Health Management Strategies for Medical Health Records Incorporating Graph Theory Methods

Medical Health Record (EHR) data refers to a longitudinal patient electronic medical information collection system that can record all data generated by a patient at a healthcare facility.EHR contains a wide variety of data and information about a patient, such as patient demographics, medical history, medication and allergy history, immunization status, lab test results, radiological images (e.g., X-rays, etc.), vitals, personal data such as age, height, weight, etc., medical procedure records, payment information, etc. This information plays a vital role in analyzing patient characteristics and helping physicians make decisions. [30].

It is still difficult to directly apply readily available mathematical formulas to computationally analyze a patient’s medical and health records. Instead, some analytical methods in complex networks and graph theory can be employed to map multiple data and information about patients onto the structure of networks and graphs for intuitive visual representation [31]. Quantitative computational analysis is performed through the dynamics of the model to understand and analyze the laws and properties embedded in the EHR.

The use of finite graphs to describe the EHR process uses vertices and undirected edges, which together then form an undirected graph G = G(V,E), which can be accurately represented as an adjacency matrix if there are a total of N vertices in the graph, each of which can be differentially represented by the notation i(i = 1,2,⋯,N). in the form of A = (a_i,j), where: (1) ai,j={ 1,∀e(i,j)∈E0, Otherwise \[{{a}_{i,j}}=\left\{ \begin{array}{*{35}{l}} 1,\forall e\left( i,j \right)\in E \\ 0,\text{ }Otherwise \\ \end{array} \right.\]

Therefore, if this undirected graph G = G(V,E) is quantized and analyzed, it becomes possible to use algebra and matrices for some calculations.

In addition, this undirected graph can be represented by another association matrix B = (b_i,j) of N×K, where the corresponding term b_i,j in the matrix is equal to 1 when the vertex i(i = 1,2,⋯,N) is connected to the associated edges i(i = 1,2,⋯,N) , k∈K , while the corresponding term is equal to 0 if the vertex is not connected to an edge. The corresponding term b_i,j in the matrix is: (2) bi,j={ 1,∀ek∈E0, Otherwise \[{{b}_{i,j}}=\left\{ \begin{array}{*{35}{l}} 1,\forall {{e}_{k}}\in E \\ 0,\text{ }Otherwise \\ \end{array} \right.\]

At this point, the connection between the behavior and the data is established using some basic methods of graphs.

When there are a total of N vertices in this undirected graph G = G(V,E), the properties of a vertex can be analyzed and compared, i.e., the degree of centrality of a vertex can be calculated, which is called degree centrality. The degree centrality of a vertex i(i = 1,2,⋯,N) in an undirected graph can be expressed in terms of the degree of the vertex i, which is actually the number of edges of a vertex i(i = 1,2,⋯,N) connected to other vertices. It is used to indicate the importance of vertex i. The notation k_i is used to denote the degree of vertex i: (3) Dic=ki=∑j=1Nai,j \[D_{i}^{c}={{k}_{i}}=\sum\limits_{j=1}^{N}{{{a}_{i,j}}}\]

So the more edges a vertex i is connected to other vertices in an undirected graph, the more the degree of that vertex i is at the center of many vertices in the graph, i.e., the greater the centrality of that vertex i. The distribution of degrees in an undirected graph can also be calculated. If the total number of vertices in a network graph is N, and the number of vertices with k connected edges in the vertices is N_k, then the distribution of its degree is expressed by equation (4): (4) pk=NkN \[{{p}_{k}}=\frac{{{N}_{k}}}{N}\]

The distribution of degrees describes the conceptual problem of analyzing the complexity of graphs in undirected graphs.

