Rx-refill Graph Neural Network to Reduce Drug Overprescribing Risks (Extended Abstract)

1 Introduction

The dispensation of prescription (aka Rx) drugs requires legal medical prescriptions since they can have powerful effects on the human brain and body, some of which are dangerous. Prescription drugs are easy to abuse. For example, opioid painkillers can bring intense pleasure and well-being feelings in the treatment of chronic diseases while making people increase the dose, which may lead to overdose deaths. The United States is amid opioid overdose [Hu et al., 2021] and drug abuse epidemic [Schuchat et al., 2017]. Opioidinvolved overdose deaths rise from 21,088 in 2010 to 46,802 in 2018 [Hedegaard et al., 2020]. Increasing rates of opioid overdose has become a prominent topic in public health. Early identification of overprescribing may prevent the problem from turning into a drug addiction [Qian et al., 2021].

∗ Full version of this paper was originally published at the 2021 ACM International Conference on Information and Knowledge Management (CIKM) and received the Best Paper Award in Full Paper Track ([Zhang et al., 2021]).

#: Corresponding authors.

The prescription drug monitoring program (PDMP) is a jurisdictionally operated electronic database collected from pharmacies on controlled substances and Rx drugs dispensed to patients in a state. Although PDMP is developed to curb drug overprescribing, its utilization among prescribers is low [Haffajee et al., 2015]. Recent studies have reported significant barriers when using the PDMP database, including difficulty in accessing the database and lack of medical knowledge of its usage [Garcia et al., 2017]. For example, Grecu et al. [Grecu et al., 2019] and Meara et al. [Meara et al., 2016] found that PDMP has inconsistent and limited effects on detecting drug abuse. Fundamentally, it is due to a lack of effective PDMP data modeling to identify overprescribing behaviors which may cause drug abuse in patients. The challenges for modeling PDMP data are as follows:

• C1: When physicians consult the PDMP, they have access to various types of information about prescriptions. Every prescription includes information about physicians, patients, medication, and dispensing instructions. Therefore, the first challenge is how to model prescribing and dispensing (P&D) relationships (e.g., a patient visits physicians) among different Rx entries (e.g., patients, physicians).
• C2: The prescriptions are filled at different times, making the P&D interactions (relationships) in C1 dynamic and evolutionary. Also, the irregular prescription refill and various medication days' supply [Yang et al., 2015] make the distribution of refills highly non-uniform, and the elapsed time between Rx records vary from days to months. Thus, the second challenge is how to model dynamic interactions and medical condition variation.

• C3: Rx drugs are usually prescribed repeatedly and therefore patients would have multiple prescriptions which have an immediate impact on medication safety [Vaduganathan et al., 2020]. The prescriptions refilled at different times have various significance on the risk of overprescribing [Gangal et al., 2020]. Hence, the third challenge is how to capture the dosing patterns associated with overprescribing and capture informative patterns.

In light of the above challenges, we propose a novel model called RxNet to model PDMP data and predict overprescribing that is specifically referred to patients at high risk of drug abuse or opioid overdose. We introduce a P&D heterogeneous graph (P&D graph) to construct heterogeneous relationships (interactions) among different Rx entries. Based on P&D graph, we employ a graph neural network (GNN) [Fan et al., 2022] to learn node embeddings by aggregating P&D information in the graph. To capture dynamics and explore the medical condition variation of patients, we design an Rxrefill LSTM (RxLSTM) that can deal with irregular Rx refill intervals by differentiating recent and historical information in cell state. Furthermore, a dosing-adaptive network (DAN) extracts and recalibrates dosing patterns concealed in prescriptions through convolution operation. The major contributions of this paper include: (1) We propose the problem of overprescribing detection for patients, which is important and meaningful; (2) To handle dynamic heterogeneous relationships among Rx entries, medical condition variation, and dosage patterns of patients, we develop the RxNet model by integrating graph neural network, recurrent neural network, and convolutional operation; (3) We collect a 1-year PDMP dataset and conduct extensive experiments. Promising results demonstrate the effectiveness of our model by a comparison with state-of-the-art methods for predicting overprescribing, i.e., patients at high risk of opioid overdose or drug abuse.

2 Methodology

Our model RxNet for modeling a patient's Rx refill records in PDMP is shown in Figure 1, which includes a temporal P&D graph, an Rx-refill LSTM, and a dosing-adaptive convolutional network.

