Improving the performance of the prediction analysis of microarrays algorithm via different thresholding methods and heteroscedastic modeling

Abstract

This dissertation considers different methods to improve the performance of the Prediction Analysis of Microarrays (PAM). PAM is a popular algorithm for high-dimensional classification. However, it has a drawback of retaining too many features even after multiple runs of the algorithm to perform further feature selection. The average number of selected features is 2611 from the application of PAM to 10 multi-class microarray human cancer datasets. Such a large number of features make it difficult to perform follow up study. This drawback is the result of the soft thresholding method used in the PAM algorithm and the thresholding parameter estimate of PAM. In this dissertation, we extend the PAM algorithm with two other thresholding methods (hard and order thresholding) and a deep search algorithm to achieve better thresholding parameter estimate. In addition to the new proposed algorithms, we derived an approximation for the probability of misclassification for the hard thresholded algorithm under the binary case. Beyond the aforementioned work, this dissertation considers the heteroscedastic case in which the variances for each feature are different for different classes. In the PAM algorithm the variance of the values for each predictor was assumed to be constant across different classes. We found that this homogeneity assumption is invalid for many features in most data sets, which motivates us to develop the new heteroscedastic version algorithms. The different thresholding methods were considered in these algorithms. All new algorithms proposed in this dissertation are extensively tested and compared based on real data or Monte Carlo simulation studies. The new proposed algorithms, in general, not only achieved better cancer status prediction accuracy, but also resulted in more parsimonious models with significantly smaller number of genes.