After representing a complex behavior as an undirected graph with N vertices, the linkage efficiency of the graph can be evaluated. For an undirected graph G = G(V,E) with two vertices i and j, assume that the linkage efficiency between i and j can be denoted as e_i,j, which is equal to the reciprocal of the distance d_i,j between the two vertices, and therefore can be denoted as ei,j=1di,j${{e}_{i,j}}=\frac{1}{{{d}_{i,j}}}$. If there is no edge connecting the two vertices i and j, their distance can be denoted as d_i,j = ∞ , which means that the linkage efficiency e_i,j of the two vertices i and j is equal to 0. Then the efficiency of the undirected graph can be denoted by the degree distribution. G = G(V,E) efficiency: (5) Ef=1N(N−1)∑i=1N∑j=1j≠iN1di,j \[{{E}_{f}}=\frac{1}{N\left( N-1 \right)}\sum\limits_{i=1}^{N}{\sum\limits_{\begin{smallmatrix} j=1 \\ j\ne i \end{smallmatrix}}^{N}{\frac{1}{{{d}_{i,j}}}}}\] is the average of the efficiency e_i,j between all two vertices i and j, so if the connection distance between two vertices is shorter, then the efficiency of the inter-vertex link represented by the undirected graph is higher.

With the development of graph neural networks, dynamic graph neural networks have received attention for their ability to flexibly model temporal information. In addition, multimodal methods also shine in various fields of deep learning. Multimodal can utilize multiple forms of information, and through certain fusion methods, the effect is better than the effect of unimodal methods. [32].

The Dynamic Hypergraph Neural Network based Disease Prediction Model (DHG4DP) designed in this paper is shown in Figure 1. The model first processes the dataset. The symptom information of the patient is extracted first, and this information is used to initialize patient embedding. Then, the model extracts the global disease relationship graph and constructs the local disease hypergraph and sudden disease hypergraph based on this graph.In the second step, the model distinguishes the diseases into persistent and emergent diseases and performs hypergraph convolution and feature fusion on the disease embedding according to the two sub-hypergraphs constructed in the previous step to obtain the disease embedding. In the third step, the model handles the temporal relationship to categorize the impact of the disease on the patient into long-term disease, emergent-associated disease, and emergent-unassociated disease, and then through the attention mechanism to Generate the embedding of each hospitalization record of the patient, and then model the temporal information of the patient through the M-GRU module to get the final embedding of the patient. Finally, the model processes the final embedding of the patient through the MLP layer to calculate the probability of the patient’s disease and then obtains the disease prediction results.

Figure 1.

DHG4DP overall framework

SYMBOL DESCRIPTION: During a medical visit, a patient may be diagnosed with one or more conditions, which are usually indicated by specific medical codes.

Given an electronic medical record dataset {γ_u|u∈U}, where U denotes a collection of patients, and γu=(V1u,V2u,⋯,VTu)${{\gamma }_{u}}=\left( V_{1}^{u},V_{2}^{u},\cdots ,V_{T}^{u} \right)$ denotes a sequence of historical visits for patient u . Each visit Vtu={ Ctu,Etu }$V_{t}^{u}=\left\{ C_{t}^{u},E_{t}^{u} \right\}$ is recorded in the visit record with a subset Ctu⊂ℂ$C_{t}^{u}\subset \mathbb{C}$ of medical codes and a subset Etu⊂E$E_{t}^{u}\subset \mathbb{E}$ of clinical events. ℂ = {c₁,c₂,⋯,c_|ℂ|} refers to the set of diseases in the EHR dataset, where medical codes represent diseases. In addition, E = {E₁,E₂,⋯,E_|E|} is the set of clinical events in the EHR dataset, where |E| denotes the number of clinical events. For patient u, the ith clinical event Eriu$E_{ri}^{u}$ of his t visit consists of an event type q_i∈ℚ and a set of clinical event features { Ai1,⋯,Ai| mi | }$\left\{ A_{i}^{1},\cdots ,A_{i}^{\left| {{m}_{i}} \right|} \right\}$, where |m_i| denotes the number of clinical features. Each clinical feature Aik$A_{i}^{k}$ is a meta-ancestor (nik,vik)$\left( n_{i}^{k},v_{i}^{k} \right)$ consisting of a feature name nik∈ℕ$n_{i}^{k}\in \mathbb{N}$ and a feature value vik∈X$v_{i}^{k}\in \mathbb{X}$, where ℕ and X represent the set of feature names and the set of feature values, respectively.

