, the ulnar head articular surface was used as a reference plane. On preoperative axial bone-window CT images, CT HU was measured in the cancellous bone of the distal radius at a level 3.0 cm proximal to the ulnar head articular surface. The region of interest was placed within trabecular bone while avoiding cortical bone, fracture lines, obvious focal sclerosis or collapse, and imaging artifacts. Each measurement was repeated three times, and the average value was used [10] (Fig. 2).

Fig. 2.

Measurement of distal radius CT Hounsfield Units (HU). A: The measurement plane was positioned 3.0 cm proximal to the ulnar head articular surface. B–D: At this level, regions of interest (ROIs) were placed in the trabecular bone of the distal radius, excluding cortical bone and fracture lines. Three measurements were obtained, and the average value was used for analysis

Volar tilt [11]: Measured on preoperative lateral wrist X-rays as the angle between a line along the distal radial articular surface and a line perpendicular to the longitudinal axis of the radius. Volar tilt is positive and dorsal tilt is negative. The normal value is approximately 11° (common range: 6–16°).

Radial inclination [3]: Measured on preoperative anteroposterior wrist X-rays as the angle between a line connecting the most radial and most ulnar points of the distal radial articular surface and the longitudinal axis of the radius. The normal range is 19–25°.

Radial shortening [3]: Measured on preoperative anteroposterior wrist X-rays as the vertical distance from the distal radius to the distal ulna. Radial shortening > 3 mm was considered clinically significant and used for binary classification in the analysis.

AO fracture classification [12]: Classified as type A (extra-articular), type B (partial articular), or type C (complete articular) according to the AO/OTA system, based on preoperative anteroposterior and lateral X-rays and CT scans.

Articular step-off [3]: Evaluated on preoperative CT multiplanar reconstructions. Step-off > 2 mm was defined as malalignment of the articular surface.

Inflammatory indices:

• NLR [13]= neutrophil ÷ lymphocyte: reflects the balance between neutrophil-driven innate immunity and lymphocyte-mediated adaptive immunity; higher values indicate increased systemic inflammatory burden and potential immune suppression.

• PLR [13]= platelet ÷ lymphocyte: reflects the interaction between inflammation, coagulation, and tissue repair; elevated values are associated with inflammatory and hypercoagulable states.

• SIRI [13]= (neutrophil × monocyte) ÷ lymphocyte: integrates neutrophil and monocyte-mediated inflammatory activation with lymphocyte-mediated immune regulation, higher values indicate stronger systemic inflammatory drive.

Statistical analysis

Descriptive statistics were calculated for all variables. Only patients with complete clinical, imaging, and follow-up data were included in the final analysis; therefore, no imputation for missing data was performed, and all analyses were based on complete-case data. Normality of continuous variables was assessed within each group using the Shapiro–Wilk test. Continuous variables that were normally distributed in both groups were compared using independent-samples t tests; otherwise, the Mann–Whitney U test was applied. Categorical variables were summarized as counts and percentages and compared using the chi-square test.

Associations between each variable and radiocarpal TA were assessed using Spearman’s rank correlation coefficients (ρ). Variables that showed statistical significance in either univariate analysis or correlation analysis (P < 0.05) were included as candidate predictors in the LR and SVM models.

