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I. Introduction
Coronary artery disease (CAD) is a major cause of disability in adults and a major cause of death in developed countries resulting in several illnesses, disabilities, and deaths as well. It should be noted that cardiovascular diseases are characterized by prolonged length of stay (LOS) [1]. LOS is defined as the number of days that a patient is hospitalized in a hospital or a similar medical facility. There has been considerable interest in controlling hospital costs, particularly in cardiac diseases; thus, hospitals try to make LOS as short as possible [2]. The length of hospital stay is an actual parameter applied to identify health care resource utilization, health cost, and severity of illness [3]. The use of LOS is highly predictive of inpatient costs as a marker of resource utilization [4]. Hospitals have severely limited beds to hold inpatients, and as most of them are facing substantial financial pressure, it is extremely important to find ways to reduce health care costs [5]. One solution is to predict and determine the discharge date and LOS of each patient by a number of complementary techniques and technologies, such as data mining [6]. For a hospital administrator to be considered successful, predicting and evaluating LOS data is laborious but essential [7]. Precise prediction of LOS facilitates the efficiency of bed occupancy management in hospitals. Therefore, exact and proper prediction of LOS has become increasingly important for hospital management and health care systems [4]. Meanwhile, awareness of factors and elements that determine LOS could promote the development of efficient clinical pathways and optimize resource utilization and management [8]. In addition, many hospitals cannot predict and measure future admission requests. Many hospitals have no ability to predict and measure future admission requests. Also, successful prediction of discharge dates and duration of hospital stay allows the corresponding scheduling of elective admissions, leading to diminished variance in bed occupancy [9]. Providing an efficient and accurate model to predict LOS for different types of diseases is one of the issues considered by researchers. Obviously, developing models for predicting and determining LOS in hospitals can be very useful for hospital management, particularly for prioritizing health care policies and promoting health services, comprising the appropriate allocation of health care resources according to differences in patients' LOS along with considering patients' health status and social-demographic features [3]. Ideally, better prediction models are needed to facilitate the decision-making process and cannot be replaced by judgment. For these reasons, providing an efficient and accurate model to predict LOS for various types of diseases is one of the issues considered by researchers. However, there has been relatively little research related to LOS prediction. Therefore, we applied data mining techniques to extract useful knowledge and suggest a model to estimate length of stay for coronary artery patients in cardiovascular centers.
1. Literature Review
Studies on factors contributing to LOS have regularly appeared in the literature. One study conducted to determine the factors affecting LOS in public hospitals in Lorestan Province, Iran demonstrated that, first, an increase in age would lead to an increase in average LOS and, second, the average LOS of men is longer than that of women. The t-test, one-way ANOVA, and multifactor regression were used for the analysis. They did not provide any prediction model, because they focused on descriptive analysis based on traditional statistical methods [10]. Rowan et al. [8] proposed and implemented a software package demonstrating that artificial neural networks (ANNs) could be used as an effective LOS stratification instrument in postoperative cardiac patients. Blais et al. [11] designed a screening and rating tool to quantify variables related to LOS in a medical psychiatric unit. The findings from this study showed that 25 variables, including patient, illness, and treatment variables, were likely to be related to LOS. Tu and Guerriere [12] indicated that ANNs can be used as a predictive tool to identify patients at increased risk for prolonged intensive care unit LOS following cardiac surgery. They claimed that the back propagation algorithm had not previously been developed for this area. Lin et al. [13] explored the prediction of hospital stays for first-time stroke patients in a rehabilitation department by a proportional hazard regression (HR) model. They proposed using the HR model to predict the mean LOS of stroke patients. Jiang et al. [5] studied the use of four data mining techniques (logistic regression, neural network, decision tree, and ensemble model) to analyze the inpatient discharge data for average LOS based on input variables. The findings from this research showed that the ensemble model was the best fit, and age and chronic disease were the important predictors. Misclassification and average squared error were used to assess the models. The ensemble model had the lowest average squared error (0.21), and the decision tree had the highest average squared error (0.22). Wrenn et al. [14] were able to predict LOS for an emergency department through developing and validating an ANN. The results were promising and showed that ANN can predict a patient's LOS within an average of <1.99 hours. Using a cohort of prospectively identified heart failure patients, Wright et al. [1] found that peripheral edema, chest pain, fatigue, serum albumin, serum sodium at admission and peak creatinine could result in hospital stays longer than six days. Blais et al. [11] studied factors that differentiated psychiatry patients' short LOS (7 days or less) and long LOS (more than 14 days). Age, impairment level, and +6 independent functioning levels were all independent predictors of LOS.
