The paper proposes a methodology for using static Bayesian networks (BN) in the tasks of influence the surrounding environment pollution on immunity. The methods for constructing the BNs structure, their parametric learning, validation, sensitivity analysis and scenario analysis «What-if» are considered. The model was designed in collaboration with medical experts, as well as pharmacists, experts in the selection and quantification of input and output variables.
The problem of air pollution in cities is one of the most urgent environmental problems facing modern society worldwide. The connection between pollution and health is usually examined in an attempt to determine the dominant cause of pollution and its influence on health outcomes.
This problem has a critical environmental situation allowing serious negative consequences for human health. In particular, this issue is relevant industrial regions, one of which is the Krivy Rig basin in Ukraine.
Modeling the influence of air pollution on health (taking into account all relevant variables) is quite complex from a theoretical point of view, because of the link between environment and health, as a rule, characterized by a complex structure of dependence. Computational problems are also evident, as the analysis of large database takes long processing time and can be handled only with adequate computing infrastructure. When resources are limited and studies are carried out mainly on the basis of open data, there is a need for models that may inherently identify, depending on the basis of the variability of functions and thus may further utilize the expertise to enhance the predictability of the models. To solve this problem the most appropriate computational tools are Bayesian networks.
It is known that the immune system responds to changes in the environment, in particular exposure to harmful substances, which affects the functional performance of the organism.
Accordingly, the immunological parameters are one of donosological health indicators. Therefore, to solve the problem of morbidity of the population of the city of Krivy Rig, along with the study of environmental factors in the region requires the development of probabilistic and deterministic models allow more locally to explore the effects of chemicals on the state of children's health.
In this paper we explore the use of Bayesian networks to determine the probability structure of the relationship between the environment and health. It consists of the exposure levels (the concentration of pollutants in the air) and the results for the children's health (indicators of the immune system).
In recent years, Bayesian methods have become the preferred method for reasoning with uncertainty due to their mathematical basis. Although Bayesian theory does not solve all the problems of probabilistic thinking, it gave scientists a solid basis for the submission and pragmatic analysis of uncertainty. Considering the system from the probabilistic point of view, the constructed models are clearly uncertainties in the basic system. 2
Having a set of known data - chemical indicators of pollution and immunological parameters, we need to determine the effect of pollution on the performance characteristics of the immune population.
The main problem is the construction of a network structure of the Bayesian network and setting its parameters, taking into account the nature of the relationships between nodes and the predetermined conditional probabilities ancestral nodes network with the subsequent validation of the resulting model.
Since Bayesian networks allow to identify the basis of variability depending on
different functions, they are widely used in medicine [
In environmental science, Bayesian networks are an effective tool for structuring
environmental research [
There are two ways of applying them [
In the second case study focuses on the assessment, checking the model and provide empirical information that is quantitative, useful and relevant to the key environmental variables.
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In general, studies have shown that the advantage of using Bayesian networks is
their resistance to incomplete, inaccurate and noisy information. In these cases, the
result will reflect the most likely outcome [
A pair <G, В> called a Bayesian network (BN), when the first part of G is a acyclic
directed graph corresponding to random variables [
The BN’s cumulative probability PB ( X 1,..., XN ) iN1 PB (Xi | Pa(Xi )) .
The BN represents a model for getting probabilistic dependencies, as well as the absence of these dependencies. At the same time, the A→B relationship can be causal, when event A causes B to occur. So that is, at the time, when there is a mechanism whereby the value accepted by A affects the value adopted by B. When all BN’s connections are causal, so BN is called causal.
The sensitivity analysis of the Bayesian network allows you to set for each of the network parameters a function expressing the output probability from the point of view of the parameter being studied.
To derive the probability, we will consider the posterior marginal probability of the form y p a | e , where a is the value of the variable A and e means available evidence. Each of the network parameters has the form x p bi | , where bi is the value of the variable B and is an arbitrary combination of the values of the set of parents П pa B of B.
Denote p a | e х as a function expressing the a posteriori marginal probability
p a | e in terms of the parameter x. In the future, we will assume that in a sensitivity
analysis, as the parameter x p bi | changes, each of the probabilities p bj |
changes accordingly. The function y(x), obtained as a result of sensitivity analysis, is
a quotient of two linear functions in x [
The purpose of modeling is to identify whether the impurities affect contained in the air on the human immune system. The initial data we have the results of laboratory tests and identified the following indicators of environmental pollution (dust, hydrogen sulfide, formaldehyde, metal impurities, etc.), which, in our opinion, could serve as criteria for our study.
