Bayesian Models for Healthcare Data Analysis

Review Article

Austin J Biomed Eng. 2014;1(3): 1013.

Bayesian Models for Healthcare Data Analysis

Xiaoshan Xie1*, Gang Zhang1, Ying Huang1 and Shanxing Ou2*

1School of Automation, Guangdong University of Technology, China

2Department of Radiology, Guangzhou General Hospital of Guangzhou Military Command, China

*Corresponding author: :Xiaoshan Xie, School of Automation, Guangdong University of Technology, Guangzhou, 510006, China.

Received: May 15, 2014; Accepted: June 16, 2014; Published: June 18, 2014

Abstract

The rapid increasing amount of healthcare data poses great challenges to data mining and machine learning study and applications. Recently a large number of algorithms and models have been proposed to discover knowledge and information from large scale healthcare datasets. In medical applications, confidence measured by posterior probability is well accepted since it can quantify the certainty or severity of targets. In this article, we propose a sparse Bayesian model for healthcare data analysis. The proposed model utilizes a set of basic functions and it learns a sparse weight vector to combine them together. Our model is a fully Bayesian method which can incoporate a prior and derive a likelihood function from a given training data set. Working with the images of Pulmonary Embolism diagnosis dataset and Breast Cancer clinical dataset from KDDCup, our experiments demonstrate that the Bayesian approach lead to 83% and 80% test accuracy in modeling principles of healthcare data and it significantly improves the performance of its couterparts.

Introduction

With the increasing availability of biomedical and healthcare data with a wide range of sophisticated characteristics, healthcare data analysis has been an popular and challenging work in recent years. Therefore, a large number of algorithms in data mining have been proposed to model the uncertainties that come with the problem, including Decision Tree (DT), Neural Network (NN), Bayesian methods, association rule mining and so on. Currently, benefit from natural advantages of mining and learning in recognizing significant facts, relationships, trends and anomalies, mining and learning techniques have been widely applied in healthcare domain [1,2]. As early as 1997, to improve the quality of care as well as to help control spiraling costs in healthcare industry, Rogers et al. [3] applied the SAS technology to solve critical bussiness solutions with the healthcare industry. Moreover, Sellappan et al. [4] developed a web-based Intelligent Heart Disease Prediction System (IHDPS) by using Decision trees, Naive Bayes and Neural Network, which was considered as one of a prominent model [5]. And it also can be implemented to better understand key indicators involving quality outcomes and encounters of care. Liu Peng et al. [6] proposed to utilize decision tree, Naive Bayesian classifiers and feature selection methods to predict inpatient length of stay. A PSO-SVM based on association rules in automatic detection of erthemato-squamous diseases obtain higher accuracy [7,8]. And detection of fraudulent insurance claims, making better health policy, forecasting treatment costs are also applications of data mining in healthcare domain [9,10]. Nevertheness, according to the survey of [11], few data mining methods are treated as practically valuable tools for clinical purposes. To better solve these issues, Bayesian method has been attached more importance in theorical study and some new algorithms based on it have been proposed to solve practical problems.

Bayesian method is the powerful one that emerges as a method for discovering patterns in biomedical data and has better speed and accuracy for huge datasets [8,12,13]. Naive Bayesian Classifier (NBC) uses probability to represent each class and trends to find the most possible class for each sample, which always performs well in practice [6]. And the Naive Bayesian Imputation (NBI) proposed in [14] is used for missing data handling. Zhao et al. [15] proposed a Bayesian-based Personalized Laboratory Test prediction (BPLT) to predict laboratory tests for a given group of patients. By considering the aquisition of data from different sources, Martijin described a new formalism named multilevel Bayesian networks for the analysis of hierarchical health care data [16].

In this article, we attempt to construct a sparse model based on Bayesian learning methods. The proposed method tries to model the generative principles of the target data set. Mathematically, we often express a generative model as following:

y= w t Φ(x)+ε         (1) [email protected]@[email protected]@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadMhacqGH9aqpcaWG3bWaaWbaaSqabeaacaWG0baaaOGaeuOPdyKaaiikaiaadIhacaGGPaGaey4kaSIaeqyTduMaaeiiaiaabccacaqGGaG[email protected][email protected]

where y∈R is a target variable and d x∈Rdis a d- dimension feature vector. Φ is a set of basic functions, where Φ i (x): R d R [email protected]@[email protected]@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabfA6agnaaBaaaleaacaWGPbaabeaakiaacIcacaWG4bGaaiykaiaac[email protected]@ ∈ is Gaussian noise with zero mean and unknown variance. In this work, we limit Φ to be a set of random initialized Gaussian distributions. The goal is to derive the posterior distribution p(w|D) given training dataset D and the predictive distribution p(y|x,D) given training dataset D and a test example x. Moreover, to cut down the computational cost of both training and test, a sparse combination is preferred, meaning that in the weight vector w, there are a lot of elements are zero. We will show that the problem of finding a sparse weight vector can be solved by a Relevant Vector Machine (RVM), which is a Sparse Bayesian Learning (SBL) model [17,18]. Figure 1 sketches the main idea of this article.