Abstract: BACKGROUND: The incidence of hip fracture patients is increasing day by day. Because of their poor physical condition, these people often need to stay in hospital for a long time. However, the prolonged length of stay leads to a decrease in bed circulation rate and an increase in economic burden. At present, there are few prediction models for delayed discharge of hip fractures. This study aims to find the best model for delayed discharge of hip fractures and guide clinical decision-making.  
OBJECTIVE: To explore the risk factors of prolonged length of stay in patients with hip fractures, establish two different risk prediction models, obtain the best risk prediction tools, and provide a reference for clinical intervention and management.
METHODS: Data from 683 elderly patients with hip fractures in Tianjin Hospital from January 2019 to December 2021 were retrospectively analyzed. All patients were randomly divided into a modeling group (479 cases) and a verification group (204 cases) according to the ratio of 7:3. The 75th percentile of length of stay was taken as the cut-off point (> 28 days), and they were divided into extended hospitalization group and normal group. Single-factor and multifactor Logistic regression analysis and variable importance ranking were used to screen the best prediction model; the nomogram and random forest models were constructed. The prediction efficiency of the two models was evaluated by the receiver operating characteristic curve area, accuracy, sensitivity, specificity, positive prediction value and negative prediction value.  
RESULTS AND CONCLUSION: (1) Logistic regression analysis showed that bone traction, pneumonia, refolding, multiple trauma, venous thrombosis, lung infection and age-adjusted Charlson Comorbidity Index were the risk factors of prolonged length of stay of hip fracture patients. (2) The random forest model showed that age, bone traction, surgical type, age-adjusted Charlson Comorbidity Index and pneumonia were the first five indexes according to the average reduction of the Gini index, which had an important influence on the prediction of delayed discharge. (3) The area under the receiver operating characteristic curve, accuracy, sensitivity, specificity, positive prediction value and negative prediction value of the Logistic regression model and random forest prediction model were 0.774(95%CI: 0.696-0.853) and 0.708(95%CI: 0.627-0.789), 60.78% and 90.85%, 80.39% and 23.53%, 50.82% and 78.09%, 86.01% and 46.15%, respectively. The results exhibited that the Logistic model had good prediction efficiency. (4) Above findings confirm that the Logistics regression model and random forest model have high predictive value for a prolonged length of stay in patients with hip fractures, which is of great significance for clinical medical staff to identify high-risk patients in time and take effective intervention measures to reduce the length of stay of patients with hip fractures.

Key words: hip fracture, length of stay, delayed discharge, random forest model, Logistic regression, age-adjusted Charlson Comorbidity Index, risk factor, risk prediction, prediction model, nomograms