Determining whether to proceed with a clinical intervention can be a challenging task due to the numerous variables at play. One of the most crucial piece of information for making this decision is a precise assessment of the intervention's efectiveness, but it tends to be a complex calculation for healthcare professionals. In hemodialysis patients, the presence of a functional arteriovenous fistula (AVF) is essential to achieve a suficient dialysis dosage and prevent various complications. Percutaneous transluminal angioplasty (PTA) is a commonly employed procedure to restore the patency of AVFs. However, it carries the disadvantage of causing long-term vessel damage, thereby reducing the lifespan of the AVF. In this preliminary study we explore Dynamic Bayesian Network (DBN) to estimate the efectiveness of the next PTA from the elaboration of routinely collected clinical data. We build a DBN to predict the risk of problems of AVF and simulate how the next PTA could impact this prediction. The outcomes of this research could contribute to the development of a decision support system for vascular surgeons, aiding in the optimization of the decision-making process regarding whether to proceed with a PTA and/or consider alternative solutions.
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Percutaneous transluminal angioplasty (PTA) stands out as a common surgical intervention
to treat stenosis or occlusion of a malfunctioning arteriovenous fistula (AVF) [
Our dataset was composed of 143,454 AVF assessments referred to 4,718 hemodialysis patients from Portugal and collected between 2015 and 2022. The dataset was composed of 7 parameters that characterize the AVF functioning and the history of AVF problems (number of PTAs and failures in the past). We exploit two metrics (average and delta) of the Arterial and Venous Pressure in the last 30 days as proxy of blood flux in the AVF. These two pressures are measured by the dialysis treatment machine and represent the pressure of the blood in the line carrying the blood from the patient to the machine (venous line) and the pressure in the line carrying the blood from the machine to the patient (arterial line). The variables used in the model are described in the following: • AVF Failure: is a discrete variable that describe the status of the AVF. It can assume 3 values: - No Failure: the AVF worked fine during the month, PTA: a PTA was performed during the month - Failure: a problem prevented the use of the AVF during the month • Count PTA: number of PTAs previously performed. • Mean Venous Pressure: Average venous pressure measured by the dialysis machine during the month. • Delta Mean Venous Pressure: Relative diference between the mean venous pressure measured in the month with that measured in the previous month. • Mean Arterial Pressure: mean arterial pressure measured by the dialysis machine during the month. • Delta Mean Arterial Pressure: Relative diference between the mean arterial pressure measured in the month and that measured in the previous month. • Stenosis: Presence of a stenosis during the month. This variable is only partially observed.
In fact, we are certain of a stenosis only if specific tests are carried out or if PTA is performed.
All this information are routinely recorded through the Fresenius Medical Care health care
system called EuCliD® [
Bayesian Networks (BNs) are probabilistic network models [
∗ represents the variables at a generic time t. – 2TBN ⊂ 2TBN × 2TBN is the set of edges: ∗ 0 = ( 0 × 0) ∩ 2TBN: is the set of edges enconding the relations among the variable at time 0 ∗ = ( × ) ∩ 2TBN: is the set of edges enconding the relations among the variable at time a generic time t ∗ ,+1 = ( 0 × ) ∩ 2TBN: is the set of edges enconding the relations among the variables through time from a generic time to + 1 .
The strength of DBNs is that they employ the same solving and learning algorithms used for BNs. As for the inference phase, it is possible to use the inference algorithms used for BNs but the DBN must be unrolled first.
In this section, we aim to utilize a 2TBN to analyze the temporal dependencies of various factors
associated with AVF development and failure. By constructing a 2TBN model using expert
knowledge and patient data, we can explore the dynamic interactions between variables and
estimate the intervention free period for an AVF. Exploring the dataset we found 2,598 PTAs and
4,837 events classified as AVF failure (stopping AVF use or an important medical intervention on
AVF). As a result, the AVF intervention free period decreases with each PTA (Table 1). However,
these values vary greatly from patient to patient. These observations are in line with those
obtained by the authors of [
We decided to base the identification of the structure of the 2TBN on domain knowledge and the result is depicted in Figure 1. We can split the structure in three main components: TIME 0 The left side of Figure 1 represents the nodes 0, the edges 0 and models the dependencies among the variables for the first time slice (month 0). In this component, the pressures depends on the presence of stenosis. All the edges completely contained on the right side of the figure (green edges) have no temporal connotation and do not describe any evolution. TIME t The right side of Figure 1 represents the nodes , the edges and describe the dependencies among the variables at a generic month > 0. Similarly to the previous paragraph, also in this case all the edges completely contained on the right side of the figure (red edges) have no temporal connotation and do not describe any evolution.