Multicollinearity among candidate predictors was evaluated using variance inflation factors (VIF), with values < 5 indicating no concerning collinearity. A multivariable logistic regression model (enter method) was fitted to identify independent risk factors, and results were reported as odds ratios (ORs) with 95% confidence intervals (CIs) and p values. An additional model comparison was performed to assess the contribution of distal radius CT HU to the logistic regression model. The model including CT HU was compared with the corresponding model after removing CT HU, and model fit was additionally compared using the Akaike information criterion (AIC) and likelihood ratio test. Overall model fit was assessed using the Hosmer–Lemeshow goodness-of-fit test and the events-per-variable (EPV) criterion (EPV ≥ 10). Discrimination was evaluated using accuracy, precision, recall, F1 score, specificity, area under the receiver operating characteristic curve (ROC AUC), and area under the precision–recall curve (PR AUC). Calibration was assessed using calibration plots and the Brier score. For the logistic regression (LR) model, calibration was additionally quantified using logistic recalibration (calibration slope and intercept). The optimal decision threshold was selected by maximizing the Youden index. The dataset was randomly split into a training set (70%) and an independent test set (30%) using stratified sampling by the outcome, with a fixed random seed (42) to ensure reproducibility. Internal validation and model selection were performed within the training set using 10-fold stratified cross-validation, and final model performance was evaluated on the held-out test set. For SVM model development, continuous predictors were standardized, whereas categorical variables were entered using their original coding. Preprocessing was performed within the training data and then applied to the test data to avoid information leakage.

For comparison, an SVM classifier was developed using the same training/test split. Hyperparameters were tuned via grid search using 10-fold stratified cross-validation within the training set, and the finalized SVM model was evaluated on the independent test set. Because SVM is not likelihood-based, the Hosmer–Lemeshow test and logistic recalibration parameters (calibration slope and intercept) are not applicable; however, calibration of SVM probability estimates was evaluated using calibration plots and the Brier score.

Because follow-up duration ranged from 12 months to 3 years, additional analyses were performed to evaluate whether variation in follow-up length influenced the observed associations. Follow-up duration was compared between the TA and non-TA groups. In addition, follow-up duration was entered into a multivariable logistic regression model together with the main predictors to assess whether the associations remained stable after accounting for differences in observation time. To further reduce the potential influence of heterogeneous follow-up, TA diagnosed within 12 months after surgery was analyzed as an alternative fixed-time outcome using the three previously identified independent imaging predictors.

All analyses were conducted using SPSS 26.0 (IBM Corp., Armonk, NY, USA), R 4.0.5, and Python 3.8 (scikit-learn).

Results

Patients were classified into a non-TA group (n = 133) and a TA group (n = 93) following distal radius fracture surgery. The interobserver agreement for evaluating imaging variables was substantial, with a Cohen’s kappa value of 0.84, indicating strong consistency.

Among categorical variables, the TA group showed a significantly higher proportion of AO type C fractures (61.29% vs. 15.79%, P < 0.001), articular step-off > 2 mm (75.27% vs. 12.78%, P < 0.001), and radial shortening > 3 mm (82.80% vs. 25.56%, P < 0.001) than the non-TA group. Concomitant ulnar styloid fractures were also more frequent in the TA group (64.52% vs. 52.63%), although the difference was not statistically significant (P = 0.10). The proportion of male patients was higher in the TA group (49.46% vs. 36.09%, P = 0.06), whereas the prevalence of diabetes was similar between the two groups (9.68% vs. 6.77%, P = 0.59) (Table 1).

Table 1.

