The mixture-of-experts (ME) network uses a modular type of neural network architecture optimized for supervised learning. This model has been applied to a variety of areas related to pattern classification and regression. In this research, we applied a ME model to classify hidden subgroups and test its significance by measuring the stiffness of the liver as associated with the development of liver cirrhosis.

The data used in this study was based on transient elastography (Fibroscan) by Kim et al. We enrolled 228 HBsAg-positive patients whose liver stiffness was measured by the Fibroscan system during six months. Statistical analysis was performed by R-2.13.0.

A classical logistic regression model together with an expert model was used to describe and classify hidden subgroups. The performance of the proposed model was evaluated in terms of the classification accuracy, and the results confirmed that the proposed ME model has some potential in detecting liver cirrhosis.

This method can be used as an important diagnostic decision support mechanism to assist physicians in the diagnosis of liver cirrhosis in patients.

Medical diagnostic decision support systems have become an established component of medical technology and their use will be growing, fueled by electronic medical records and automatic data capture [

Many methods have been applied for pattern of classification in biostatistics communities. The main idea of these methods is called 'divide-and-conquer principle that is often used to attack a complex problem by dividing it into simpler problems whose solutions can be combined to yield a solution to the complex problem [

Inputs are presented to the network, and each individual classifier makes an assessment. These outputs from the classifiers are then weighted by the relevant gate, which produces a weight using the current inputs, and this is propagated further up the hierarchy [

Based on this, many applications using ME model were carried out. Ubeyli [

Transient elastography (Fibroscan; The Princess Grace Hospital, London, UK) is a rapid and non-invasive method to measure liver stiffness and this allows the assessment of liver fibrosis. In the past study, Kim et al. [

The aim of this study was to apply ME model for classifying of the hidden subgroups and testing the significance of measuring the liver stiffness associated with the development of liver cirrhosis and explored the feasibility of the ME model in diagnostic decision support system.

The remainder of this paper is organized as follows. In second section, ME architecture used in this study is briefly explained and the liver stiffness data is described. Also, EM algorithm used for estimating the ME architecture is presented. In third section, the application results of the ME networks to the liver fibrosis data are described. Finally, in the last section the study is concluded.

Liver fibrosis is the most important factor that determines the prognosis in chronic liver disease patients. Liver cirrhosis which is the extreme of liver fibrosis is an independent risk factor for liver cancer, chronic hepatitis B is the most important cause (62.5-73%) in Korea [

Transient elastography (Fibroscan) is a rapid and non-invasive method to measure liver stiffness and this allow the assessment of liver fibrosis [

In this study, the liver stiffness data is taken from 228 HBsAg positive patients whose liver stiffness was measured by Fibroscan between March 2005 and September 2005. Liver biopsy examinations were performed in 34 patients. The fibrosis (F) was staged on a 0-4 scale according to the Ludwig classification. Kim et al. [

In this subsection, we briefly review the ME architecture [_{i}

_{i}_{i}x

where _{i}_{i}_{i}

where _{i}

The ME architecture can be given a probabilistic interpretation. For an input-output pair (_{i}_{i}_{i}

where Φ includes the expert network parameters as well as the gating network parameters. Moreover, the probabilistic component of the model is generally assumed to be a Bernoulli distribution in the case of binary classification, a multinomial distribution in the case of multiclass classification and a Gaussian distribution in the case of regression. Based on the probabilistic model, a learning algorithm for the ME architecture is treated as a maximum likelihood estimation problem. Jordan and Jacobs [

Suppose that the training set is given as _{i}^{(t)}_{t}_{t}

The M-step solves the following maximization problems:

and

where

For each data pair (_{t}_{t}_{i}^{(t)}

For each expert network _{i}^{(s+1)}

For the gating network, solve the maximization problem in ^{(s+1)}

Iterate by using the updated parameter values.

The ME architecture used for the diagnosis of liver cirrhosis is shown in (

There are a total of 228 HBsAg positive patients whose liver stiffness was measured by Fibroscan between March 2005 and September 2005. The diagnosis of liver cirrhosis (LC) were considered such as LC with compensated, LC with decompensated and hepatocellular carcinoma (HCC) cases.

Statistical analysis was performed by R 2.13.0 (software available at

Receiver operating characteristic (ROC) curves were shown for comparing classical logistic regression and ME model from this data for the validation of model.

A total of 228 patients were enrolled in this study. The mean age of the patients was 45.9 years and 177 patients were male. In diagnosis, 29 (12.7%) patients were inactive carrier, 106 (46.5%) patients had chronic hepatitis, 63 (27.6%) patients had LC with compensated, 26 patients had LC with decompensated and 4 (1.8%) patients were HCC. The mean age of the liver biopsy patients was 39.4 years and fibrosis stage 1 (portal fibrosis) was 4 (11.8%) patients, stage 2 (periportal fibrosis) was 12 (35.3%) patients, stage 3 (septal fibrosis) was 2 (5.9%) patients and stage 4 (cirrhosis) was 16 (47.1%) patients (

According to the clinical diagnosis, the median values of liver stiffness were 7.0 ± 2.7 kPa for inactive carriers (n = 29), 8.3 ± 5.3 kPa for chronic hepatitis patients (n = 106), 15.9 ± 8.3 kPa for compensated cirrhosis patients (n = 63), 31.8 ± 20.3 kPa for decompensated cirrhosis patients (n = 26), and 45.1 ± 34.5 kPa for HCC patients (n = 4). The degree of liver stiffness was statistically significant (

In classification, the aim is to assign the input patterns to one of several classes, usually represented by outputs restricted to lie in the range from 0 to 1, so that they represent the probability of class membership [

According to the confusion matrix, 8 patients were classified incorrectly by ME as non-LC patient in low risk group and no patient was classified as non-LC in high risk group.

The values of statistical parameters are given in (

The performance of the ME model can be evaluated by plotting a ROC curve for the test (

In this work, we have presented the use of ME structure to improve accuracy of liver cirrhosis detection in Fibroscan since the overall structure predictive performance is superior to any of the individual experts. In order to detect hidden-subgroup, two local experts and a gating network were used and these experts were divided by low/high risk group. The EM algorithm was used for estimating the ME structure, which is like the maximum problem. The classification results which are the values of statistical parameters and ROC curves were presented for assessing performances of the ME and standalone logistic regression model in liver stiffness data. This shows that the performance of the ME is higher than that of the stand-alone logistic regression.

The proposed ME structure method for diagnostic decision support is a flexible approach that is applicable to assist physicians in the treatment of liver cirrhosis patients. Extending the modified ME structure for the longitudinal data may be developed. Another extension interest is the ME structure for the censored data, simply modifying experts into Cox proportional hazard regression.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0013877).

No potential conflict of interest relevant to this article was reported.

The architecture of mixture of expert.

Configured mixture of experts structure for diagnosis of liver cirrhosis.

Receiver operating characteristic (ROC) curves of the stand-alone logistic regression and mixture of experts network structure used for diagnosis of liver cirrhosis.

Characteristics of the study patients

Liver stiffness according to the clinical diagnosis

LC: liver cirrhosis, HCC: hepatocellular carcinoma.

Confusion matrix

LC: liver cirrhosis.

Parameter estimation for logistic regression and mixture of experts (ME) architecture in liver stiffness data

AST: aspartate aminotransferase, ALT: alanine aminotransferase, AFP: alpha-fetoprotein, SE: standard error.