As previously mentioned, most of the research on LOS has been conducted in rehabilitation and psychiatric fields [15]. Most models in the cardiac disease area have predicted in-hospital mortality [16], and statistical methods, especially descriptive analyses, have been applied in that research. Hence, raising our awareness of factors that have an impact on cardiac patients' LOS is essential in order to determine and develop a useful and efficient model to predict LOS. This research aims to investigate the important factors that can be assessed to predict the LOS of patients with coronary artery diseases.
2. Data Mining Algorithms
Finding undiscovered information and useful patterns in a database is often referred to as data mining [17]. Data mining is heavily used in the health and medical field in applications such as disease prediction and patient management [18]. Relationships, rules, and essential information about or from the data cannot be easily extracted because of database size and other features. We used some of the most common predictive data mining methods for our goals as follows.
1) Artificial neural networks
ANNs are used to perform multivariate analysis to identify both linear and non-linear patterns among data variables [19]. Due to their good predictive performance, ANNs are the most popular method in various areas of medicine [20] and lead to appropriate decisions. An ANN consists of many connected processing elements, including multiple input nodes and weighted interconnections. The radial-basis-function (RBF) ANN was developed to recognize CAD.
2) Support vector machines (SVMs)
A category of classification that has received increasing attention in recent years is the SVM. It is a new method for classification of both linear and non-linear data [21], and in terms of predictive accuracy, it is a powerful algorithm. In fact, SVM is a linear learning machine constructed through an algorithm that uses an optimization criterion. We apply RBF kernel mode because of its good general performance and because it has the smallest number of parameters [22].
3) Decision tree
Generally, a decision tree as a visual and analytical decision support tool is a graphic representation of obtained knowledge in the form of a tree (flow chart like structure), where each non-leaf node denotes a test on an attribute, and each branch indicates an output of the test [23]. It uses a combination of mathematical and computational techniques to aid description and classification, and to extract knowledge of data set [24]. Because nodes and branches are organized hierarchically, they are easy to understand and interpret. They are reliable and have better accuracy in clinical decision-making [25]. C5.0 decision trees are the most current decision tree algorithms. The C5.0 algorithm with 10-fold cross validation and 20 trials using boosting was applied in this research.
II. Methods
1. Patient Population
The cohort consisted of hospitalized patients during the study period, which started on July 18, 2006 and ended on December 30, 2011. We identified 4,948 patients who were admitted to the Academic and Educational Hospital of Rajaei Cardiovascular Medical & Research Center in Tehran, Iran with heart disease-related diagnoses. Only CAD data were included in the study (n = 3,512). Significant CAD was defined as at least one point of 50% or greater diameter stenosis in at least one coronary artery vessel [26].
2. Data Set
The data sets were stored in a database management system of Microsoft structured query language (MS-SQL) database. We extracted and constructed a new data set for LOS of CAD. However, 246 patients were removed from the analyses, because patient records data, such as identification, were unavailable from the data set. Thus, 3,266 patients were included in the final data set for further analysis. Table 1 shows features with acceptable class and values. The data set contained 36 attributes. Finally, we organized the data set into two groups, including categorical and numerical features. We categorized data values and derived new fields from existing data in the following features: ejection fraction, diastolic blood pressure, systolic blood pressure, smoking, triglyceride, low-density lipoprotein, high-density lipoprotein, hemoglobin, serum cholesterol, and fasting blood sugar. These features were changed to categorical attributes for better analysis and to obtain good results.
