Hybrid deep learning model for risk prediction of fracture in patients with diabetes and osteoporosis

Abstract

The fracture risk of patients with diabetes is higher than those of patients without diabetes due to hyperglycemia, usage of diabetes drugs, changes in insulin levels, and excretion, and this risk begins as early as adolescence. Many factors including demographic data (such as age, height, weight, and gender), medical history (such as smoking, drinking, and menopause), and examination (such as bone mineral density, blood routine, and urine routine) may be related to bone metabolism in patients with diabetes. However, most of the existing methods are qualitative assessments and do not consider the interactions of the physiological factors of humans. In addition, the fracture risk of patients with diabetes and osteoporosis has not been further studied previously. In this paper, a hybrid model combining XGBoost with deep neural network is used to predict the fracture risk of patients with diabetes and osteoporosis, and investigate the effect of patients’ physiological factors on fracture risk. A total of 147 raw input features are considered in our model. The presented model is compared with several benchmarks based on various metrics to prove its effectiveness. Moreover, the top 18 influencing factors of fracture risks of patients with diabetes are determined.

Keywords

XGBoost / deep neural network / healthcare / risk prediction

1 Introduction

Diabetes is a disease that causes blood glucose to rise, which further causes several other severe diseases. One of such diseases is osteoporosis, which leads to bone fragility and increases fracture risk. Osteoporosis and related fractures are clinically underestimated problems in diabetes [1,2]. First, insulin deficiency and decreased insulin sensitivity in patients with diabetes can cause bone metabolism disorders. Second, solute diuresis due to hyperglycemia increases the excretion of urine calcium, phosphorus, and magnesium, which leads to osteoporosis. Various hypoglycemic treatments may influence bone metabolism. The literature reported that 24 h urine protein and inflammatory cytokines in patients with diabetic nephropathy are closely related to osteoporosis [3]. The risk of hip fractures in patients with type 1 and type 2 diabetes has increased substantially [4]. Severe vertebral fractures in patients with type 2 diabetes are even related to all-cause mortality [5]. Diabetes fractures have attracted increasing attention, which challenges how to control the risk of fractures in patients with diabetes and osteoporosis. Comprehensive control must be implemented, but indepth research on the fracture risk of osteoporosis with diabetes and diabetic nephropathy is lacking. Previous AI research focused on the diagnosis and treatment of diabetes [6], and research related to osteoporosis is lacking. Therefore, this paper describes the development and validation of a fracture prediction model for patients with diabetes and osteoporosis.

Several tools, such as fracture risk assessment tool (FRAX), trabecular bone score, and high-resolution peripheral quantitative computed tomography, are used to assess fracture risk using bone mineral density (BMD), dual energy X-ray absorptiometry (DXA), or other factors. At present, the World Health Organization (WHO) recommends the application of the FRAX tool, which can be used to calculate the risk of hip fractures and any major osteoporotic fracture in the next 10 years. However, these tools underestimate the fracture risk of patients with diabetes [5]. Risk factors for fractures considered in FRAX include age, gender, low bone density, low body mass index, previous fragility fractures, parental hip fractures, glucocorticoid use, smoking, excessive drinking, and other causes of secondary osteoporosis diseases and rheumatoid arthritis. In a prospective cohort study published in 2014, the FRAX score considerably underestimated the risk of fragility fractures. More than half of the participants were deemed with a low to moderate fracture risk according to the FRAX tool before the first fragile fracture occurred [7]. In addition, hyperglycemia can consume proteins in the bone matrix; thus, patients with diabetes are more likely to suffer a fracture than those without diabetes. The FRAX tool may underestimate fracture risk in patients with diabetic osteoporosis. The prediction model of fracture risk in patients with diabetes needs to be further studied.

