In this paper we propose an early stage decision support system for personalized arteriovenous fistula (AVF) management. The goal of the model is to identify an optimal strategy to recognize the onset of a stenosis and intervene to prevent the failure of the AVF. We used an Influence Diagram (ID) that combines a risk model, clinical tests, angioplasty and searches a series of policies that optimizes the cost of treatment.
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One of the complications related to AVF is the stenosis. A stenosis is a reduction of the
vascular lumen that determines a decrease of the blood flow and increases the chances of AVF
failure. Early detection of a stenosis facilitates correction through angioplasty which increases
the survival rate of the AVF. In order to identify a stenosis several methods have been developed
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Bayesian Networks (BNs) are probabilistic network models [
The construction of a BN requires to learn both the qualitative component and the
quantitative component . The learning phase can be carried out using data, expert knowledge or a
mixed strategy. The latter approach can be efectively applied in healthcare where the domain
expert knowledge can be integrated with data [
BNs can be used as the basis for performing inference and analysis of the domain. Decision options and utilities associated with these option can be integrated into a BN: the resulting model is ID. ID is an efective model for representation and analysis of decision-making under uncertainty. Similarly to Bayesian networks an ID is formally described as follows: ℐ = ( , , , ) . Where is the set of random variables and decision variables, is a DAG, is a set of conditional probability distributions and is a set of utility functions. The DAG = ( , ) , contains nodes representing random variables, decision variables and utility functions.
Recognizing a stenosis as early as possible, increases the probability of an efective intervention in order to reestablish the patency and prolong the AVF life. For this reason, diferent diagnostic Stenosis techniques have been developed, including PE, Qa, angiography and risk models. Our goal is to develop an ID and combine all the detection techniques in one tool capable of defining a set of optimal policies for the stenosis identification.
The structure identification of an ID is a critical task. In fact, if the structure doesn’t represent the underling process, the model is not able to find an efective policy. For this reason we decided to involve into the structure identification process a domain expert. We introduced some simplifications to maintain the model governable and interpretable: 1. The model imposes an order in the decision-making sequence, 2. The model uses only a subset of the possible tests for stenosis identification. 3. The model is based only on the current state of the patient. We depicted the resulting model in Figure 1 using the three types of nodes made available from the ID model: Decision variables: ModelRisk, PE, Qa, Angioplasty. Random variables: Stenosis: binary variable representing the presence or absence of the stenosis. ModelRisk_result: variable representing the result of the model if we decided to use the ModelRisk. Otherwise, it is set to none. PE_AVF_patency: variable representing the result of the PE if it has been performed. Otherwise, it is set to none. Qa_AVF_patency: variable representing the result of the Qa if it has been performed. Otherwise, it is set to none. Failure: binary variable representing the failure of the AVF. Cost Function: PE_cost: costs related to the physical examination. Qa_cost: costs related to the Qa test. Cost: combined costs of angiography, angioplasty, failure of the AVF.
The predictive variables used for the ModelRisk could influence our a priori knowledge on the efectiveness of Qa and PE tests. However, we preferred to exclude these variables from the decision model as we have no data to estimate their influence on the probability distribution of the tests. For this reason we decided not to insert the predictive variables of the ModelRisk in our influence diagram.
For the parameters learning task we combined expert knowledge and medical literature ([
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The probability distribution of the Stenosis node and the Failure node (Table 2) have been retrieved from the literature .
The costs of the tests and the angioplasty can vary a lot among the diferent clinics. We decided to use plausible values suggested by a domain expert (Table 3). However, these values intended to be used only for the evaluation of the model.
The main goal of our model is to generate a set of policies to improve diagnostic efectiveness through the minimization of the overall cost function. It should be noted that the cost function can incorporate some measures about patient health outcomes and quality of life index.
We used the pyAgrum tool [
The elicitation of utilities and probabilities is a delicate task. During the development of our ID we have encountered particular dificulties in specifying the costs of the treatments. Since the Yes Yes Yes Yes Yes Yes Yes Yes Yes
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cost of a treatment and its availability can widely change among diferent clinics we decided to
conduct a one-way sensitivity analysis [
The results reported in Table 5 show that the intervals in which the parameters can vary without afecting the optimal policies are quite large. Furthermore, the current values of the Qa_cost, PE_cost and Cost are centered with respect to these intervals.
In this exploratory paper we introduced an ID for the early detection of stenosis in patients with an AVF. The decision support system combines a Model Risk with two clinical tests (PE and Qa) to quantify the risk of stenosis and evaluate the possibility of proceeding with angioplasty. The model is in an early stage, and it has many simplifications. First the strong order among the decision variables is not realistic especially for PE and Qa. Furthermore, the model doesn’t take into account any measure specifically designed to evaluate the health and the quality of life of the patient or the long therm efects of the angioplasty; we simply minimize the cost of the decision sequence. Despite this the model seems to suggest a reasonable policy. In the future we would like to address these limits and expand the model by introducing new tests. After a comparison with domain experts we realized that another simplification of the model is the possibility of carrying out each test only once. In clinical practice tests are often repeated before submitting the patient to angioplasty.
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In conclusion, we are aware of the large limitations of such a simple model. However, we are convinced that this paper can be a starting point for the development of a collaboration with doctors and nurses that could make the model a valid tool for personalized AVF management.