3. Data Pre-processing
Data cleansing and preprocessing are essential to have optimal results [27]. Therefore, we performed the following cleansing and preprocessing: repeated records, fields with spelling errors, additional tokens, other irregularities, and irrelevancies were deleted. The next step of pre-processing was the handling of patient records with missing and outlier data.
4. Dealing with Missing Values
The hospital data set had many features with missing values. Several replacement strategies were adopted to fill the missing values. First, if a feature was encountered in more than 50% of records with missing values, that characteristic was determined not to be an effective feature in the analysis. As a result, such a feature, such as weight or job, was removed. Second, if a feature was encountered in less than 12% of records with missing values, the mean values of records were replaced instead of missing values in the numeric features. For example, creatinine showed 11.2% missing data. The mean value was replaced according to its accepted class (Table 2). If the feature was in nominal or ordinal type, mode values were replaced. The comorbidity, ejection fraction, hemoglobin, and diagnosis features followed the mentioned rule (Table 2).
In the third strategy, the C5.0 algorithm was applied to those features showing missing values in more than 10% of records. We filled the missing values of these features using this algorithm with the highest accuracy according to Table 3.
To resolve outliers in each feature, we transformed the data to Microsoft Excel format and detected outlier data that was clear using methods such as sorting. Otherwise, the nearest acceptable non-outlier value for that feature was used to replace the outlier value [28].
5. Attribute Coding
Data was coded by some valid resources, such as heart disease associations and the Wikipedia Website. Scaling and coding features are given in Table 1.
6. Training and Test Data Sets
After cleaning and preprocessing, 2,064 completed records were extracted and obtained for data mining tasks. Separating the data into training and testing sets is an important part of evaluating data mining models. We partitioned the data set into a training set and a testing set; 80% of the data (1,643 records) was used for training, and 20% of the data (421 records) was used for testing. The training set was used to adjust the parameters of the models, and the testing set was used to evaluate its predictive ability.
III. Results
1. Statistical Analysis
The mean age of 2,064 patients was 58.2 ± 13.0 years (aged 15-94) with most subjects between 54-64 years old. The sample was composed of 1,266 (61.3%) men and 798 (38.6%) women. 1,264 (61.2%) patients were diagnosed with CAD and 800 (38.8%) without CAD. LOS class 3 included most patients (39.3%); LOS class 1 and LOS class 2 comprised 35.8% and 24.9%, respectively. Table 4 demonstrates statistical results of the data set.
These data mining models were developed by a data mining classification tool. We evaluated the model created using training data and then applied test data to compare the results. We used SPSS Clementine 12 (SPSS Inc., Chicago, IL, USA) to build mining models.
The performance of a diagnostic method is usually evaluated in terms of classification accuracy, sensitivity, and specificity. In fact, accuracy is the percentage of correct decisions if CAD is predicted when the test is true and a non-CAD is predicted when the test is false [29]. Sensitivity is the true positive, and specificity is the true negative rate of CAD.
Table 5 shows the sensitivity, specificity, and accuracy of different classification techniques. A confusion matrix was obtained to calculate sensitivity, specificity, and accuracy. The overall accuracy of SVM was 96.4% in the training set. The ensemble algorithm showed a stronger performance than other algorithms with a sensitivity of 98.2%.
2. Important Features
The relative importance of each variable in evaluating the model is associated with the importance of each feature in making a prediction, and it does not relate to the model accuracy [30]. Also, the sum of the values for all variables in algorithms is 1.0. The SVM model, with earlier parameter setting, was used to extract important factors. In Table 6, features with great impact on CAD are listed in order of variable importance. The most significant variables were drug categories, such as nitrates and anticoagulants as well as CAD diagnosis. Comorbidity is also a strong predictor of prolonged LOS. Sex was significant in predicting LOS since men had longer LOS than women. Age played a notable role as well since analysis revealed that patients aged <50 and ≥80 statistically had increased mean LOS. LOS class 1 comprised mostly single patients (64.3%) and 24.5% of married patients, 41.2% of married patients were in LOS class 3 and 34.3% were married in LOS class 2. Furthermore, insurance type had a predictive power. Patients with social security and rural medical insurance were in LOS class 3. Thus, the most notable factors influencing LOS obtained by algorithm are drugs (nitrates), being diagnosed with CAD, comorbidity, hemoglobin, ejection fraction, insurance type, smoking, family history, and sex. These factors were extracted with 99.1% accuracy by the SVM.