With the improvement of computing power and the availability of large-scale data sets, more deep learning is applied in medical data processing and diagnosis. First, medical imaging can benefit from recent advances in image classification and target detection using deep learning, such as in determining whether a patient’s X-ray film contains a malignant tumor, and in the complex diagnosis of dermatology [8,9], radiology [10–13], ophthalmology [14–16], and pathology [17–20], which can help doctors by providing second opinions and labeling areas in the image. The deep learning model has achieved a high accuracy in various diagnostic tasks, including recognizing nevus and melanoma [8,9], diabetic retinopathy, cardiovascular disease risk, fundus screening [14,15], X-ray breast disease monitoring, and spinal MRI image analysis. Second, natural language processing focuses on analyzing text and speech, inferring meaning from words, which plays an important role in medical care, electronic health records (EHR), and other fields. With the popularization of electronic medical records, the EHR of a large medical institution can capture medical transactions of more than 10 million patients in 10 years, and these data are of valuable importance. Recurrent neural networks are suitable for integrating these data to build a generalizable system [21,22], which can help doctors record medical treatment and analyze and predict future medical events [23–26] such as mortality, readmission rate, and length of stay. Third, reinforcement learning (RL) is a technology used to train agents to interact with the environment to achieve specific goals. In robot-assisted surgery and other medical fields, RL can play a very good role; thus, RL can evolve from a highly dependent surgeon remote operation to a surgical robot to enhance its adaptability by sensing the surrounding environment and learning the doctor’s actions [27,28]. In other highly repetitive, time-sensitive tasks, such as surgical stitching and knotting [13], the computer can analyze and generate the optimal path of stitching from the image using the RL model [29], and realize autonomous action to realize a fully automatic robot surgery.

In this paper, a hybrid model [30] of XGBoost and multilayer perceptron (MLP) for prediction is presented. XGBoost transforms the input patient features into filtered binary features, and MLP uses these transformed features in making predictions. XGBoost provides the interpretability of the model and greatly increases the performance of MLP.

In this paper, a deep learning model is established for classified tasks based on a real-world data set. All possible prediction variables are taken as the input of the model, and the loss evaluation is finally made between the predicted results of the model and the actual marked results. The multifold cross validation method is used. Factors with a substantial influence on the fracture risk of patients with diabetes are found from hundreds of possible factors.

2 Materials and methods

2.1 Inclusion criteria

Patients in Xinhua Hospital’s outpatient and inpatient HIS database between July 2012 and November 2017 were included in the study: 14 419 patients with diabetes, of which 8002 had diabetes combined with osteoporosis.

2.2 Exclusion criteria

Patients with fractures before diagnosis of diabetes, patients with fractures before diagnosis of osteoporosis, and patients with hybrid disease and other diseases that seriously affect bone metabolism were excluded from the study.

2.3 Data collection

Three types of characteristic data of the patient population, including demographic data (such as age, height, weight, and gender), medical history data (such as smoking history, drinking history, menopause, blood pressure, and whether fractures occur), and inspection data (such as bone mineral, blood routine, urine routine, DXA bone density, blood biochemical analysis, glycosylated hemoglobin (HbA1c) level, blood glucose, and abdominal ultrasound examination results) were collected.

2.4 Terms in machine learning of this study

Patients with diabetes and osteoporosis have a high fracture risk due to their poor bone quality, while current tools of predicting fracture risk underestimate their fracture risk [5]. Thus, machine learning methods were used to extract critical physiologic measures that influence the fracture risk of patients with diabetes and present a model to make predictions accurately. Before introducing our model, several terminologies in machine learning are introduced. A feature is a measurable property of objects. In our model, the physiologic measures of patients with diabetes are treated as input features. A label is a known value used for training. In our experiment, the label of a patient is “1” if he/she has a fracture and “0” otherwise. Overfitting is the phenomenon that the model is too complex to predict unseen data accurately. Loss function describes the gap between the result produced by the model and the expected result, which was aimed to be reduced during the training.

2.5 Input of our model

The physiologic measures of patients with diabetes can be represented using a vector x= {x₁, x₂, ..., x_d}^T. Each entry of x describes one physiologic measure (such as age, pH). The prediction of the fracture risk of patients with diabetes is denoted as y, which is the output of our model. The measure set X= {x¹, ..., x^N}, where xⁱ denotes the physiologic measures of one patient with diabetes, serves as the input of our model.

A hybrid model combining XGBoost [31] with MLP is proposed to predict the fracture risk of patients with diabetes and conduct several experiments to evaluate the performance of this model for predicting the probability of fracture in patients with diabetes based on a real-world data set. Details of our data set and experiments are described in the following section.

2.6 Overview of the prediction model

The structure of our hybrid model is shown in Fig. 1. To predict the fracture risk of patients with diabetes accurately, our model needs to consider all possible factors, while it should be able to select several factors that really matter and avoid interference from others. Thus, XGBoost, which is a powerful tree boosting system, is used to perform feature transformations [30] and select important features among numerous factors. A neural network is then applied on these transformed features to make predictions on fracture risks.

