Machine learning, decision tree and nomogram for predicting screw loosening after PLIF in osteoporotic patients: a retrospective multicenter study

Abstract

Objective To develop and validate machine learning models and an individualized nomogram for predicting pedicle screw loosening after posterior lumbar interbody fusion (PLIF) in osteoporotic patients using preoperative clinical, imaging, and bone metabolism-related medication profiles. Methods A retrospective analysis was conducted on 630 osteoporotic patients who underwent PLIF at three spine surgery centers. Patients were divided into a non-loosening group (n = 450) and a loosening group (n = 180) according to the presence of implant loosening on imaging within 12 months postoperatively. Univariate analysis was used to screen candidate variables, and LASSO–logistic regression with 10-fold cross–validation was applied to extract independent predictors. Four models (naïve Bayes, logistic regression, linear discriminant analysis, and decision tree) were constructed based on the selected features and evaluated using the area under the curve (AUC), calibration curves, and decision curve analysis (DCA). The structure of the optimal model (decision tree) was visualized, and a nomogram was built using multivariable logistic regression. Results Univariate analysis showed significant differences between the two groups in age, bone mineral density T-score, pelvic incidence, lumbar lordosis, sex, hypertension, diabetes mellitus, foraminal morphology, history of glucocorticoid use, calcium supplementation, and vitamin D supplementation (all P < 0.05). LASSO regression identified 11 independent predictors (λ.min = 0.0325). Among the four models, the decision tree showed the highest discrimination, achieving an AUC of 0.975 (95% CI 0.961–0.989) in the training set and 0.971 (95% CI 0.955–0.987) in the test set, with good calibration (Hosmer-Lemeshow test P = 0.418). DCA demonstrated a significant net benefit across a clinically relevant threshold probability range (0–50%). The decision tree identified the bone mineral density T-score as the root splitting variable; a T-score < –3.6 classified patients as being at extremely high risk for loosening. Among those with T-score ≥ –3.6 who did not take calcium, lack of vitamin D supplementation was associated with a very high risk. Among those with T-score ≥ –3.6 who took calcium, female sex combined with lumbar lordosis ≥ 51° indicated an elevated risk. The nomogram integrated the 11 factors and yielded a C-index of 0.928 (95% CI 0.903–0.953) with good calibration (Hosmer-Lemeshow test P = 0.372). Conclusion The decision tree model demonstrated favorable predictive performance for pedicle screw loosening after PLIF. Its interpretable classification rules facilitate rapid screening of high-risk patients, while the nomogram enables individualized probability estimation for surgical planning. Together, these complementary tools offer a potentially useful framework for preoperative risk stratification and personalized management of osteoporotic patients undergoing PLIF