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 Healthc Inform Res > Volume 24(1); 2018 > Article
Kuo, Yu, Chen, and Chan: Comparison of Models for the Prediction of Medical Costs of Spinal Fusion in Taiwan Diagnosis-Related Groups by Machine Learning Algorithms

### Objectives

The aims of this study were to compare the performance of machine learning methods for the prediction of the medical costs associated with spinal fusion in terms of profit or loss in Taiwan Diagnosis-Related Groups (Tw-DRGs) and to apply these methods to explore the important factors associated with the medical costs of spinal fusion.

### Methods

A data set was obtained from a regional hospital in Taoyuan city in Taiwan, which contained data from 2010 to 2013 on patients of Tw-DRG49702 (posterior and other spinal fusion without complications or comorbidities). Naïve-Bayesian, support vector machines, logistic regression, C4.5 decision tree, and random forest methods were employed for prediction using WEKA 3.8.1.

### 2. Performance of Models

Table 2 summarizes the performance of all five models analyzed in this study, with accuracies ranging from 76.68% for the naïve-Bayesian model to 84.30% for the random forest model. The random forest model achieved better predictive performance than the other methods, with the highest accuracy, sensitivity, specificity, and AUC. The model achieved an accuracy of 84.30%, with a sensitivity of 71.40%, a specificity of 92.20%, and an AUC of 0.904. The next best model was logistic regression, with an 82.16% accuracy, a 69.80% sensitivity, an 89.70% specificity, and an AUC of 0.860. The worst model in terms of predictive value was the naïve-Bayesian model, with an accuracy of 76.68%, a sensitivity of 56.90%, a specificity of 88.70%, and an AUC of 0.815 (see details in Appendix 1).

### IV. Discussion

To the best of our knowledge, this study was the first to use machine learning to analyze DRG medical costs. The medical costs of performing spinal fusion in Tw-DRG49702 (posterior and other spinal fusion without complications or comorbidities) in a regional hospital in Taoyuan city in Taiwan were predicted, and the factors associated with profit and loss in terms of medical costs in Tw-DRG49702 were analyzed, using various machine learning techniques. The results of the study showed that the length of stay, number of intervertebral cages, lumbar disc displacement, lumbar atresia fracture, and scoliosis were important factors associated with the medical costs of Tw-DRG49702. In addition, we found that the random forest model had the best predictive performance in comparison with the logical regression, SVM, C4.5 decision tree, and naïve-Bayes models. We were able to successfully predict 84.30% of the patients' medical costs of Tw-DRG49702 using the random forest method.
The length of stay was an important variable in terms of determining medical costs for patients undergoing spinal fusion, the loss group having a significantly longer length of stay. Future management leading to expected reductions in hospital stay will be based on continuous co-operative efforts to improve clinical guidelines or apply lean methods to produce standardized clinical pathways [25].
In our study, in comparison with the C4.5 decision tree classifier, the random forest model had better classification accuracy, their accuracies being 78.51% and 84.30%, respectively. The random forest algorithm, which is one of the most powerful ensemble algorithms, is an effective tool for prediction. Because of the law of large numbers it does not overfit [22]. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble [26]. Hu et al. [27] experimentally compared the performance of SVM, C4.5, bagging C4.5, AdaBoosting C4.5, and random forest methods for the analysis of seven microarray cancer data sets. The experimental results showed that all ensemble methods outperformed C4.5. Masetic and Subasi [28] confirmed the superiority of the random forest method over the C4.5 and SVM methods for the detection of congestive heart failure.
This study also found the random forest model to be superior to traditional logistic regression, a result similar to those of previous studies. The random forest model was more accurate than logistic regression in predicting clinical deterioration. A study of the accuracy of mortality prediction for patients with sepsis at the emergency department found that the random forest model was more accurate (AUC = 0.86) than the logistic regression model (AUC = 0.76, p ≤ 0.003), and the random forest model was more accurate in predicting mortality after elective cardiac surgery than the logistic regression model [29]. Raju et al. [23] also found that the random forest model had the highest accuracy when used to explore factors associated with pressure ulcers in comparison with decision tree and logistic regression models. These results implied that the random forest model is suitable for classification of the medical costs of Tw-DRG49702.
The strength of this study was that it explored spinal fusion medical cost predictive models and identified important factors; however, there were some limitations of our study. First, the accuracy of this model was 84.30%, meaning that there still are other potential factors that could affect the medical costs of spinal fusion. Second, the study was only performed at a single hospital and with small sample size. It is recommended that data from larger hospitals are analyzed in future study.
Our study demonstrated that the random forest model can be used to predict the medical costs of Tw-DRG49702 (posterior and other spinal fusion without complications or comorbidities), and based on the important factors identified, this study can inform hospital strategy in terms of increasing the efficiency of management of this type of operation in financial terms. Furthermore, methods of this type can also be used to address related problems, such as predicting the costs of other DRGs.

### Acknowledgments

This study was supported by the Taoyuan General Hospital, Ministry of Health and Welfare, Taiwan (No. PTH10307).

### Notes

Conflict of Interest: No potential conflict of interest relevant to this article was reported.

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### Appendix 1

#### Performance results of five different models

AUC: area under the receiver operating characteristic curve, SVM: support vector machine.

### Spinal fusion Tw-DRG49702 patient characteristics

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

CCs: complications or comorbidities.

**p<0.01, ***p<0.001.

### Comparison of performance of various prediction models

AUC: area under the receiver operating characteristic curve, SVM: support vector machine.

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