The structural model of the influence of pollution on the immune system is presented in Figure 1.
The proposed model is not limited to a rigid unidirectional action, and can be used to detect causative characteristics and predict the consequences. Arrows indicate the flow of information between the allocated blocks. All indicators X associated with Y (presence \ absence), also has a relationship of pollution data with laboratory tests: X2Immunoglobulins, OxidsImmunoglobulin, X2Other laboratory tests. 5.1
Data To determine the immunological criteria for assessing the factors of the environment on the human body have been conducting research lymphocyte subpopulations using monoclonal antibodies and immunoglobulin classes using basic enzyme immunoassay analyzers.
Studying the performance of the immune system conducted in different populations: the newborn (healthy) children aged 7-10 years.
In addition to the neonatal immune system has been studied in children aged 7-10 years and in adults. The choice contingent of children aged 7-10 years was due to the relatively stable performance of the immune system in children of this age, absence of bad habits and environmental factors.
The basic immunological parameters in children Krivy Rig industrial region are presented in Table 1.
Criteria
Environmental
pollution indicators Lab test results
Designation of the node in the model
To determine the subpopulations of lymphocytes used monoclonal antibodies CD (T cells), CD4 (T-helper), CD (T-suppressor killers), CD (NK-cells). In addition to identifying the main populations and subpopulations of lymphocytes, the subjects were determined such indicators of activation markers as HCT test (hematocrit). To determine the non-enzymatic bactericidal activity of cells, the number of lysosomalcationic granulocyte proteins (LCG) was determined.
As can be seen in Fig. 1, the network contains four key nodes: Oxides - summarizes the concentration of oxides present in the air, Other chemicals - summarizes the concentration of the remaining impurities, metals and chemical compounds present in the air, Immunoglobulins - summarizes the results of all tests for immunoglobulins, Other laboratory tests - summarizes the results of the remaining laboratory tests, which include:
It should be noted that due to the specifics of the Bayesian networks, all the conclusions of this model regarding the information sought are probabilistic in nature and are presented in the form of a ranked list (according to the values of the probability of fidelity of a particular conclusion). The final decision to confirm the effect between pollution data and test results, as well as the appointment of treatment, is made by the doctor.
The Bayesian network construction problem was solved using the GeNIe 2.3 Academic software environment. After sampling, the source data table acquired the form shown in Fig. 2.
Let nodes X1-X10 represent observational data (history). Nodes Y1-Y10 - laboratory studies and the results of analyzes. All nodes have three states: - state s0 - means the absence of this feature; - state s0 - means uncertainty; - state s2 - means the presence of this symptom in the clinical picture.
We have observations of air pollution indicators, supported by analyzes performed over the same time period.
A model of a static Bayesian network focused on solving the problem of determining the dependence of immunity on pollution is presented in Figure 3.
2.
If it is possible to minimize the concentration of carbon monoxide, nitric oxide and sulfur oxide, the total content of oxides in the air will decrease by 27% (from 35% to 8%) compared with the initial concentration.
Immunoglobulins increase by 9% (from 33% to 42%) compared with the initial state if the concentration of phenol in the air reaches a maximum (Fig. 5).
Other chemicals increases from 34% to 51% (17%) compared with the initial state at: X4 maximum, X5 maximum, X7 minimum, X8 maximum, X9 minimum.
Provided that the air is polluted as much as possible (oxids = max, other chemicals = max), the results of laboratory tests, as well as immunoglobulin tests increase by 15% (from 39% to 54% and from 37% to 52%, respectively) compared with the initial state (Fig. 6).
The resulting Bayesian model was tested on various data sets using various sampling methods. Given that a Bayesian network is a probabilistic approach in the presence of various types of uncertainty, the resulting model is adequate to the processes under study.
It is shown that validation with subsequent verification ensures the reliability of the model and also significantly increases the accuracy of the resulting model. The proposed model allows researchers to find the optimal combination of key pollution factors that can significantly improve the value of immune indicators and, accordingly, improve children's health. 7
The developed BN model can contribute to the implementation of hygienic measures to improve the quality of the ecological state of the city and find its application in improving the mechanisms for managing hygienic measures by the city authorities of the city of Krivy Rig, which will affect the state of general morbidity in this region.
In future studies, it is planned to apply other structural learning algorithms, as well as to use the approach of dynamic Bayesian networks in order to trace the levels of the effect of pollution on the immunological parameters of the child population at different time slices.