Prediction of Postoperative Length of Stay in Patients with Hip Fracture: A Two-Stage Machine Learning Approach

Abstract

Objectives

This study aimed to apply machine learning (ML) techniques to predict postoperative length of stay (LOS) in patients with hip fracture. Because LOS varies widely across individuals owing to complex clinical factors, accurate prediction remains challenging. To address this challenge, an enhanced two-stage approach was developed and compared with a conventional one-stage approach.

Methods

Data from 3,118 surgically treated patients with hip fracture were extracted from a hospital information system. Demographic and perioperative variables were analyzed, and the dataset was divided into training and test sets at a 70:30 ratio. ML algorithms were applied using a two-stage modeling approach. In the first stage, a classification model categorized LOS as short stay or long stay. In the second stage, regression models predicted the number of hospital days within each group. Performance was evaluated using accuracy, precision, recall, and F1-score for classification and mean absolute error (MAE), root mean square error (RMSE), and mean relative error (MRE) for regression.

Results

In the one-stage approach, the support vector machine model showed the lowest prediction error, with an MAE of 2.20, RMSE of 3.18, and MRE of 0.42. The two-stage approach, which integrated classification and regression, outperformed the one-stage approach, achieving an MAE of 1.46, RMSE of 1.86, and MRE of 0.35.

Conclusions

The two-stage approach outperformed the one-stage approach, suggesting that LOS stratification improves prediction accuracy. This improvement may help hospitals anticipate resource needs, plan postoperative care, and manage bed allocation more effectively.

I. Introduction

Hip fractures are a major global public health problem, particularly among older adults [1,2]. The number of cases was estimated at approximately 1.31 million in 1990 and is projected to reach 6 million by 2050 [1,3]. Beyond this clinical burden, hip fracture management is associated with substantial healthcare costs because nearly all affected patients require medical attention and hospital resources [4]. Postoperative disability or complications are often accompanied by prolonged hospital length of stay (LOS), adding further financial strain to healthcare systems [5].

Accurate LOS prediction is essential for early risk assessment and enables healthcare teams to manage resources efficiently, plan appropriate rehabilitation strategies for high-risk patients, and reduce avoidable costs [1,6–8]. Current predictive approaches typically rely on statistical analyses of preoperative variables [8,9]. However, when relationships among variables are nonlinear, conventional statistical models may perform poorly or produce biased estimates because their assumptions may not hold [6,10,11].

Machine learning (ML) has been widely adopted in healthcare for disease diagnosis and prognosis [1,12]. Recent studies have applied ML to hip fracture management and reported high predictive performance [2,12]. These applications may reduce clinical workload and diagnostic time. Although this evidence supports the broader use of ML in clinical decision-making, its application to discharge planning and LOS prediction remains limited. A major challenge is accuracy, because LOS is a continuous outcome with substantial variability and marked skewness [7,13].

To improve the accuracy of LOS prediction in the clinically complex population of patients with hip fracture, this study implemented a two-stage ML framework as an alternative to the conventional one-stage approach. In this framework, a classification model first categorizes patients into short-stay and long-stay groups, and subgroup-specific regression models then estimate LOS. By reducing the effect of the highly skewed LOS distribution, this framework was designed to improve prediction accuracy and provide more reliable LOS estimates for resource planning and postoperative care.

II. Methods

1. Dataset of Hip Fracture Patients

This study used medical records of patients with hip fracture treated at Phrae Hospital between 2012 and 2024, with an initial dataset of 3,118 individuals. The dataset included demographic information, clinical characteristics, and treatment-process time points. Eligible participants were required to be at least 50 years old and to have undergone surgical management of hip fracture. For inclusion in the analysis, complete information was required for the date of injury, date of hospital admission, date of surgery, and LOS.

After data completeness was verified, exploratory analysis was conducted to examine the LOS distribution. As shown in Figure 1A, most patients had an LOS of 3–10 days, with a distinctly right-skewed distribution, indicating substantial variability in hospitalization duration. The LOS box plot in Figure 1B shows a median of approximately 6–7 days and an interquartile range of 4–12 days, with a large number of outliers. Overall, these visualizations indicate that the dataset had substantial variability and numerous extreme outliers, particularly beyond approximately 18 days.

Figure 1.

Distribution of postoperative length of stay. (A) Histogram showing the right-skewed length of stay distribution. (B) Box plot showing multiple high-value outliers.