2.1 P&DGraph Neural Network

P&D graph in each period t represents the interactions (relationships) of different entries (nodes) during that period. We design a P&D graph neural network to model heterogeneous relationships and learn embeddings of patients. Firstly, let h0 be the initial node representation at t = 0. Nevertheless, nodes of various types have unequal feature dimensions. To address feature heterogeneity, we project the feature vector of the node of type A, i.e., x ∈ RdA , onto a new feature space via a transformation matrix: h0 = WTAx, where WA ∈ RdA×d0 . Then, let htv denote the embedding of node v at time t. Considering different nodes have different appearance time, we further introduce a time decay factor to quantify time influence and reformulate htv as follows:

where ∥ is the concatenation operator and Φv(t) is time decay factor. Node appearing long before may have less impact on the current relationships and the node representations. Therefore, we formulate the decay factor as: Φv(t) = exp(-η · |t - τv|) (τv: the time when v appears), where the decay coefficient η > 0 and 0 < Φ ≤ 1. Then, we employ a self-attention [Vaswani et al., 2017] to perform neighbor information aggregation and update node embeddings:

where N t v denotes the neighbor set of node v at t, etvu ∈ Rde is edge feature, Wtq ∈ R(d0+1)×dh ,WtK,WtV ∈ R(|N t v |×(d0+1+de))×dh . The three projection matrices capture the interactions in P&D graph using time information and neighboring node/edge features. Figure 1 (b) shows an illustration of P&D GNN.

2.2 Rx-refill LSTM

Since P&D graph is dynamic, we can employ the recurrent neural network (e.g., LSTM) to update patient embeddings. However, the memory cell of a standard LSTM tackles all historical prescription refills without distinction. Hence, we develop an RxLSTM (as shown in Figure 1 (c)) to infer a patient's medical condition variation ϵt (i.e., the indicator of an overdose) while updating the current representation ht by considering elapsed time δt between consecutive refills:

where ht ∈ Rd is computed as the Hadamard product (◦) of the output gate of an ON-LSTM network (see [Zhang et al., 2021] for more details). The master forget gate ˜Ft of the ONLSTM controls the erasing behavior of the network, indicating where to store the medical condition information. Hence, we define the medical condition variation ϵt as follows:

A large ϵt makes most historical information abandoned, indicating that the medical condition has largely changed, that is, a patient may have an overdose. The above definition is given by a non-differentiable function. Thus, we approximate it by the following estimation which approaches the probability that the ith entry of ˜Ft takes value 1:

where ϱ is the split point that divides the cell state into two segments: the 0-segment and the 1-segment, indicating a medical condition variation.

2.3 Dosing-Adaptive Network

The dosing patterns are similar for a certain medical condition, yet varies across different medical conditions [Jain et al., 2015]. Hence, we develop a dosing-adaptive network to extract and recalibrate dosing patterns behind the prescriptions by fusing dynamic embedding of patient through a convolution operation, as shown in Figure 1 (d). Given a sequence of historical hidden states [ht-s , . . . , ht-1 , ht ], and medical condition variations [ϵt-s , . . . , ϵt-1 , ϵt ] in previous s steps (checkup window) before time t, we employ the convolutional network with filter kernels Kt = [κt1 , κt2 , . . . , κtm] to generate the dosing pattern:

where κti is a 1D spatial kernel that acts on the corresponding channel of Ht (s) ∈ Rd×(s+1) . Particularly, -→φ (ϵt (s)) ∈ [0, 1]s+1 quantifies the probabilistic distances between the current refill record and historical refill records, whose values are monotonically increasing. A large value means the medical condition of ht-s+i greatly differs from the current medical condition of ht . The input embeddings Ht (s) are weighted by the medical condition distance in each convolution. Therefore, the computed zti of each kernel can extract dosing patterns for representing the whole medical condition. The convolution output Zt = [zt1 , zt2 , . . . , ztm] is then produced by summarizing multiple patterns through all channels, where the channel dependencies are embedded in κti .

