Title: The analyses of array CGH data and current status data
Description: In this dissertation; the focus is on developing a new methodology to analyze current status data under an Accelerated Failure Time (AFT) model and in developing appealing procedures for analysing correlated high-dimensional data, motivated by two brain tumor Array-based Comparative Genomic Hybridization (aCGH) datasets. The AFT model is a popular alternative to the most frequently used Cox's proportional Hazards model for analyzing censored survival data. Existing inference procedures for analyzing current status data with the AFT model involves estimating the baseline distribution function which have undesirable properties. Tumoral tissues tend to generally exhibit aberrations in their DNA sequence of copy numbers which have been shown to be associated with the development and progression of cancer. Consequently interests lie in identifying the true underlying sequence of copy numbers along the entire genome. The analysis of aCGH data seeks to accomplish this. In Chapter 1 , a rank-based inference procedure for the AFT model with current status data is developed. Under this model, we extend ideas that have been successfully developed for right-censored data, applying them to current status data. The proposed procedure does not require the estimation of the baseline distribution function which tend to have undesirable properties. The proposed estimators are shown to be consistent and asymptotically normal.

Chapter 2 presents a novel approach of assessing population level genetic instability with aCGH data via a moving average technique. While relaxing the common assumption of independence of clones as well as strong model assumptions, we establish meaningful associations between tumor types and chromosomal copy number ratios observed at several locations as well as on several chromosomes. Covariates are incorporated through a possibly mis-specified working model. In Chapter 3 , a predictive model is proposed, one that exploits the fact that aCGH data tend to be high dimensional and correlated. We used the observed sequence of copy number ratios to predict or to classify a dichotomous outcome. Inference procedures for evaluating the accuracy of such binary classifiers are developed.