Data preprocessing involved deriving additional clinically relevant variables, specifically the intervals from fall or injury to hospital admission and surgery, as well as operative duration. These variables quantified delays in the treatment process that may affect patient outcomes. To ensure data integrity, strict exclusion criteria were applied. Records with missing LOS values, outliers identified through distributional analysis, or incomplete time data were excluded. These procedures yielded a final analytic sample of 2,922 patients.

For variables with missing values, numerical features were imputed using the mean, whereas categorical features were imputed using the mode. Categorical variables were then transformed using one-hot encoding to allow their use in ML algorithms requiring numerical input. The outcome variable was defined in two forms to support the two-stage modeling framework. For the classification stage, LOS was categorized as “short stay” (LOS ≤7 days) or “long stay” (LOS >7 days). For the regression stage, LOS was defined as a continuous variable, and separate regression models were developed for each subgroup identified during classification. This framework was designed to accommodate the heterogeneous, right-skewed LOS distribution through subgroup-specific regression modeling.

Table 1 summarizes the variables included in this study. The variable set captured multiple dimensions of patient care, including demographic information, baseline clinical variables, time-related variables, treatment-related information, service-related factors, and LOS, which was used in both the classification and regression models. Including these domains was intended to improve model robustness and relevance to real-world clinical settings.

Table 1.

Variables and statistical characteristics of the patient dataset

Variable	Statistical information	Type
Clinical and patient characteristics
Sex		Category
Male	739 (25.29)
Female	2,183 (74.71)
Age (yr)	76.21 ± 9.38	Numeric
BMI (kg/m2)	20.84 ± 3.37	Numeric
Living		Category
Home	2,918 (99.86)
Center	4 (0.14)
Clinical characteristics
Fracture type		Category
Femoral neck fracture	840 (28.75)
Trochanteric fracture	1,924 (65.84)
Subtrochanteric fracture	158 (5.41)
ASA score	2.55 ± 0.54	Numeric
CCI score	3.98 ± 1.73	Numeric
Albumin (g/dL)	3.33 ± 0.54	Numeric
Hemoglobin (Hb)		Category
Normal	1,786 (61.12)
Low	1,136 (38.88)
Hematocrit		Category
Normal	2,920 (99.93)
Low	2 (0.07)
Time-related variables
PreHospital (hr)	73.26 ± 343.17	Numeric
FallingToOR (hr)	116.99 ± 347.41	Numeric
AdmitToOR (hr)	43.91 ± 47.92	Numeric
Surgical and perioperative data
Surgery type		Category
Total hip arthroplasty	146 (5.00)
Bipolar hemiarthroplasty	582 (19.92)
Austin-Moore prosthesis	27 (0.92)
Dynamic hip screw	220 (7.52)
Gamma nail	521 (17.83)
Proximal femoral nail antirotation	1,422 (48.67)
Cannulated screws	4 (0.14)
Operation time (min)	65.37 ± 30.37	Numeric
PRC bags	0.33 ± 0.65	Numeric
Hospital service data
Transportation		Category
Ambulance	400 (13.69)
Refer	1,672 (57.22)
Relative	850 (29.09)

Values are presented as number (%) or mean ± standard deviation.

BMI: body mass index, ASA: American Society of Anesthesiologists physical status classification, CCI: Charlson Comorbidity Index; PRC: packed red cell.

2. Experiment Environment and Model Architecture

The research framework shown in Figure 2 outlines the overall workflow for developing and comparing the one-stage and two-stage modeling approaches for LOS prediction. The framework consists of sequential steps, including data review, visualization, preprocessing, model construction, and performance evaluation. Both modeling strategies were developed using the same dataset and evaluation protocol to ensure a fair comparison.

Figure 2.

Research framework. LOS: length of stay, ANN: artificial neural network, RF: random forest, SVM: support vector machine, KNN: k-nearest neighbors, GBT: gradient-boosted trees, MAE: mean absolute error, RMSE: root mean square error, MRE: mean relative error.

The process began with retrieval of patient records from the hospital information system, including demographic characteristics, clinical factors, treatment-related time variables, surgical procedures, and LOS. Initial data exploration was performed using visualizations, including histograms and box plots, to examine distributional patterns, variability, and outliers. These steps were followed by data cleaning, feature engineering, missing-value handling, and data transformation.

All models were developed using Altair AI Studio (https://web.altair.com/academic-hub-ai-studio), a visual ML platform for data preprocessing, model development, and performance evaluation. The platform supports automated model training, hyperparameter tuning, and validation, enabling an efficient and reproducible development pipeline. The final dataset was split into training and test sets at a 70:30 ratio. The training set was used for model construction, stability assessment with 10-fold cross-validation, and hyperparameter tuning via grid search, whereas the test set was used for final model evaluation.