3. Extract Rules
This section describes how these significant rules were extracted. Based on the C5.0 algorithm with the previously mentioned parameter setting, 11 rules, which are interpreted as IF (antecedent) and Then (consequent) in Table 7, were generated with a mean estimated accuracy of 95.3%. The presence of comorbidities such as lung and digestive disorders, ejection fraction <2, currently being a smoker, and insurance type = 5 in coronary artery patients was associated with them having a longer LOS than other subjects. Absence of comorbidities, being a nonsmoker, being single, not having chest pains, and having medical service insurance had a positive effect on decreasing LOS. The extracted rules are interpreted in Table 7. However, more investigation with more features and larger data sets is still required.
IV. Discussion
This study investigated the determinants of length of hospital stay in patients' representative of CAD admitted to a cardiovascular center. Many studies of length of hospital stay predict the duration of stay based on laboratory parameters or other quantifiable variables [1]. Our findings showed that a LOS greater than 10 days was associated with comorbidity and diastolic blood pressure features. There was a significant tendency for LOS to be longer in patients with lung or respiratory disorders and high blood pressure. Hence, comorbidities such as lung disorders and hemorrhage have an impact on long LOS and are important features in predicting LOS. However, Appelros [31] in his study demonstrated that comorbidities do not significantly influence LOS, while smoking has an inverse effect on acute LOS. They claimed that stroke severity is an important predictor of both acute and total LOS. Some studies have reported that patient demographics and hospital attributes were the two major factors that contributed to identifying patient LOS [3], and the most useful patient feature for predicting LOS was patient's age [32]. In many studies, age has been found to be a very significant predictor of LOS [5]. Our results from the retrospective study of LOS replicate a number of previously reported findings.
In this study, the extracted rule demonstrated that patients with normal levels of hemoglobin, medical services insurance, ejection fraction with class 1 (good level, 50-75), and those with no past history of cardiac disease and comorbidities and also non-smokers had a normal LOS in hospital. We found that married men had longer LOS than single men and women. Patients who were using statins and blood anticoagulant drugs had a prolonged LOS. These findings did not conform to those of other study [2].
Our promising results indicate that SVM and an ensemble model, which applies three data mining algorithms, can predict patient's LOS, but still SVM is the best fit. We suggest that the SVM model is optimal for predicting mean LOS of CAD. According to other studies, SVM has the highest forecasting accuracy among other data mining algorithms. Today, this algorithm is becoming increasingly common in the medical and health field [33].
In addition to disease-related factors, LOS may be affected by factors unrelated to the disease, such as availability of hospital beds and rehabilitation facilities as well as discharge possibilities [31]. Due to the lack of medical facilities, staff shortages, and the increasing cost of health care, it is extremely important to optimize LOS and to identify factors affecting it. Note that LOS is influenced by individual characteristics such as weight, disease status, patient management style, hospital management, organizational characteristics, and other features [34,35].
This study was confined to the exploration of length of hospital stay of CAD patients with no consideration of other factors, such as the ethnic and socio-cultural environment of each patient and admission status. Health care data is generally not structured, and it is distributed over various locations. In terms of practicality, the primary limitation of this study is that all data were obtained from a specialized cardiovascular center. The factors selected for LOS prediction tended to be less social and more condition specific (e.g., presence of cardiac coronary artery bypass graft). Some important variables could not be considered, including factors such as alcohol consumption, other comorbidities, distance between patients' place of residence and the hospital, and admission type (elective and urgent). However, we attempted to identify the primary factors related to longer LOS. These data should also be collected uniformly to increase prediction accuracy.
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