Problem Statement: Predict the diseases that will be diagnosed in a patient’s T + 1 th visit. Specifically, given a patient u with a history of T visits, the method is to predict y^T+1∈{0,1}^|ℂ|, y^T+1 is a vector representing the probability of various diseases appearing in the patient’s T+1 visits.

Since the patient possesses multiple visits, and each visit the patient is not diagnosed with exactly the same disease, a dynamic hypergraph can be obtained for the patient’s historical visits. In this section, let G = {G¹,G²,⋯,G^T} represent the dynamic ultrasound and G^t = (P^t,H^t) represent the ultrasound at the patient’s t visit. P^t ⊂ C represents the set consisting of all nodes in the hypergraph G^t, i.e., the set consisting of all diseases diagnosed at the patient’s t visit. Similarly, H^t denotes the edge of the hypergraph H^t. G^t has an adjacency matrix O^t of size |P^t|×|H^t|. Oc,ut$O_{c,u}^{t}$ is 1 when Patient u has Disease c_i in the t visit record and 0 otherwise.

In practice, a disease diagnosed at a single visit may be either a persistent disease or a sudden-onset disease. In order to model the fine-grained higher-order relationship between persistent and emergent diseases, for the set D^t consisting of diseases in the record (|t|≥2) of the tth visit, this section further classifies these diseases into persistent and emergent diseases:

Persistent Disease: Dpt=Dt∧Dt−1∈{ 0,1 }| ℂ |$\mathbb{D}_{p}^{t}={{\mathbb{D}}^{t}}\wedge {{\mathbb{D}}^{t-1}}\in {{\left\{ 0,1 \right\}}^{\left| \mathbb{C} \right|}}$, when a disease is present in the t visit record and also in the t–1 visit record.

Sudden illness: Dem t=Dt∧¬(Dt−1)∈{ 0,1 }| ℂ |$\mathbb{D}_{em\text{ }}^{t}={{\mathbb{D}}^{t}}\wedge \neg \left( {{\mathbb{D}}^{t-1}} \right)\in {{\left\{ 0,1 \right\}}^{\left| \mathbb{C} \right|}}$, when an illness is present in the record of the t visit but not in the record of the t–1 visit.

After categorizing the diseases diagnosed at the t visit into two types, this section constructs subgraphs of both types based on the hypergraph G^t:

Localized Disease Hypergraph GDt\[\text{G}_{D}^{t}\] : This is a hypergraph consisting of persistent diseases diagnosed at visit t, where the persistent diseases serve as nodes in the hypergraph and visit t serves as an edge in the hypergraph.

Sudden illness hypergraph GDNt\[\text{G}_{DN}^{t}\] : This is a hypergraph describing the relationship between each sudden illness and persistent illness. In this hypergraph, diseases are used as nodes in the hypergraph and visit t is used as an edge in the hypergraph.

In real healthcare scenarios, a disease diagnosed in a single visit by a patient may be long-standing or sudden in onset. To capture these effects, in the dynamic hypergraph learning module, this section extracts the local context as well as the abrupt context.

Local context: for each diagnostic node (i.e., the node corresponding to the diagnosed disease in the hypergraph), this section aggregates the representations of the diagnostic nodes connected to it in the hypergraph GDt\[\text{G}_{D}^{t}\] and aggregates the representations of the sudden disease nodes connected to it in the hypergraph GDNt\[\text{G}_{DN}^{t}\] (i.e., the node corresponding to the diagnosed sudden disease in the hypergraph) as shown in Eq: (6) ZDt= Hyper GCN(GDt)+ Hyper GCN(GDNt) \[Z_{D}^{t}=\text{ }Hyper\text{ }GCN\left( \text{G}_{D}^{t} \right)+\text{ }Hyper\text{ }GCN\left( \text{G}_{DN}^{t} \right)\] Where Hyper GCN(·) denotes the hypergraph convolution operation. GDt\[\text{G}_{D}^{t}\] denotes the localized disease hypergraph of the patient’s t visit. GDNt\[\text{G}_{DN}^{t}\] denotes the sudden disease hypergraph of the patient’s t visit.