The input features of the model are obtained from the physiologic measures of patients with diabetes, which are preprocessed by eliminating abnormal data. These raw features are used to train the boosted decision tree (DT), which utilizes XGBoost. XGBoost can handle features in different patterns and deal with missing values, which is very suitable for managing the physiologic measures of patients. As a tree ensemble model, new trees are created to fit the residual of the previous trees during the training. At each node of a tree, one of the features is used to split the instance sets into two, and XGBoost uses the exact greedy algorithm to find the best split. Every instance falls into one leaf of each tree, and the leaves are used as they fall as new features, x_M, to train the deep neural network (DNN). The boosted DT in Fig. 1, which is composed of two trees with four leaves on the left tree and two leaves on the right tree, is taken as an example. Given the physiologic measures of a patient with diabetes, if it falls into the second leaf on the left tree and the first leaf on the right tree, it will be encoded as x_M = [0, 1, 0, 0, 1, 0], where the ith digit indicates whether this instance is on the ith leaf. In this manner, high-dimensional input features are transformed into representative binary features, which are more effective for the neural network to learn.

After obtaining the transformed features, a DNN is trained to make the predictions. For each layer of the neural network,

(1)z_d^{[l+\mathrm{1}]}=W_d^{[l+\mathrm{1}]T}{a}_d^{[l]}+b_d^{[l+\mathrm{1}]},

(2)a_d^{[l+\mathrm{1}]}=\mathrm{g}(z_d^{[l+\mathrm{1}]}),

where W_d^{[l+\mathrm{1}]} is a matrix of parameters, b_d^{[l+\mathrm{1}]} is the bias, g(z) = max(0, z) (ReLU) is the activation function, and a_d^{[\mathrm{1}]} is the input of the DNN x_M, that is, the transformed features. To prevent the model from overfitting, L2 regularization is applied to all layer weights \mathrm{W}.

The prediction of the model is given by the following:

(3)\mathrm{p}(\mathrm{y}=\mathrm{1}|\mathrm{x})\mathrm{}=\sigma (W_d^{[lf+\mathrm{1}]T}{a}_d^{[lf]}+b_d^{[lf+\mathrm{1}]}),

where x is the transformed feature, y is the label of fracture in patients with diabetes for binary classification, s(·) is the sigmoid function, a_d^{[lf]} is the last activation of the neural network, W_d^{[lf+\mathrm{1}]T} is the weights applied on a_d^{[lf]}, and b_d^{[lf+\mathrm{1}]} is the bias.

To train the neural network, the existing labeled data of fracture risks of patients with diabetes is used. The loss function is defined as the cross entropy of the predicted fracture risk and the label:

(4)\mathrm{L}=-(\mathrm{ylog}(\mathrm{p})+(\mathrm{1}-\mathrm{y})\log (\mathrm{1}-\mathrm{p})),

where y is the actual observation label, and p is the predicted fracture risk.

In the experiment, adaptive moment estimation (Adam) methods [32], which are shown in Algorithm 1, were performed on the DNN.

2.7 Data set description

According to ICD-10: International Statistical Classification of Diseases and Related Health Problems (10th Revision), diabetes diagnosed in this study includes E10 insulin-dependent diabetes, E11 noninsulin-dependent diabetes, and E12 diabetes associated with malnutrition; osteoporosis includes M80 osteoporosis with pathological fractures, M81 osteoporosis without pathological fractures, and M82* osteoporosis classified in other diseases; fracture events include M84 bone continuity diseases, including M84.2 delayed fracture healing, M84.3 stress fracture, M48.4 spine stress fracture, M48.5 vertebral collapse NEC, and M80 pathological fracture in osteoporosis.

The EHRs of outpatients and inpatients were collected between July 2012 to November 2017 from the database of a public hospital: 14 419 patients had diabetes and 8002 of them also had osteoporosis.

A total of 147 factors that can influence the fracture risks of patients with diabetes were divided into three categories as features, including demographic features (such as age, height, weight, and gender), medical history features (such as smoking, alcohol consumption, and menopause), and inspection features (such as BMD, blood routine, and urine routine), as shown in Table 1. Demographic features and most of inspection features were continuous. A minority of inspection features, such salt crystal, transparency, and color in urine routine, was categorical. For example, the color in urine routine was categorized into red, yellow, and green. All medical history features were labels, except age of menopause, which was continuous. The medical history features were labeled “1” if the patient had the history and “0” otherwise. For example, if the patient had ever smoked, the label of smoking was “1” and “0” otherwise. Finally, abnormal data were eliminated, and 1603 patients with diabetes combined with osteoporosis were extracted such that patient statistics had no null value. The label used for the binary classification was whether the patient had a fracture after he/she had diabetes combined with osteoporosis. The patient was labeled “1” if the patient had a fracture and “0” otherwise. The missing values were filled with the mean of the corresponding features.