Time dependence All the edges crossing from the left side to the right side of Figure 1 (orange edges) are the edges ,+1 and describe the dependencies of the variables at a generic month given the variables of the previous month. These are the only edges that have a temporal connotation and describe the evolution of the process over time. 1In this study, diferent types of failures are taken into account. However stenosis is on of the most frequent causes.
TIME 0 AVF Failure
Count PTA Stenosis
TIME t
Stenosis AVF Failure
Count PTA
Mean Venous Pressure
Observing the right component and the crossing edges we can see that all the pressures mainly depend on the presence/absence of stenosis. Furthermore we can see how the failure of the AVF or the need to do a PTA depend solely on the information from the previous month.
The parameters of the 2TBN are learned from the dataset. First of all, we discretized the
continuous variables (pressure). We experimented with various methods during the discretization
process, including uniform, quantile-based, and expert knowledge-based approaches. We
discovered that discretization based on expert knowledge was the most efective solution. Specifically,
we categorized the data into five pressure levels: very low pressure, low pressure, normal
pressure, high pressure, and very high pressure. Then, since we have a partially observed
variable (stenosis) we used the Expectation Maximization algorithm to learn the parameters [
and the edges ,+1
(Figure 2).
Classical BN exact or approximate algorithms [
True
Our developed 2TBN can serve as a tool for predicting the AVF intervention free period post PTA, assisting doctors in determining the need for a new AVF creation for the patient. In particular, the described model can be utilized in the subsequent manner: when a vascular surgeon determines that a patient needs to undergo a PTA, inputs the relevant data from the current month into the model. Then, the physician hypothesizes performing a PTA in the upcoming month and requests the model to predict the chances of failure or the requirement for an additional PTA over the span of 6 months following the initial procedure. To evaluate the performance of the learned model we randomly selected 70% of the patients as train and we used the remaining 30% of the patients as test. Of the 2,598 PTAs reported in the dataset, 2,106 are in the train set and 492 are in the test set. Of the 492 PTAs present in the test set, 226 failed within 6 months following the operation. We learned the model on the train set and then we used the test set to see how well it predicts the AVF intervention free period using the AUC score obtaining a value of 0.64.
A well functioning AVF is essential for performing efective hemodialysis treatment and
maintaining the overall health of a patient dependent on dialysis. Nevertheless, this vascular access
can undergo biological alterations, potentially rendering it unsuitable for dialysis procedures.
One primary factor contributing to issues associated with AVF is the stenosis. This problem is
often treated with a surgical procedure called PTA, that generally restores the patency of the
AVF in the short term but can cause vessel damage and problems in the long term. Every time a
stenosis is detected, the physician must ask himself whether a PTA is suficient or whether it is
necessary to create a new AVF. To help the doctor in this dificult decision we developed a model
that predicts the risk of AVF problems when a PTA is performed. We selected DBN paradigm
to tackle this problems for two main reasons. First, we evaluated as important the use of an
approach able to exploit the information coming from data and experts knowledge. Second, in
this problem, the risk of having AVF failure is influenced by the PTA and the PTA influences
the future risk of AVF failure, so to represent this kind of loop we needed an approach able to
consider the relationship among variables along time. The standard BNs do not accomplish this
requirement while DBNs do. Specifically, we developed a 2TBN were each time slice covers a
month. The presented model is in an early stage and presents many limitations. First of all, the
ifnal accuracy of the prediction (AUC=0.64) that is insuficient for the clinical use. This limited
accuracy might be related to the fact that we are ignoring the location of the stenosis in the
AVF. Diferent locations can have diferent efects on the pressures. In the future we would
like to add this information so we can include it in the model. Another strong limitation is the
requirement to discretize the variables. Especially for pressures, this operation is extremely
delicate and can lead to a distortion in the data. One potential solution to address the issue
of discretization could involve the implementation of semi-parametric BNs [