Model development used both one-stage and two-stage modeling approaches. The predictive framework was designed for use in the early postoperative phase by integrating preoperative characteristics with intraoperative variables, such as surgical duration. Once these data are available, LOS predictions can be generated to support clinical decision-making, including discharge planning, bed allocation, resource management, and early identification of patients at risk for prolonged hospitalization.

In the one-stage approach, LOS was directly predicted as a continuous outcome using a single regression model. In the two-stage approach, patients were first stratified by a classification model into short-stay (≤7 days) and long-stay (>7 days) groups. The 7-day cutoff was chosen based on clinical expert recommendations to represent a practical 1-week stay. Statistically, this threshold falls between the median (5 days) and the 75th percentile (8 days) of the dataset, making it a meaningful indicator for identifying prolonged hospitalization. Based on the classification result, each patient was then assigned to the corresponding subgroup-specific regression model for LOS prediction. Separate regression models were constructed for each subgroup using the training dataset, partitioned according to observed LOS ranges of 1–7 days for short stay and 8–17 days for long stay. Stratification before regression reduced the effect of the skewed LOS distribution and enabled more effective learning of group-specific patterns, resulting in improved predictive performance compared with the one-stage approach.

This study employed five ML algorithms. The support vector machine (SVM) algorithm was selected for its ability to construct optimal decision boundaries [14,15], whereas k-nearest neighbors (KNN) provided a nonparametric approach for capturing local and nonlinear relationships [16]. Ensemble methods, specifically random forest (RF) and gradient-boosted trees (GBT), were used because of their robustness in high-dimensional data and their respective strengths in variance reduction and error correction [17–19]. An artificial neural network (ANN) was also incorporated to model complex relationships through adaptive weight optimization [20,21].

Final performance evaluation was conducted on the test set after model selection to reduce the risk of data leakage and bias. For the two-stage model, each patient was first classified into either the short-stay or long-stay group. The corresponding regression model was then applied to predict LOS. These predictions were combined into a single dataset to calculate overall performance metrics, including mean absolute error (MAE), root mean square error (RMSE), and mean relative error (MRE). This approach enabled direct comparison with the baseline one-stage model.

Model performance was evaluated using metrics appropriate to each task. Classification models were assessed using accuracy, precision, recall, and F1-score to evaluate discrimination between short-stay and long-stay patients, with attention to performance across classes. Regression models were evaluated using MAE, RMSE, and MRE, which measure average prediction error, sensitivity to larger prediction errors, and relative error across LOS durations, respectively. Model selection was based on performance in the training dataset, prioritizing classification models with balanced discrimination and regression models with lower MAE, RMSE, and MRE.

To improve model transparency and support clinical interpretability, Shapley additive explanations (SHAP) analysis was performed on the best-performing models. This approach enabled identification of key predictors and quantification of their contributions to predicted LOS.

3. Ethical Considerations

All personally identifiable information, including names, addresses, and contact details, was removed before analysis. Dataset access was restricted to authorized investigators. This study used retrospective, de-identified data and did not involve direct patient contact. In accordance with the institutional guidelines of Phrae Hospital, formal ethical approval was waived because no identifiable patient information was accessed. Patient confidentiality was maintained throughout the study.

III. Results

Grid search was used to optimize the hyperparameters of each algorithm and identify the best-performing models. The training set was used for stability assessment with 10-fold cross-validation during the tuning process. Optimal parameters, such as the number of trees, maximum depth, and learning rate, were configured for both classification and regression stages before the final models were evaluated on the test set.

Table 2 shows that, among the one-stage regression models, SVM outperformed the other algorithms, achieving the lowest MAE (2.20) and MRE (0.42). Although its RMSE was higher, MAE and MRE were prioritized for model selection because they provide a more robust assessment of typical performance and are less sensitive to extreme LOS outliers that can distort RMSE.

Table 2.

Performance evaluation of each model on the test set

Algorithm	Performance (regression) in one-stage model			Performance (classification) in two-stage model				Performance (regression) in two-stage model
	MAE	RMSE	MRE	Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)	Short-stay model			Long-stay model
								MAE	RMSE	MRE	MAE	RMSE	MRE
SVM	2.2	3.18	0.42	79.04	79.19	95.16	86.45	1.34	1.71	0.38	2.15	2.68	0.19
KNN	2.33	2.99	0.59	81.16	80.14	97.05	87.79	1.27	1.54	0.45	2.05	2.53	0.18
RF	2.37	2.95	0.64	81.62	80.24	97.71	88.12	1.2	1.47	0.42	2.12	2.58	0.19
GBT	2.28	2.98	0.53	81.39	81.73	94.44	87.62	1.23	1.51	0.41	2.08	2.61	0.19
ANN	2.22	2.94	0.53	82.99	81.91	97.05	88.84	1.23	1.54	0.4	2.45	2.84	0.24

MAE: mean absolute error, RMSE: root mean square error, MRE: mean relative error.