Descriptive Statistics and Univariate Analysis of Variables

Variables	Non-TA (n = 133)	TA (n = 93)	U /Chi-square test		Spearman Correlation Analysis
			Statistic	P	Coefficient (ρ)	P
Sex, n (%)			3.49	0.06	-0.13	0.05
Male	48 (36.1%)	46 (49.5%)
Female	85 (63.9%)	47 (50.5%)
Ulnar styloid fracture, n (%)			2.70	0.1	0.12	0.08
Yes	70 (52.63%)	60 (64.52%)
No	63 (47.37%)	33 (35.48%)
AO type, n (%)			50.38	< 0.001	0.47	< 0.001
A	1 (0.75%)	0 (0.00%)
B	111 (83.46%)	36 (38.71%)
C	21 (15.79%)	57 (61.29%)
Articular step-off > 2 mm, n (%)			87.64	< 0.001	0.63	< 0.001
Yes	17 (12.78%)	70 (75.27%)
No	116 (87.22%)	23 (24.73%)
Radial shortening > 3 mm, n (%)			72.12	< 0.001	0.56	< 0.001
Yes	34 (25.56%)	77 (82.80%)
No	99 (74.44%)	16 (17.20%)
Diabetes, n (%)			0.30	0.59	0.05	0.43
Yes	9 (6.8%)	9 (9.7%)
No	124 (93.2%)	84 (90.3%)
Age, median (Q1, Q3)	54.00 (42.00, 60.00)	55.00 (41.00, 64.00)	5814	0.44	0.05	0.44
CT HU, median (Q1, Q3)	-17.40 (-54.10, 25.30)	-81.00 (-126.50, -28.60)	8945	< 0.001	-0.38	< 0.001
Volar tilt, median (Q1, Q3)	5.00 (-17.20, 14.40)	2.50 (-19.50, 15.30)	6315	0.79	-0.02	0.79
Radial inclination, median (Q1, Q3)	13.90 (6.80, 18.40)	11.50 (-13.50, 16.50)	7165	0.04	-0.14	0.04
WBC, median (Q1, Q3)	6.73 (5.35, 8.85)	6.24 (5.15, 8.23)	6596.5	0.39	-0.06	0.4
Neutrophil, median (Q1, Q3)	4.51 (3.25, 6.76)	4.12 (3.20, 6.28)	6543.5	0.46	-0.05	0.46
Lymphocyte, median (Q1, Q3)	1.50 (1.14, 1.83)	1.44 (1.17, 1.84)	6203	0.97	0	0.97
Monocyte, median (Q1, Q3)	0.35 (0.27, 0.45)	0.34 (0.26, 0.43)	6475.5	0.55	-0.04	0.53
Platelet, median (Q1, Q3)	232.00 (188.00, 268.00)	218.00 (188.00, 253.00)	6743.5	0.25	-0.08	0.25
NLR, median (Q1, Q3)	2.76 (1.88, 4.65)	2.50 (1.78, 4.73)	6332	0.76	-0.02	0.76
PLR, median (Q1, Q3)	150.36 (118.18, 203.12)	148.77 (108.15, 195.33)	6261	0.88	-0.01	0.87
SIRI, median (Q1, Q3)	0.98 (0.60, 1.90)	0.97 (0.57, 1.70)	6444	0.59	-0.04	0.59

CT HU Computed Tomography Hounsfield Unit, NLR Neutrophil-to-Lymphocyte Ratio, PLR Platelet-to-Lymphocyte Ratio, SIRI Systemic Inflammation Response Index

Among continuous variables, the median distal radius CT HU was significantly lower in the TA group (− 81.00 HU; IQR, − 126.50 to − 28.60) than in the non-TA group (− 17.40 HU; IQR, − 54.10 to 25.30; P < 0.001). Radial inclination was also lower in the TA group (11.50°; IQR, − 13.50 to 16.50) than in the non-TA group (13.90°; IQR, 6.80 to 18.40; P = 0.04). In contrast, age (55.00 vs. 54.00 years, P = 0.44), volar tilt (2.50° vs. 5.00°, P = 0.79), white blood cell count (P = 0.39), neutrophil count (P = 0.46), lymphocyte count (P = 0.97), monocyte count (P = 0.55), platelet count (P = 0.25), NLR (P = 0.76), PLR (P = 0.88), and SIRI (P = 0.59) were comparable between the two groups (Table 1).

Normality testing and group comparisons: The Shapiro–Wilk test revealed that none of the continuous variables in the non-TA group followed a normal distribution (all P < 0.05). In contrast, age, distal radius CT HU, lymphocyte count, and platelet count were normally distributed in the TA group (P > 0.05), whereas the remaining variables were not. Because no variable was normally distributed in both groups simultaneously, the Mann–Whitney U test was used for all between-group comparisons of continuous variables. Chi-square analysis showed that the TA group had significantly higher proportions of articular step-off > 2 mm, radial shortening > 3 mm, and AO type C fractures (all P < 0.001). The TA group also showed significantly lower distal radius CT HU (P < 0.001) and radial inclination (P = 0.04). No significant between-group differences were observed for the remaining variables listed in Table 1.

