Statistical Methods for Data Integration and Disease Classification

Abstract

Classifying individuals into binary disease categories can be challenging due to complex relationships across different exposures of interest. In this thesis, we investigate three different approaches for disease classification using multiple biomarkers. First, we consider combining information from literature reviews and INTERHEART data set to identify the threshold of ApoB, ApoA1 and the ratio of these two biomarkers to classify individuals at risk of developing myocardial infarction. We develop a Bayesian estimation procedure for this purpose that utilizes the conditional probability distribution of these biomarkers. This method is flexible compared to standard logistic regression approach and allows us to identify a precise threshold of these biomarkers. Second, we consider the problem of disease classification using two dependent biomarkers. An independently identified threshold for this purpose usually leads to a conflicting classification for some individuals. We develop and describe a method of determining the joint threshold of two dependent biomarkers for a disease classification, based on the joint probability distribution function constructed through copulas. This method will allow researchers uniquely classify individuals at risk of developing the disease. Third, we consider the problem of classifying an outcome using a gene and miRNA expression data sets. Linear principal component analysis (PCA) is a widely used approach to reduce the dimension of such data sets and subsequently use it for classification, but many authors suggest using kernel PCA for this purpose. Using real and simulated data sets, we compare these two approaches and assess the performance of components towards genetic data integration for an outcome classification. We conclude that reducing dimensions using linear PCA followed by a logistic regression model for classification seems to be acceptable for this purpose. We also observe that integrating information from multiple data sets using either of these approaches leads to a better performance of an outcome classification.