For the two-stage model, ANN demonstrated the best classification performance. It achieved the highest accuracy (82.99%), precision (81.91%), and F1-score (88.84%) while maintaining high recall (97.05%). Although RF and KNN had slightly higher recall, ANN provided the most balanced performance across all four metrics, suggesting reliable discrimination between short-stay and long-stay patients. In the regression stage, model performance differed between the short-stay and long-stay groups. For short-stay prediction, RF achieved the lowest MAE (1.20) and RMSE (1.47). Although SVM yielded a slightly better MRE, RF was selected because it minimized absolute error in these more tightly clustered values. For long-stay prediction, KNN outperformed all other algorithms, with the lowest MAE (2.05), RMSE (2.53), and MRE (0.18). These findings suggest that KNN was particularly effective in handling the greater variability and complexity of long hospital stays.

Table 3 shows that the two-stage approach outperformed the one-stage approach. The two-stage approach reduced MAE from 2.20 to 1.46 and RMSE from 3.18 to 1.86, indicating fewer large prediction errors. The decrease in MRE from 0.42 to 0.35 also indicates greater consistency across different stay durations. Overall, these results suggest that stratifying patients before regression helped address data variability and improved the stability and accuracy of clinical predictions.

Table 3.

Comparison of one-stage and two-stage model performance on the test set

Evaluation metric	Performance
	One-stage model	Two-stage model
MAE	2.20	1.46
RMSE	3.18	1.86
MRE	0.42	0.35

MAE: mean absolute error, RMSE: root mean square error, MRE: mean relative error.

To evaluate the robustness of cutoff selection, sensitivity analysis was conducted using alternative LOS thresholds of 3, 5, and 8 days, corresponding to the 25th, 50th (median), and 75th percentiles of the data distribution, respectively.

As shown in Table 4, the model demonstrated stable performance across cutoff values between 5 and 8 days, indicating that the proposed two-stage framework was relatively robust to variation in LOS stratification. In contrast, the lower cutoff of 3 days resulted in substantially higher prediction errors, likely because of imbalance between subgroups.

Table 4.

Sensitivity analysis of the two-stage model using different length-of-stay cutoff thresholds

Cutoff threshold	MAE	RMSE	MRE
3 days	1.82	2.55	0.31
5 days	1.48	1.96	0.32
7 days	1.46	1.86	0.35
8 days	1.52	1.86	0.39

MAE: mean absolute error, RMSE: root mean square error, MRE: mean relative error.

These findings suggest that very low thresholds may not adequately capture the underlying structure of LOS data, particularly when the distribution is right-skewed. The 7-day cutoff achieved the best overall balance between prediction accuracy and subgroup stratification. Statistically, this threshold falls between the median and the 75th percentile of the dataset, while also representing a clinically recommended and meaningful 1-week hospitalization period.

Figure 3A–C shows scatter plots of actual versus predicted LOS for the prediction models. Because of the split architecture of the two-stage model, short-stay and long-stay predictions were visualized separately to improve clarity and avoid visual discontinuities. Short-stay predictions showed close alignment with the reference diagonal, indicating consistent accuracy across the 1–7-day interval. Long-stay predictions retained some variability, but dispersion was reduced compared with the one-stage model, suggesting greater stability in this high-variance subgroup. In contrast, the one-stage model showed a tendency toward underestimation and wider variance across the full LOS spectrum. These visual findings support the quantitative results, indicating that the two-stage approach reduced large prediction errors and provided more reliable estimates.

Figure 3.

Comparison of actual and predicted postoperative length of stay (LOS). (A) Two-stage model, short-stay group. (B) Two-stage model, long-stay group. (C) One-stage model.

Figure 4A–4C shows residual plots used to assess prediction error across actual LOS values. The two-stage model produced residuals that were less dispersed within both the short-stay and long-stay groups, indicating more consistent performance within each subgroup. In contrast, the one-stage model showed larger and increasingly dispersed residuals as LOS increased, suggesting reduced stability in predicting prolonged hospital stays.

Figure 4.