Spearman correlation analysis identified significant positive associations between radiocarpal TA and articular step-off > 2 mm (ρ = 0.63, P < 0.001), radial shortening > 3 mm (ρ = 0.56, P < 0.001), and AO fracture classification (ρ = 0.47, P < 0.001). A significant negative correlation was observed with distal radius CT HU (ρ = − 0.38, P < 0.001). Weak negative correlations were also noted with radial inclination (ρ = − 0.14, P = 0.04) and sex (ρ = − 0.13, P = 0.05). No statistically significant correlations were found for age, ulnar styloid fracture, volar tilt, diabetes, or any hematologic indices including WBC, neutrophil count, lymphocyte count, monocyte count, platelet count, NLR, PLR, or SIRI (all P > 0.05) (Table 1; Fig. 3).

Fig. 3.

Spearman Correlation Matrix of Variables Related to radiocarpal TA. Figure 3 illustrates the Spearman correlation coefficients matrix between various variables and radiocarpal TA. The color range spans from deep blue (negative correlation) to deep red (positive correlation), with color intensity indicating the strength of the correlation. Numeric values represent the specific correlation coefficients.

Multicollinearity was assessed prior to multivariable analysis. The variables included in the logistic regression model were: articular step-off > 2 mm, radial shortening > 3 mm, distal radius CT HU, sex, AO fracture classification, and radial inclination. All variance inflation factor (VIF) values were < 5, indicating an absence of multicollinearity. The highest VIF was observed for articular step-off > 2 mm (2.24), followed by AO fracture classification (1.96) and radial shortening > 3 mm (1.55); the lowest was for sex (1.06) (Table 2).

Table 2.

Multicollinearity and Multivariate Logistic Regression Analysis of Risk Factors

Variables	OR	95% CI Lower	95% CI Upper	P	VIF
Step-off > 2 mm	6.12	1.79	20.94	0.004	2.24
Radial shortening > 3 mm	8.02	2.55	25.21	< 0.001	1.55
CT value	0.99	0.99	1.00	0.010	1.09
Sex	0.79	0.31	2.05	0.63	1.06
AO type	0.93	0.27	3.22	0.91	1.96
Radial inclination	1.02	0.99	1.05	0.23	1.09

OR Odds Ratio, CI Confidence Interval, VIF Variance Inflation Factor

Multivariate logistic regression analysis revealed three independent risk factors for postoperative radiocarpal TA after DRF: articular step-off > 2 mm (OR = 6.12, 95% CI: 1.79–20.94, P = 0.004), radial shortening > 3 mm (OR = 8.02, 95% CI: 2.55–25.21, P < 0.001), and lower distal radius CT HU (OR = 0.99, 95% CI: 0.99–1.0, P = 0.01). For clinical interpretability, this corresponds to an OR of approximately 1.10 (95% CI: 1.05–1.16) for every 10-HU decrease in CT HU. In contrast, sex (OR = 0.79, 95% CI: 0.31–2.05, P = 0.63), AO fracture classification (OR = 0.93, 95% CI: 0.27–3.22, P = 0.91), and radial inclination (OR = 1.02, 95% CI: 0.99–1.05, P = 0.23) were not significant. (Table 2).

Given that the final follow-up duration ranged from 12 months to 3 years, follow-up-related results were further examined. The median follow-up duration for the overall cohort was 16 months (IQR, 13–19 months), including 15 months (IQR, 13–19 months) in the non-TA group and 16 months (IQR, 13–20 months) in the TA group, with no significant between-group difference (Mann–Whitney U test, P = 0.253).