Sudden context: for each sudden disease node, this section aggregates the representations of the diagnostic nodes connected to it in the hypergraph GDNt\[\text{G}_{DN}^{t}\], in order to obtain the sudden context, as shown in the following equation: (7) ZNt=HyperGCN(GDNt) \[Z_{N}^{t}=HyperGCN\left( \text{G}_{DN}^{t} \right)\] Where Hyper GCN(·) denotes the hypergraph convolution operation. GDNt\[\text{G}_{DN}^{t}\] denotes the sudden illness hypergraph of the patient’s tth visit.

The above operation captures the fine-grained higher-order relationships of diseases in the same visit, and it is obvious that there are some relationships between diseases in different visits, in order to further capture the relationships between diseases in different visits, this section designs a transfer function to extract the transfer context from the historical visits, as follows.

For sudden-onset disorders Demt\[D_{em}^{t}\] diagnosed in a single visit, they are often induced by a combination of historical disorders. In this section, we design a click-attention as a transfer function to capture the bursty transfer context, and the corresponding formula for this operation is shown below: (8) Zent=Att(ZNt−1,ZNt−1,ZDt) \[Z_{en}^{t}=Att\left( Z_{N}^{t-1},Z_{N}^{t-1},Z_{D}^{t} \right)\] Where Zent\[Z_{en}^{t}\] denotes the abrupt transfer context in the tth visit. The corresponding equation for the click attention function is shown below: (9) Att(Q,K,V)=softmax(QWq(KWk)⊤a)VWv \[Att\left( Q,K,V \right)=soft\max \left( \frac{Q{{W}_{q}}{{\left( K{{W}_{k}} \right)}^{\top }}}{\sqrt{a}} \right)V{{W}_{v}}\] Where W_k, W_q, and W_v are the attentional weights and a is the attentional scaling factor.

In the case of persistent disorders, since they have been diagnosed several times in previous visits, this section provides that the representation of such disorders remains the same from visit to visit.

Using M-GRU to capture the interaction between the persistent disease representation Ipt$I_{p}^{t}$ in visit t and the abrupt transfer context Zent$Z_{en}^{t}$ in visit t, the transfer output Zpt$Z_{p}^{t}$ for visit t is obtained as shown in Eq: (10) Zpt=GRU(Concat(Ipt,Zent),hpt−1) \[Z_{p}^{t}=GRU\left( Concat\left( I_{p}^{t},Z_{en}^{t} \right),h_{p}^{t-1} \right)\] Where hpt−1\[h_{p}^{t-1}\] represents the output from the M-GRU in the t–1 th visit. Concat(·) represents the concatenate operation.Specifically, when t = 1, since no sudden illness has been diagnosed at the first visit, this section orders Ppt=Dp1\[\text{P}_{p}^{t}=\text{D}_{p}^{1}\] and uses the M-GRU model with an initial hidden state of hp0=0\[h_{p}^{0}=0\] to compute the transfer output for the first visit using the following formula: (11) hp1=GRU(Ip1,hp0) \[h_{p}^{1}=GRU\left( I_{p}^{1},h_{p}^{0} \right)\] Where Ip1\[I_{p}^{1}\] indicates an indication of persistent illness diagnosed at the first visit.