A total of 1603 EHRs of patients with diabetes were collected. The average time from the examination data to the fracture event was 1.8 days. The medical tests of the patients in this study were performed within two weeks, and the test data collected in an interval longer than two weeks were discarded. Among 1603 patients, 123 had a fracture after they had diabetes, and the remaining 1480 patients with diabetes did not have a fracture. Oversampling and undersampling were performed on patients with diabetes and fractures because the data set was imbalanced (123:1480). First, the data set was randomly split into the training set and the test set. Then, oversampling and undersampling were separately performed on both sets.

2.8 Evaluation metrics and benchmarks

Four categories describe the matching of prediction and reality that are related to our metrics. True positive is a sample that is positive in reality and prediction. False positive is a sample that is negative in reality but positive in prediction. True negative is a sample that is negative in prediction and reality. False negative is a sample that is negative in prediction but positive in reality.

The evaluation metrics used in the experiments were accuracy, precision, recall, F1-score, and area under curve (AUC). Accuracy is the ratio of the number of correctly predicted samples to the total number of predicted samples regardless of whether the predicted samples are positive or negative. Precision describes how many of all predicted positive samples are real positive samples. Recall shows how many positive examples in the sample are predicted correctly. The F1-score is equal to the harmonic average of precision and recall, which is intended to refer to two indicators. Their formulas are shown below:

(5)\mathrm{Accuracy}={\displaystyle \frac{TP+TN}{TP+FP+TN+FN}}

(6)\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}}

(7)\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}}

(8)\mathrm{F1}-\mathrm{score}={\displaystyle \frac{\mathrm{2}}{\mathrm{1}/precision+\mathrm{1}/recall}}

The benchmarks for comparison are described as follows:

Logistic Regression (LR): The traditional linear regression analysis model is often used to predict the probability of a certain class. In medical research, LR is often used to analyze the risk factors of a disease, such as analysis of age, smoking, drinking, diet, and other risk factors for type 2 diabetes.

Support Vector Machine (SVM): SVM is a classical supervised learning model. Given a set of training samples from two categories, SVM learns to maximize the margin between the two kinds of samples and classify new examples. It can simultaneously minimize the empirical error and maximize the geometric edge area. The parameters are type of Gaussian kernel, C, and g.

Decision Tree (DT): This classical machine learning method for classification and regression builds up a tree whose parent nodes and root are attributes, and whose leaf nodes are categories. A DT contains three types of nodes: decision node, opportunity node, and endpoint. DT is a frequently used technology in data mining, which can be used to analyze data and make predictions.

K-Nearest Neighbor (KNN): The main idea of the KNN algorithm is to determine its own category according to the neighbor category with similar distance, which is easy to implement and suitable for sparse sample classification. However, given unbalanced samples, it may be inclined to the majority of large-scale samples when calculating the nearest neighbor of new samples, which will affect the classification effect and have poor interpretability. Thus, it cannot provide rules like a DT.

Random Forest (RF): This algorithm integrates multiple trees through the idea of integrated learning. The basic unit of RF is the DT, and its essence belongs to a large branch of machine learning—ensemble learning. It can effectively run on large data sets and process input samples with high-dimensional characteristics without dimension reduction. RF can also be used to deal with default value problems.

Extremely Randomized Trees (ERT): ERT is a variant of RF, where each DT uses the original training set. Compared with RF, the variance of the model is further reduced, but the bias is increased. In several cases, extra tree has better generalization ability than RF.

Gradient Boosting Decision Tree (GBDT): GBDT is an optimization algorithm for general loss function, which uses the negative gradient of loss function in the current model to simulate the approximate value of residual in classification problem. GBDT adds the results of all weak classifiers to obtain the predicted value and then uses the next weak classifier to fit the residual of the error function to the predicted value.

AdaBoost: This iterative algorithm combines multiple weak classifiers, which are generally single-layer DTs, making it a strong classifier. The weight of the samples is initialized according to the size of the training set, and changed and normalized by formula after iterations.