After including follow-up duration in the multivariable logistic regression model, articular step-off > 2 mm (OR = 8.18, 95% CI: 3.62–18.48, P < 0.001), radial shortening > 3 mm (OR = 4.91, 95% CI: 2.14–11.26, P < 0.001), and lower distal radius CT HU (OR = 0.990, 95% CI: 0.985–0.995, P < 0.001) remained significantly associated with postoperative radiocarpal TA, whereas follow-up duration itself was not significant (OR = 1.02, 95% CI: 0.95–1.10, P = 0.520).

When TA diagnosed within 12 months after surgery was used as the outcome, the associations remained directionally consistent. Articular step-off > 2 mm (OR = 6.19, 95% CI: 2.83–13.56, P < 0.001), radial shortening > 3 mm (OR = 3.79, 95% CI: 1.67–8.58, P = 0.001), and lower distal radius CT HU (OR = 0.993, 95% CI: 0.988–0.998, P = 0.003) were all independently associated with TA diagnosed within 12 months.

LR model performance: On the test dataset, the LR model achieved an accuracy of 82.35%, precision 80.77%, recall 75.00%, F1 score 77.78%, specificity 87.50%, ROC AUC 90.71%, and PR AUC 87.98%. The Youden index at the optimal threshold was 0.67. The Brier score was 0.123. The Hosmer–Lemeshow goodness-of-fit test (10 risk deciles, g–2 degrees of freedom) yielded P = 0.718, indicating no significant lack of fit. Logistic recalibration yielded a calibration slope of 1.28 and an intercept of 0.11, with good visual agreement between predicted and observed probabilities (Figs. 4, 5 and 6; Table 3). Here, the test-set results were obtained from the independent 30% hold-out set, whereas 10-fold stratified cross-validation was conducted within the training set for internal validation and model selection.

Fig. 4.

Calibration curve of the logistic regression (LR) model. The blue curve shows the agreement between predicted probabilities and observed outcomes in the independent test set. Ten-fold stratified cross-validation was performed within the training set for internal validation and model selection, indicating acceptable calibration. The Brier score of 0.123 reflects good consistency between predicted and actual risks. The calibration slope was 1.2800, and the intercept was 0.1100

Fig. 5.

Receiver operating characteristic (ROC) curve of the LR model. The ROC curve illustrates the trade-off between sensitivity and specificity for the LR model predicting post-traumatic arthritis after distal radius fracture. The blue curve represents model performance, with an AUC of 90.71%, indicating excellent discriminative ability

Fig. 6.

Precision–recall (PR) curve of the LR model. The PR curve depicts the relationship between precision and recall for the LR model. The blue curve suggests high accuracy in detecting true positives despite potential class imbalance, with a PR AUC of 87.98%

Table 3.

Confusion matrix, performance metrics, and cross-validation results of the models

	Logistic Regression	Support Vector Machine
True Positive	21	20
False Positive	5	4
True Negative	35	36
False Negative	7	8
Accuracy, %	82.35	82.35
Precision, %	80.77	83.33
Recall, %	75	71.43
F1 Score, %	77.78	76.92
Specificity, %	87.5	90
ROC AUC	90.71	91.34
PR AUC, %	87.98	87.61
Youden Index	0.67	0.72
Brier Score	0.123	0.123
Hosmer–Lemeshow P	0.718	NA
Calibration slope	1.28	NA
Calibration intercept	0.11	NA
CV Accuracy, %	82.33 ± 9.66	81.03 ± 7.94
CV Precision, %	81.28 ± 12.89	79.79 ± 11.52
CV Recall, %	77.67 ± 15.34	74.00 ± 16.33
CV F1 Score, %	77.78 ± 12.04	75.62 ± 11.08
CV Specificity, %	86.59 ± 11.58	85.88 ± 9.76
CV ROC AUC, %	89.99 ± 8.08	88.66 ± 5.93
CV PR AUC, %	88.14 ± 8.49	86.27 ± 8.16

CV Cross Validation, ROC AUC Area under the Receiver Operating Characteristic Curve, PR AUC Area under the Precision–Recall Curve

The training dataset contained 65 events and 6 predictors, resulting in EPV = 10.83. Ten-fold stratified cross-validation showed relatively stable performance, with mean accuracy 82.33% ± 9.66% and ROC AUC 89.99% ± 8.08% (Table 3).