After that, this section uses the maximum pooling operation on the transfer output to generate the visit representation v^t for the tth visit, as shown in the formula below: (12) vt=maxpooling(hpt) \[{{v}^{t}}=\max pooling\left( h_{p}^{t} \right)\]

Finally, this section utilizes the attention mechanism to calculate the impact of each visit in a patient’s history on the predicted outcome to obtain the final visit representation, as shown in the following equation: (13) α=softmax([ v1,v2,…,vT ]wα) \[\alpha =soft\max \left( \left[ {{v}^{1}},{{v}^{2}},\ldots ,{{v}^{T}} \right]{{w}_{\alpha }} \right)\] (14) Ov=α[ v1,v2,…,vI ]⊤ \[{{O}_{v}}=\alpha {{\left[ {{v}^{1}},{{v}^{2}},\ldots ,{{v}^{I}} \right]}^{\top }}\] Where AA is the trainable parameter, BB is the final visit representation, and VV denotes the attention score.

After constructing two dynamic sub-hypergraphs in the previous subsection, this paper uses the hypergraph convolution module to process them. Before that, the inputs of hypergraph convolution are clarified.

The different relationships between disease and patient will directly lead to different impacts on the patient. Therefore, we create different disease embedding for the same disease from two aspects, respectively:

Direct disease. The disease is diagnosed directly by the patient and this embedding is recorded as E_d.

For the convenience of subsequent calculations, both diseaseembedding have the same dimensions, i.e., E_d, E_n∈ℝ^|D|×|dim_d|. In order to integrate patientembedding and diseaseembedding, a bridge needs to be built between the two, i.e., the relationship between disease and patient. In this paper, we construct a disease-patient relationship graph, represented by the adjacency matrix A_dp∈{0,1}, such that if patient p suffers from disease d in any hospitalization record, then let A_dp[p][d] = 1. Meanwhile, let c^t and n^t be the multihot vectors denoting the diseases that are directly diagnosed in the hospitalization record t and the diseases that are adjacent to the directly diagnosed diseases, respectively, we can fuse the embedding of the patient and the diseases according to the following two equations: (15) Zdt=AdpEpWpd+ct⊙Ed+hyperconv(Hct,Ed)+hyperconv(Hnt,En) \[\begin{align} & Z_{d}^{t}={{A}_{dp}}{{E}_{p}}{{W}_{pd}}+{{c}^{t}}\odot {{E}_{d}}+hyperconv\left( H_{c}^{t},{{E}_{d}} \right) \\ & +hyperconv\left( H_{n}^{t},{{E}_{n}} \right) \end{align}\] (16) Znt=nt⊙En+hyperconv(Hot,En)+hyperconv(Hnt,Ed) \[Z_{n}^{t}={{n}^{t}}\odot {{E}_{n}}+hyperconv\left( H_{o}^{t},{{E}_{n}} \right)+hyperconv\left( H_{n}^{t},{{E}_{d}} \right)\] Where A_dpE_pW_dp denotes the ordinary graph neural network aggregation method and W_dp is a learnable parameter matrix responsible for mapping the patient embedding into the vector space of disease embedding. ⊙ denotes element-by-element dot product, and c^t⊙E_d filters out the diseases that the patient in E_d directly suffers from and makes the value indicating other diseases in E_d to be 0. hyperconv( ) denotes the hypergraph convolution module.

After the calculation of the above two formulas, we get the two disease embedding at the time of hospitalization record t, i.e., the direct disease Zdt$Z_{d}^{t}$ and the indirect (neighboring) disease Znt$Z_{n}^{t}$, and then we input them into the fully-connected layer and the LeakyReLU activation function to obtain the final disease embedding F{ d,n }t$F_{\left\{ d,n \right\}}^{t}$: (17) F{ d,n }t=LeakyReLU(Z{ d,n }tWrelu) \[F_{\left\{ d,n \right\}}^{t}=Leaky\operatorname{Re}LU\left( Z_{\left\{ d,n \right\}}^{t}{{W}_{relu}} \right)\] Where W_relu is the learnable parameter matrix.

In this paper, diseases are divided into three categories in terms of temporal relationships:

Long-term diseases. The vector is denoted as xlt=ct∧ct−1$x_{l}^{t}={{c}^{t}}\wedge {{c}^{t-1}}$, which represents diseases that are present at both the t and t–1 moments of the hospitalization record.