Residual analysis of postoperative length-of-stay (LOS) predictions by actual LOS. (A) Two-stage model, short-stay group. (B) Two-stage model, long-stay group. (C) One-stage model.

SHAP analysis was applied to the best-performing regression models in both the short-stay and long-stay groups. Figure 5 presents the SHAP summary plots, which show the relative importance and directional effect of each feature on predicted LOS. In this context, positive SHAP values indicate that a feature increases predicted LOS, whereas negative values indicate a decrease.

Figure 5.

Shapley additive explanations (SHAP) summary plots for feature importance in the two-stage model. (A) Long-stay model using k-nearest neighbors (KNN). (B) Short-stay model using random forest (RF). BMI: body mass index, CCI: Charlson Comorbidity Index.

For the long-stay model, treatment-delay variables had the largest contribution to predicted LOS. The time from injury to surgery (FallingToORHrs) was the most important predictor, followed by time from admission to surgery (Admit-ToORHrs) and prehospital delay (PreHosHrs). Longer delays were consistently associated with increased predicted LOS, indicating that preoperative delay variables contributed substantially to predictions of prolonged hospitalization.

In contrast, the short-stay model was more strongly influenced by time from admission to surgery (AdmitToORHrs), along with patient-related and perioperative factors, including surgery type and comorbidity burden, measured using the Charlson Comorbidity Index. Higher comorbidity burden and longer treatment delays were associated with longer predicted LOS.

Overall, SHAP analysis indicated that surgical timing contributed to LOS predictions in both groups, but the relevant timing variables differed. In the long-stay model, prolonged predicted LOS was most strongly associated with delays before surgery, particularly the time from injury to operation. In the short-stay model, predicted LOS reflected both admission-to-surgery time and baseline health status. These findings are consistent with current clinical practice and suggest that minimizing preoperative delays may help shorten the hospital stay.

IV. Discussion

The analysis revealed distinct patient characteristics among those with short and long hospital stays. This observation reflects the right-skewed distribution of LOS, which poses a substantial challenge for accurate prediction [13]. Previous studies of patients with hip fracture have reported that LOS is strongly influenced by clinical profiles, supporting the need for outcome stratification. The characteristics observed in our dataset are consistent with these prior findings and suggest that effective predictive models should account for outcome heterogeneity. This consideration provided the primary rationale for developing a two-stage modeling approach designed to accommodate highly skewed LOS distributions.

ML can handle large datasets and capture complex nonlinear relationships when predicting postoperative outcomes [22]. In this study, stratifying patients into short-stay and long-stay groups balanced the detection of prolonged hospitalization risk with prediction accuracy for the majority of cases. This approach is consistent with attribute-grouping strategies previously shown to enhance predictive performance in datasets with high variability and inherently skewed distributions [13].

The findings of this study demonstrate that LOS prediction is heterogeneous, with different algorithms performing best in the short-stay and long-stay groups. These results suggest that subgroup-specific models are more appropriate than a single modeling strategy for capturing the distinct characteristics of each patient group. Accordingly, the two-stage framework outperformed the one-stage approach, reducing MAE to 1.46. This value falls within the MAE range of 1.11–2.37 days reported in previous studies of clinical LOS prediction [23,24].

Although formal decision curve analysis was not conducted, predicted LOS values may still support clinical care and hospital planning. Stratifying patients into clinically interpretable groups, such as ≤7 days and >7 days, aligns with hospital planning needs. For instance, patients predicted to have a long stay can be prioritized for early discharge planning, rehabilitation, and resource allocation. These predictions may also support daily hospital management, including bed allocation and surgical scheduling. These uses demonstrate the potential practical value of the model beyond prediction accuracy.

However, the model was not compared with clinician judgment in this study, as such an evaluation would require a prospective design with direct clinical involvement. Therefore, the model is intended to function as a decision-support tool rather than a replacement for clinicians. Future work will focus on integrating the model into clinical workflows and evaluating its performance alongside expert assessments to determine its added value in clinical practice.

This study has several limitations. First, the use of a single-center dataset may limit the generalizability of the findings. Although this design provides consistent clinical protocols, patient management, and data recording, it may not fully represent the diversity of patient populations and healthcare settings. Consequently, the model may be subject to center-specific bias, and its performance should be validated using external multicenter or registry-based datasets before broader clinical implementation.

Second, certain potentially relevant variables, such as additional laboratory measurements, were unavailable and may have affected model performance. Finally, although the proposed two-stage framework addressed the skewed LOS distribution and improved overall predictive performance, accurate prediction of extreme LOS values remains challenging and warrants further investigation.