CatBoost: This gradient lifting algorithm can automatically process category features in a special manner, including making some statistics on the category features and adding the super parameters to generate new numerical features. It also uses the relationship between features, which greatly enriches the feature dimension. The base model of CatBoost uses symmetric tree to prevent model overfitting.

Extreme Gradient Boosting (XGBoost): This popular gradient boosting method is known for its great effect, especially in the classification of two categories. XGBoost is an ensemble of weak prediction models, typically classification and DTs. XGBoost uses the RF algorithm for reference, and supports column sampling and row sampling, which cannot only reduce the risk of overfitting but also reduce the calculation.

Deep Neural Network (DNN): This neural network contains several hidden layers and MLP is a subset of DNN. In the paper, only the deep part of the model used a DNN. According to the location of different layers, the neural network layer in DNN can be divided into input layer, hidden layer, and output layer. In MLP, layer to layer is fully connected.

2.9 Experiment settings

All raw input features, including categorical features and continuous features, served as the input of the boosted DT, which performed transformation on them. The boosted DT is trained with maximum number of trees equal to 400 and L2 regularization parameter equal to 1. After one-hot encoding, the transformed features were fed into the DNN. The neural network had two hidden layers, and L2 regularization was added to avoid overfitting. Moreover, Adam methods were used as the optimizer of neural network, and an adaptive learning rate was set. The parameters of the neural network are shown in Table 2.

The ratio of training set and test set was approximately 4:1. First, oversampling was performed by adapting the synthetic minority oversampling technique to generate the minor category in the training set and the test set. Then, undersampling was performed by deleting the Tomek links in the generated data to avoid overfitting. Finally, the training set and the test set were approximately 800 and 200, respectively.

The parameters of the benchmarks are shown in Table 3. For XGBoost, the parameters were the same as those used in the hybrid model. For MLP, the parameters were adjusted accordingly because MLP used in the hybrid model had only two layers with a large regularization strength and performed badly on original input features.

3 Results

To prove the validity of oversampling and to compare the effectiveness of the hybrid model of XGBoost and MLP with the benchmarks, the data set was first randomly split into the training set and the test set. Then, random oversampling was conducted, and experiments were implemented 100 times to obtain the average metric score, as presented in Table 4.

How the number of boosted trees will influence the performance of our model was further investigated. The greater the number of boosted trees was, the more training time was needed. In Fig. 2A, AUC was selected as the evaluation metric, and our hybrid model (XGBoost+ MLP) was compared with XGBoost only. As the number of trees increased, the performance of models increased first and then fluctuated within a narrow range. Generally, the performance of the hybrid model was better than XGBoost with sufficient number of trees.

Our hybrid model was compared with XGBoost only and MLP only when reducing the size of samples, as shown in Fig. 2B. Subsampling was performed on the training set, and AUC was again used as the evaluation metric. In general, the performance of models increased as the size of samples increased. Our hybrid model can achieve almost the same performance as using the whole training set with half of the sample size and increase the AUC compared with its component models.

Our hybrid model found the top 18 factors influencing the fracture risks of patients with diabetes, as summarized in Fig. 3.

The top 18 influencing factors may not include several acknowledged influencing factors but several other related features because several features are correlated to one another, and our model judges these features only by their values without considering their physical meaning. Thus, the validity of these factors needs further verification.

4 Discussion

In the paper, a hybrid model of XGBoost and neural network was presented to predict the fracture risk of patients with diabetes and osteoporosis and to mine the interaction among 147 factors deeply. This hybrid model was compared with LR, SVM, DT, KNN, RF, ERT, GBDT, AdaBoost, CatBoost, XGBoost, and MLP based on accuracy, precision, recall, F1-score, and AUC. The effectiveness of this model was proven.

The contribution of our work is threefold. First, a hybrid model concatenating XGBoost with neural network was established for classification tasks based on a real-world data set. Second, all possible prediction variables were taken as the input of the model, and the loss evaluation was finally made between the predicted results of the model and the actual marked results. The multifold cross validation method was used. Third, 18 major factors with a considerable influence on fracture risk in patients with diabetes were found from hundreds of possible factors.