To further examine the contribution of distal radius CT HU to the logistic regression model, we compared the model including CT HU with the corresponding model after removing CT HU. The model without CT HU, which retained only articular step-off > 2 mm and radial shortening > 3 mm, showed poorer fit. After CT HU was included, the AIC decreased from 202.63 to 190.28. In addition, the likelihood ratio test showed that inclusion of CT HU significantly improved model fit (χ² = 14.35, P < 0.001). These results suggest that retaining distal radius CT HU in the model was associated with improved overall model fit after accounting for articular step-off > 2 mm and radial shortening > 3 mm.

SVM model performance: On the same test set, the SVM model achieved an accuracy of 82.35%, precision 83.33%, recall 71.43%, F1 score 76.92%, specificity 90.00%, ROC AUC 91.34%, and PR AUC 87.61%. The Youden index was 0.72, and the Brier score was 0.123. As the SVM is not likelihood-based, the Hosmer–Lemeshow statistic, calibration slope, and intercept were not applicable. Ten-fold stratified cross-validation showed relatively stable performance, with mean accuracy 81.03% ± 7.94% and ROC AUC 88.66% ± 5.93% (Figs. 7, 8 and 9; Table 3). Likewise, cross-validation results reflect internal validation within the training set, while the reported performance metrics were computed on the independent test set.

Fig. 7.

Calibration curve of the support vector machine (SVM) model. The blue curve shows the agreement between predicted probabilities and observed outcomes in the test set. The curve runs close to the ideal 45° diagonal line, indicating good calibration. The Brier score was 0.123, reflecting adequate alignment between predicted and actual risks

Fig. 8.

ROC curve of the SVM model. The ROC curve demonstrates the trade-off between sensitivity and specificity for the SVM model predicting post-traumatic arthritis after distal radius fracture. The blue curve represents model performance, achieving an AUC of 91.34%, which reflects excellent discriminative capacity

Fig. 9.

PR curve of the SVM model. The PR curve presents the relationship between precision and recall for the SVM model. The blue curve indicates reliable detection of true positives, with a PR AUC of 87.61%

Discussion

DRFs are among the most common adult fractures. In non-osteoporotic DRF patients, Lameijer et al. reported a 32% incidence of radiocarpal TA, significantly associated with postoperative changes in radial length [6]. Classic studies further demonstrated that residual articular incongruity leads to a 91% incidence of radiocarpal TA compared to just 11% when congruity is restored; marked radial shortening is also linked to poorer outcomes [14]. These findings underscore the importance of maintaining articular congruity and radial length for long-term joint health. Based on this, our study incorporates preoperative imaging predictors—preoperative articular step-off > 2 mm and preoperative radial shortening > 3 mm—alongside other clinical and radiologic data to construct and internally evaluate multivariable prediction models for radiocarpal TA after DRF, comparing the performance of LR and SVM methods.

Our findings confirm that preoperative articular step-off > 2 mm is an independent predictor of radiocarpal TA following DRF. Although anatomic or near-anatomic reduction was generally achieved intraoperatively, a greater preoperative step-off likely reflects more extensive chondral and subchondral injury at the time of trauma. Even when postoperative imaging appears satisfactory, subtle residual incongruity or irreversible cartilage damage may persist. These microscopic irregularities can result in localized stress concentration, reduced joint contact area, and elevated shear forces during wrist motion, ultimately promoting cartilage breakdown and the onset of radiocarpal TA over time [14].