The attention mechanism is then used to learn the impact of the latter two disease categories on the patient’s disease embedding generation. Noting the embedding matrix as the set of embedding for diseases that neither appear in the existing disease records nor in the direct neighbors of the diseases in the existing disease records, the attention mechanism is computed as follows: (18) hnnt=Att(xnnt⊙Fnt−1,xnnt⊙Fnt−1,xnnt⊙Fdt) \[h_{nn}^{t}=Att\left( x_{nn}^{t}\odot F_{n}^{t-1},x_{nn}^{t}\odot F_{n}^{t-1},x_{nn}^{t}\odot F_{d}^{t} \right)\] (19) hnut=Att(xnut⊙Er,xnnt⊙Er,xnnt⊙Fdt) \[h_{nu}^{t}=Att\left( x_{nu}^{t}\odot {{E}_{r}},x_{nn}^{t}\odot {{E}_{r}},x_{nn}^{t}\odot F_{d}^{t} \right)\] Where the attention module denoted by Att( ) is defined as follows: (20) Att(Q,K,V)=softmax(QWq(KWk)Ta)VWv \[Att\left( Q,K,V \right)=soft\max \left( \frac{Q{{W}_{q}}{{\left( K{{W}_{k}} \right)}^{T}}}{\sqrt{a}} \right)V{{W}_{v}}\] Where a is the dimension of attention and W_q, W_k, W_v are the attention weights.

For long-term illness xlt$x_{l}^{t}$, we modeled the temporal characteristics hlt$h_{l}^{t}$ as of hospitalization record t based on the M-GRU module in the (21) hlt=M−GRU(xlt⊙Fdt,hnnt,hnut,hlt−1) \[h_{l}^{t}=M-GRU\left( x_{l}^{t}\odot F_{d}^{t},h_{nn}^{t},h_{nu}^{t},h_{l}^{t-1} \right)\] (22) zt=σ(xlt⊙FdtWz+hlt−1Uz+bz) \[{{z}^{t}}=\sigma \left( x_{l}^{t}\odot F_{d}^{t}{{W}_{z}}+h_{l}^{t-1}{{U}_{z}}+{{b}_{z}} \right)\] (23) rt=σ(xlt⊙FdtWr+hlt−1Ur+br) \[{{r}^{t}}=\sigma \left( x_{l}^{t}\odot F_{d}^{t}{{W}_{r}}+h_{l}^{t-1}{{U}_{r}}+{{b}_{r}} \right)\] (24) h^t=ϕ(xlt⊙FdtWh+(rt⊙hlt−1)Uh+bh) \[{{\hat{h}}^{t}}=\phi \left( x_{l}^{t}\odot F_{d}^{t}{{W}_{h}}+\left( {{r}^{t}}\odot h_{l}^{t-1} \right){{U}_{h}}+{{b}_{h}} \right)\] (25) h˜t=ϕ(hnnt+hnut) \[{{\tilde{h}}^{t}}=\phi \left( h_{nn}^{t}+h_{nu}^{t} \right)\] (26) hlt=(1−zt)⊙hlt−1+zt⊙h^t+h˜t \[h_{l}^{t}=\left( 1-{{z}^{t}} \right)\odot h_{l}^{t-1}+{{z}^{t}}\odot {{\hat{h}}^{t}}+{{\tilde{h}}^{t}}\]

Here, W_{z,r,h} and U_{z,r,h} are the weight matrices of GRU and b_{z,r,h} is the bias parameter. After M-GRU, we use the maximum pooling layer to obtain the embedding v^t of the inpatient record t: (27) vt=max_pooling(hlt) \[{{v}^{t}}=\max \_pooling\left( h_{l}^{t} \right)\]

After the above computation, the location-based attention mechanism is used to fuse all the hospitalization records embedding to get the final embedding o_p of the patient :

Here W_α is the weight matrix of the learnable attention mechanism and α is the attention score.

The disease predictions of the model are then obtained through a multilayer perceptron (MLP) layer.