Predicting carcinoid heart disease with the noisy-threshold classifier

Summary

Objective

To predict the development of carcinoid heart disease (CHD), which is a life-threatening complication of certain neuroendocrine tumors. To this end, a novel type of Bayesian classifier, known as the noisy-threshold classifier, is applied.

Materials and methods

Fifty-four cases of patients that suffered from a low-grade midgut carcinoid tumor, of which 22 patients developed CHD, were obtained from the Netherlands Cancer Institute (NKI). Eleven attributes that are known at admission have been used to classify whether the patient develops CHD. Classification accuracy and area under the receiver operating characteristics (ROC) curve of the noisy-threshold classifier are compared with those of the naive-Bayes classifier, logistic regression, the decision-tree learning algorithm C4.5, and a decision rule, as formulated by an expert physician.

Results

The noisy-threshold classifier showed the best classification accuracy of 72% correctly classified cases, although differences were significant only for logistic regression and C4.5. An area under the ROC curve of 0.66 was attained for the noisy-threshold classifier, and equaled that of the physician’s decision-rule.

Conclusions

The noisy-threshold classifier performed favorably to other state-of-the-art classification algorithms, and equally well as a decision-rule that was formulated by the physician. Furthermore, the semantics of the noisy-threshold classifier make it a useful machine learning technique in domains where multiple causes influence a common effect.

Introduction

Bayesian networks have become a widely accepted formalism for reasoning under uncertainty by providing a concise representation of a joint probability distribution over a set of random variables [1]. This distribution is factorized according to an associated acyclic directed graph (ADG) that represents the independence structure between random variables. However, the construction of a Bayesian network that fully captures this independence structure for a realistic domain, has proven to be a difficult task. It requires either manual specification of the ADG by means of available expert knowledge, or large amounts of high-quality data when we resort to structure learning.

An alternative to the construction of an ADG that fully captures the independence structure that holds between variables within the domain, is to use a fixed or severely constrained graph topology for classification purposes. In the latter context we call a Bayesian network a Bayesian classifier. The use of Bayesian methods in medicine was first proposed by Ledley and Lusted in their classic 1959 paper [2], and one of the first successful implementations of Bayesian classifiers in medicine was De Dombal’s system for the diagnosis of acute abdominal pain [3]. The classifier that was used assumes independence of symptoms given the disease, and is known as the naive-Bayes classifier. Over the years, many different Bayesian classifier architectures have been proposed, and many of them focus on lifting the independence assumptions of the naive-Bayes classifier [4]. However, a standard technique such as logistic regression, which is used extensively in medicine, can also be interpreted in terms of a Bayesian classifier architecture (Fig. 1). Other examples of Bayesian classifier architectures can be found in refs. [5], [6], [7].

Although, typically, the actual joint probability distribution, and the joint probability distribution that is represented by the Bayesian classifier, differ considerably, this approach can still yield good results with respect to the classification task [8]. However, a weakness of this approach is that the ad-hoc restrictions that are placed on the underlying graph effectively reduces the Bayesian network to a black box model, making the relation between properties of the domain and classification outcome often difficult to understand. This is an undesirable property; especially in medicine, where ideally one wants to be able to interpret how the classification outcome (such as diagnosed disease or patient prognosis) relates to the available domain knowledge (its causes). The explanation of drawn conclusions is required to increase the acceptance of machine-learning techniques in practice [9], [10].

In this paper, we employ a novel Bayesian classifier, introduced in ref. [11], that facilitates this interpretation as it explicitly provides for a semantics in terms of cause and effect relationships [12]. This noisy-threshold classifier is based on a generalization of the well-known noisy-or model, which has already been used for the purpose of text classification in ref. [13]. In order to demonstrate the merits of the noisy-threshold classifier in a medical context, we apply the technique to the prediction of carcinoid heart disease(CHD); a serious condition that arises as a complication of certain neuroendocrine tumors [14]. We demonstrate that the noisy-threshold classifier performs competitively with state-of-the art classification techniques for this medically relevant problem. Furthermore, an expert physician at the Netherlands Cancer Institute (NKI) was consulted, and it is demonstrated how her knowledge concerning CHD relates to the parameters that were estimated for the noisy-threshold classifier.

This paper proceeds as follows. Section 2 introduces the necessary preliminaries and discusses the semantics of the noisy-threshold model, whereas Section 3 describes the medical problem. The use of the noisy-threshold model as a Bayesian classifier is discussed in Section 4. The results on the classification task and the medical interpretation by the expert physician is presented in Section 5. The paper is ended by some concluding remarks in Section 6.