A framework for intelligent medical diagnosis using the theory of evidence

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Abstract

In designing fuzzy logic systems for fault diagnosis, problems can be encountered in the choice of symptoms to use fuzzy operators and an inability to convey the reliability of the diagnosis using just one degree of membership for the conclusion. By turning to an evidential framework, these problems can be resolved whilst still preserving a fuzzy relational model structure. The theory of evidence allows for utilisation of all available information. Relationships between sources of evidence determine appropriate combination rules. By generating belief and plausibility measures it also communicates the reliability of the diagnosis, and completeness of information. In this contribution medical diagnosis is considered using the theory of evidence, in particular the diagnosis of inadequate analgesia is considered.

Introduction

Fault detection and diagnosis (FDD) can proceed on a number of bases, both analytical and knowledge-based [1]. Generally, fault detection via inference rules is suitable for applications with any or all of the following characteristics:

  • there is little numerical data available;

  • human experts can adequately express domain-specific knowledge in the form of rules;

  • the ability to represent knowledge analytically is deficient;

  • the system is required only to reason within a predefined context.

Rule-based FDD is particularly suitable where an expert system is designed to mimic a human operator. In complex processes, rule-based reasoning may be the most practical (or easily implemented) form of FDD. However, for such a system to operate well, it is necessary that the antecedent parts of rules capture the meaning intended by the rule. For rules derived in linguistic form, one common representation of this knowledge is fuzzy logic.

Three deficiencies have been identified in fuzzy logic when it is used in certain FDD applications. These are related to the

  • uncertainty as to which symptoms should be used in antecedent expressions;

  • inability to convey (reliability) information (that indicates the uncertainty of the diagnosis) [2];

  • specification of fuzzy operators [3].

The first two points may be partially addressed by using a relational fuzzy model in which alternative rules map the same diagnosis. In this way different combinations of symptoms (including ‘redundant information’) can be used to form diagnoses. The weights in the relation matrix can then be used to limit the conclusion (fault existence) to less than some measure of reliability.

The CADIAG-2 system [4] developed for medical diagnosis uses multiple fuzzy relations to hold information related to the certainty and reliability of diagnoses. These relations may be found by equating weights with linguistic terms such as always and often. The system copes with unspecified relations by assigning a nominal weight of 0.5.

This paper proposes that the problems encountered while using fuzzy logic for FDD can be addressed by a more rigorous treatment of information. That is, the choice of symptoms on which to base diagnoses is a question of the amount of information they provide. Reliability is related to the characteristics of the sources of the information. Likewise, combination operators should be determined by the relationships between the sources of information. In order to provide appropriate axioms, we have turned to the mathematical theory of evidence [5].

In general, the use of evidence-based reasoning for diagnosis is not a new idea. Belief measures can be considered a development on certainty factors (as used in MYCIN [6]) which have since been shown to be inconsistent [7] in that their axiomatic properties do not correlate with real-world phenomena. Other applications that use theories of evidence of various types also exist. However, belief and plausibility methods for FDD in engineering circles have almost always been rejected in favour of fuzzy logic techniques because they are much easier to apply. A closely related use of belief measures is given by Smets [8] who acknowledges that information necessary for diagnoses may be unavailable. However, Smets uses an adaptation of Bayes' rule for determining the degree of belief in a diagnosis, precluding any analogy with linguistic or relational fuzzy models. Kuncheva [9] addresses the idea of having supporting and contradicting evidence as determinants of belief but proposes a neural network based approach for reasoning.

Dexter [10], [11] also draws upon evidence theory. In this work, the belief and plausibility of a diagnosis are calculated using fuzzy similarity relations between the antecedent expressions of fuzzy rules. Although this provides information as to ambiguity in diagnoses, it does not address the indicated deficiencies in fuzzy logic.

This paper considers the use of the theory of evidence for FDD, especially for use in medical diagnosis. Two main issues are addressed for the use of evidential reasoning in this environment, namely the:

  • treatment of incomplete evidence, and

  • combination of evidence.

An example shows how the framework can be applied for the possible diagnosis of inadequate analgesia (involuntary physiological responses to painful stimuli) during anaesthesia. A number of rules are used to examine different possibilities, highlighting the capabilities of the theory of evidence framework.

Section snippets

Deficiencies in fuzzy logic for FDD

A fuzzy logic knowledge base can take many forms. Common fuzzy models include the linguistic and relational forms. The linguistic (or Mamdani) model uses rules such asIfxIsAThenDwhere A is an n-dimensional fuzzy relation and D is (usually) a one-dimensional fuzzy set. x is a crisp n-dimensional vector of observed data. A relational model can be viewed as a collection rules, each with the formIfxIsAThenDThroughRwhere R is an element of the relation matrix and limits the effect of the antecedent

Fuzzy measure theory

Evidence theory, also known as Dempster–Shafer theory [2] can be seen as a generalisation of possibility theory (as used in fuzzy set theory) and also statistical probability theory. It is concerned with bodies of evidence, which are assignments of weights to crisp events such as fault occurrence.

Given a domain X of possible events, a basic assignment m is a mappingm:P(X)→[0,1]where P(X) is the power set (set of all subsets) of the domain. For any element AP(X), the basic assignment m(A) gives

Evidential inference

The general model of evidential inference proposed in this paper has its analogue in the relational fuzzy model. D is a diagnosis to be made and X represents the set of all relevant symptoms. Then the linguistic rules are given byIfAjThenDThroughCom(D|Aj)where AjP(X) and there are j=2n−1 rules with n being the number of elements in X (that is, j indexes all combinations of individual symptoms). The completeness factors Com(D|Aj) are assigned by human experts, or some other method.

The bodies of

Diagnosis of inadequate analgesia

As a comprehensive example showing the use of the evidence-based framework, consider the diagnosis of inadequate analgesia (IA) for patients undergoing anaesthesia. IA results in involuntary physiological responses to painful stimuli. The list of symptoms includes increases in heart rate (iHR) and systolic blood pressure (iSys), and a decrease in pulse volume (iPV).

Estimates of the heart rate can be provided by at least two sources — the electrocardiogram, and the pulse oximeter. Strictly

Discussion and conclusions

This paper has described a method of using evidential reasoning for diagnostic inference. The framework described has a clear analogue in fuzzy relational models, including the ability to be created from linguistic If…Then rules. However, the evidential basis provides more guidance regarding the choice of combination operators. Antecedent and consequent expressions evaluate to bodies of evidence rather than fuzzy sets. This allows communication of reliability information as well as providing a

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