In 2007, the WHO recommended a new tool, FRAX, to evaluate clinically which patients are more in need of osteoporosis diagnosis and treatment. Risk factors for fractures assessed by FRAX include age, gender, low bone density, low body mass index, previous fragility fractures, parental hip fractures, glucocorticoid use, smoking, excessive drinking, and secondary osteoporosis and rheumatoid joint inflammation. Other factors are also closely related to fractures. For example, cancer, diabetes, and certain drugs that cause bone loss (such as aromatase inhibitors that reduce breast cancer recurrence) can also increase the risk of fractures. In addition, FRAX only calculates the individual’s fracture risk based on prospective data analysis but does not make general recommendations for the threshold of preventive treatment. FRAX neither includes other bone mass measurement methods, such as ultrasound or BMD of the lumbar spine, nor has it been updated in a timely manner according to new research information. In this paper, the findings show that height, creatinine (urine), calcium (24 h urine), urea nitrogen, alkaline phosphatase, C-reactive protein, aspartate aminotransferase, albumin (ALB), glycated hemoglobin (HbA1c), prealbumin (PA), apolipoprotein B (apoB), vaccination, DXA values of L2–L3, and DXA values of L3–L4 substantially influence fracture risk in patients with diabetes. These factors suggest that liver function, kidney function, and blood glucose concentration in patients are potential factors that affect the risk of fractures of patients with diabetes.

Previous studies indicated that diabetes is a risk factor for osteoporosis. Patients with type 2 diabetes whose HbA1c levels exceed 9.0% exhibit an increased risk of hip fracture, confirming a linear relationship [35]. Patients with microalbuminuria and macroalbuminuria (urine albumin-to-creatinine ratio≥30) have a considerably higher incidence of osteoporosis compared with subjects with normoalbuminuria [36]. Renal function measured by CG and MDRD is associated with BMD in cross-sectional analyses, and only creatinine clearance by CG predicts four-year bone loss [37]. With the aggravation of chronic kidney disease, IL-6, CRP, TNF-a, serum phosphate, serum sodium, serum potassium, and blood urea nitrogen increase gradually, while serum calcium, BMD, and vitamin D decrease substantially [38]. Osteoporosis is related to nutritional status of protein intake. In the NHANES data set, an independent association of osteoporosis and hypoalbuminemia was reported at different anatomical sites [39]. Poor nutritional status is associated with osteoporosis. Prealbumin is a more sensitive marker than albumin to assess nutritional status [40].

A study investigated the association between serum liver enzyme levels and BMD at various sites in Koreans [41]. A negative relationship was demonstrated between liver enzyme levels, including aspartate aminotransferase and BMD. It also suggested a considerable association between osteoporosis/decreased BMD and liver disorders. Apolipoprotein E plays crucial roles in maintaining bone mass by promoting osteoblast differentiation via ERK1/2 pathway and suppressing osteoclast differentiation via c-Fos, NFATc1, and NF-kB pathway [42]. CRP may be useful in screening for osteoporosis among community-dwelling elderly females and apparently acts as a surrogate for other factors directly associated with osteoporosis [37].

In addition, blood glucose, creatinine, triglyceride, and cholesterol are in the top 30 influencing factors (Table 1). One of the possible reasons why these features do not have dominant importance (Top 18) is that our model combines XGBoost and the neural network, but the top influencing factors are given by the XGBoost model only. Moreover, the model considers all the features and performs selection. Another possible reason is that medical features always have several correlations among them, and the model judges these features only by their values without considering their physical meaning.

Vaccination data have no missing value; thus, it is probably used more times in the model than other factors. Additionally, vaccination has many kinds, but in our database, vaccination is not classified and is only represented as “1” and “0” to indicate whether the patient has previously taken vaccination in the model.

However, our experiment has several limitations. (1) There is data loss of patient characteristics because the inspections each patient take are different and many null values exist if the patient does not take all the inspections. (2) The data are likely to have sampling bias due to the imbalance of raw data and the performance of oversampling and undersampling. (3) The top 18 influencing factors are provided by the XGBoost part of our model. The influencing factors selected by our model may slightly differ when the input samples and the parameters of the model vary; thus, they need further verification. (4) Although the model has a certain degree of interpretation, this interpretation is not necessarily a causal interpretation but depends on whether the selection of patient characteristics is complete. (5) Drug use is not included as a feature in the model because various drugs have different effects on bone metabolism, and the number of patients that use a specific drug is small, which brings difficulties to model training.

Two recommended directions are made for future work: (1) collect more real-world data from hospitals, and determine why the top 18 factors are selected; (2) apply more techniques to the hybrid model to improve its accuracy.

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