Preoperative radial shortening > 3 mm was also identified as an independent risk factor. Radial shortening may result in increased positive ulnar variance, shifting load toward the ulnar side of the wrist and potentially altering the load distribution across the radiolunate and radioscaphoid joint surfaces, thereby increasing the risk of cartilage wear during long-term follow-up. Moreover, radial shortening often coexists with collapse and comminution of intra-articular fractures, suggesting greater initial injury complexity and insufficient articular surface support, which may predispose the joint to subsequent degeneration [15].

Preoperative distal radius CT HU has increasingly been recognized as a surrogate marker for local bone quality [16]. While prior studies have employed varying definitions of the ROI, the underlying methodological principles remain consistent: isolate trabecular bone, exclude cortical bone, fracture lines, and metal artifacts, and average multiple measurements for reliability. In our study, the ROI was defined as the cancellous bone located approximately at 3 cm proximal to the distal radial articular surface, aligning with the classical anatomical definition of distal radius fractures and optimally reflecting local bone quality at the fracture site.

Our findings showed that lower preoperative distal radius CT HU was independently associated with postoperative radiocarpal TA. Lower CT HU may reflect reduced trabecular number, disorganized architecture, and poor mineralization, thereby weakening subchondral bone support and making the articular surface more susceptible to microfractures and collapse. This may alter articular congruity, increase stress concentration, and accelerate cartilage degeneration [17–19]. Osteoporotic bone may also delay fracture healing and increase implant subsidence risk, indirectly accelerating joint degeneration [19]. Although the odds ratio per 1-HU increase appears numerically small, CT HU is a continuous variable measured over a relatively wide range; therefore, its effect becomes more clinically interpretable over larger increments. In the present study, every 10-HU decrease in distal radius CT HU corresponded to an approximately 10% increase in the odds of postoperative radiocarpal TA. In addition, when CT HU was removed from the logistic regression model, overall model fit worsened, whereas reintroduction of CT HU improved model fit, as reflected by a lower AIC and a significant likelihood ratio test. These findings suggest that distal radius CT HU may serve as a useful complementary indicator of local bone quality in preoperative risk assessment. Therefore, for patients with markedly low preoperative distal radius CT HU values, even when satisfactory anatomical reduction is achieved, clinicians may consider closer rehabilitation progression, more individualized rehabilitation protocols, and closer radiographic and clinical follow-up to monitor for early signs of joint degeneration.

We found no significant association between preoperative NLR, PLR, or SIRI and TA after DRF. Although these inflammatory markers have been linked to osteoarthritis and post-traumatic arthritis in other joints [20, 21], local mechanical factors may outweigh systemic inflammatory responses in DRF. In addition, although hematologic indices were collected on the first day of hospital admission before surgery, these markers may still have been influenced by acute post-traumatic inflammatory responses and other short-term clinical factors. Further large-scale, longitudinal studies are warranted.

In the test dataset, both LR and SVM showed good discrimination, with only modest differences between them (ROC AUC 90.71% vs. 91.34%; PR AUC 87.98% vs. 87.61%). SVM showed slightly higher specificity (90.00% vs. 87.50%) and Youden index (0.72 vs. 0.67), suggesting a marginal advantage in reducing false positives, whereas LR achieved higher recall (75.00% vs. 71.43%) and F1 score (77.78% vs. 76.92%), potentially reducing missed diagnoses. In terms of calibration, the LR model showed acceptable agreement between predicted and observed probabilities, with a non-significant Hosmer–Lemeshow test (P = 0.718), a calibration intercept close to 0 (0.11), and a calibration slope reasonably close to 1 (1.28). The Brier score was 0.123, indicating acceptable overall probabilistic accuracy. Ten-fold stratified cross-validation showed relatively stable performance for both models, supporting their internal robustness. Overall, the LR and SVM models demonstrated promising internal predictive performance; however, because the present study was retrospective and relied on internal evaluation only, the models should be interpreted as preliminary and require prospective external validation before routine clinical application.