The dosing patterns have various significances associated with medical conditions [Gangal et al., 2020; Islam, 2019]. The network is required to capture the importance of patterns and increase the sensitivity of informative patterns. For this purpose, we squeeze global spatial information into a channel descriptor γ t and then recalibrate γ t to obtain:

where Gti measures the importance of pattern zti , Wg1 ∈ Rdg×d , Wg2 ∈ Rm×dg , b ∈ Rdg1 , and b ∈ Rdg2 . The descriptor γ t ∈ Rd at current refill is computed as the average of hidden states within the checkup window, and therefore can be regarded as the dosing regimen theme. As shown in Figure 1 (d), the recalibration is achieved by two fully connected layers: i) the dimensionality-reduction layer with the activation ReLU to compress the representation, and ii) the dimensionality-increasing layer returning to the channel dimension of patterns Zt . Finally, we rescale Zt through a channel-wise gating mechanism [Hu et al., 2018] and obtain ˜Zt = Zt ◦Gt .

2.4 Objective Function

After obtaining ˜Zt , we employ a binary classifier to predict medical condition of the patient. The objective function is to minimize the cross-entropy loss over T checkup windows:

where Wy ∈ Rm, yt denotes the prediction score of overprescribing, and ̂yt indicates the ground-truth label.

3 Experiments

3.1 Experimental Setup

Dataset. The collected PDMP data contains 2,751,137 prescriptions written by 41,303 physicians for 297,361 unique patients from the Ohio state in 2016. These prescriptions involve 90 different Rx drugs (including 16 opioids) and are (re)filled at total 2,862 pharmacies. We consider patients at high risk when their daily dose decreases in 4 consecutive refills. Among all the patients, 227,520 (77%) have taken at

9 months

12 months

least an opioid in a year, 3,495 were at high risk of opioid overdose and 4,438 were at high risk of Rx drug abuse. The labels over time indicate whether a patient is at high risk of opioid overdose or drug abuse at each time period. Training and testing ratios are 70% and 30%, respectively.

Baseline Methods and Evaluation Metrics. We compare our model to ten baseline models, including LSTM [Hochreiter and Schmidhuber, 1997], ON-LSTM [Shen et al., 2019], T-LSTM [Baytas et al., 2017], StageNet [Gao et al., 2020], EvoNet [Wu et al., 2020], GraphSAGE [Hamilton et al., 2017], CTDNE [Nguyen et al., 2018], JODIE [Kumar et al., 2019], TGAT [Xu et al., 2020], and TGN [Rossi et al., 2020]. To evaluate the model performance, we utilize two metrics: precision-recall AUC (PRAUC) and F1-score.

3.2 Performance Comparison

Table 1 shows the results on the two datasets spanning 9 and 12 months. It can be seen that all models perform better in the context of a long period of follow-up because they are highly dependent on data distribution. RxNet significantly outperforms all baseline methods in all settings. The average improvement over the best baseline method is 4.85% and 6.35% for PRAUC and F1-score, demonstrating its strong capability for overprescribing detection. From the longitudinal study perspective, the superiority of RxNet compared to others lies in its ability to explore structured and unstructured information and medical condition variation at different times.

3.3 Case Study

Figure 2 illustrates the predicted risk of Tramadol overdose for a 48-year-old female patient who has an overdose (marked as red point) in June 2016. The predicted risk remains relatively low by June 2016 and the medical condition variation has a small value. At the end of June, the variation reaches a maximum value and the predicted risk rises rapidly, indicating that the patient's medical condition becomes highly risky. Here, the medical condition of the patient is at quite high risk. In this case, physicians can take intervention in advance. To conclude, with the help of RxNet in providing time-sensitive risk prediction, physicians are able to forecast the overprescribing and prevent it in advance.

4 Conclusions

In this paper, we propose the RxNet model for detecting the Rx-refill caused overprescribing, i.e., predicting patients at high risk of opioid overdose or drug abuse. We construct a P&D graph and employ a self-attention based GNN to learn patient embeddings. To capture medical condition variations, we incorporate a newly designed RxLSTM to update dynamic patient embeddings. Moreover, we introduce a dosingadaptive network to explore and recalibrate the dosing patterns of patients. The empirical results on a 1-year PDMP data demonstrate the effectiveness of RxNet in PDMP.

Acknowledgments

This work is partially supported by the NSF under grants IIS2209814, IIS-2203262, IIS-2214376, CNS-2203261, CMMI2146076, CNS-1814825, IIS-2217239, IIS-2027127, and OAC-2218762, the NIJ 2018-75-CX-0032.