Although our models demonstrated good predictive performance, several limitations should be acknowledged. First, this was a retrospective single-center study; therefore, selection bias and residual confounding are inevitable. Radiocarpal TA was assessed at the final follow-up rather than at prespecified time points, and follow-up duration ranged from 12 months to 3 years, such that the exact timing of TA onset could not be consistently ascertained for all patients. Given this variability, we further examined the potential influence of follow-up heterogeneity. Follow-up duration was comparable between the TA and non-TA groups, and inclusion of follow-up duration in the multivariable model did not materially change the associations of articular step-off > 2 mm, radial shortening > 3 mm, and distal radius CT HU with postoperative radiocarpal TA. In addition, when the outcome was restricted to TA diagnosed within 12 months after surgery, the same three imaging predictors remained significant and directionally consistent. These findings suggest that the main results were relatively robust despite variation in follow-up length. Nevertheless, this approach cannot fully eliminate the inherent limitations of retrospective follow-up heterogeneity. In addition, no standardized radiographic grading system for wrist arthritis was uniformly applied across the cohort, so radiocarpal TA was treated as a binary endpoint rather than a graded severity outcome.

Follow-up imaging was not available for every surgically treated patient, and a substantial number of cases were excluded because of incomplete radiographic follow-up. In routine practice, patients with persistent pain, stiffness, or functional limitation are more likely to return for repeated radiographic evaluations, whereas asymptomatic patients may be less likely to undergo follow-up imaging; thus, the observed proportion of radiocarpal TA in the analyzed cohort may overestimate the true incidence among all surgically treated DRF patients. Importantly, our primary objective was to identify preoperative predictors and develop risk models among patients with available radiographic endpoints, rather than to estimate population-level incidence. In addition, several potentially important confounders, such as baseline activity level, rehabilitation adherence, and detailed injury mechanism, were not uniformly documented and therefore could not be adjusted for. Finally, the cohort included only surgically treated DRF patients, which limits generalizability to nonoperatively managed fractures, and external validation is still lacking.

Clinically, the present findings suggest that patients with preoperative articular step-off > 2 mm, radial shortening > 3 mm, and lower distal radius CT HU may warrant greater attention, as they appear to be at increased risk of postoperative radiocarpal TA. In these patients, surgeons may place greater emphasis on restoration of articular congruity and radial length, while considering the potential influence of poor local bone quality on fixation strategy. Closer radiographic surveillance and more individualized postoperative follow-up may also be appropriate. Nevertheless, these implications should be interpreted cautiously because the present models were developed retrospectively and internally evaluated only.

Conclusion

We identified three independent preoperative imaging risk factors for postoperative radiocarpal TA after DRF: articular step-off > 2 mm, radial shortening > 3 mm, and lower distal radius CT HU. Using these variables, the LR and SVM models demonstrated promising internal predictive performance. These findings may support preoperative risk stratification, but further prospective multicenter studies and external validation are required before routine clinical application.

Authors’ contributions

All authors had full access to the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis. Conceptualization, Y.L.Z. and L.L.; Methodology, Y.L.Z. and L.L.; Investigation, B.L., Z.M., S.J.W., Y.L.Z. and L.L.; Formal Analysis, Y.L.Z., L.L., B.L., Z.M. and S.J.W.; Resources, Y.L.Z. and L.L.; Writing - Original Draft, Y.L.Z. and L.L.; Writing - Review & Editing, Y.L.Z., L.L., Z.G.L., B.Y.F. and J.T.S.; Visualization, Y.L.Z. and L.L.; Supervision, L.L.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

This retrospective study was reviewed and approved by the Ethics Committee of Beijing Luhe Hospital affiliated to Capital Medical University (Approval No. 2025-LHYK-071-01). The requirement for informed consent was waived by the same Ethics Committee because this study used anonymized retrospective clinical data and posed minimal risk to participants. All procedures involving human participants and human data were performed in accordance with relevant guidelines and regulations, including the Declaration of Helsinki and its later amendments or comparable ethical standards.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.