Date on Master's Thesis/Doctoral Dissertation

8-2014

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Bioinformatics and Biostatistics

Committee Chair

Kong, Maiying

Committee Co-Chair (if applicable)

Datta, Susmita

Committee Member

Datta, Susmita

Committee Member

Kulasekera, Karunarathna

Committee Member

Wu, Dongfeng

Committee Member

Jones, Stephen P.

Subject

Regression analysis; Mass spectrometry

Abstract

The focus of this dissertation is to develop statistical methods, under the framework of penalized regressions, to handle three different problems. The first research topic is to address missing data problem for variable selection models including elastic net (ENet) method and sparse partial least squares (SPLS). I proposed a multiple imputation (MI) based weighted ENet (MI-WENet) method based on the stacked MI data and a weighting scheme for each observation. Numerical simulations were implemented to examine the performance of the MIWENet method, and compare it with competing alternatives. I then applied the MI-WENet method to examine the predictors for the endothelial function characterized by median effective dose and maximum effect in an ex-vivo experiment. The second topic is to develop monotonic single-index models for assessing drug interactions. In single-index models, the link function f is unnecessary monotonic. However, in combination drug studies, it is desired to have a monotonic link function f . I proposed to estimate f by using penalized splines with I-spline basis. An algorithm for estimating f and the parameter a in the index was developed. Simulation studies were conducted to examine the performance of the proposed models in term of accuracy in estimating f and a. Moreover, I applied the proposed method to examine the drug interaction of two drugs in a real case study. The third topic was focused on the SPLS and ENet based accelerated failure time (AFT) models for predicting patient survival time with mass spectrometry (MS) data. A typical MS data set contains limited number of spectra, while each spectrum contains tens of thousands of intensity measurements representing an unknown number of peptide peaks as the key features of interest. Due to the high dimension and high correlations among features, traditional linear regression modeling is not applicable. Semi-parametric AFT model with an unspecified error distribution is a well-accepted approach in survival analysis. To reduce the bias caused in denoising step, we proposed a nonparametric imputation approach based on Kaplan-Meier estimator. Numerical simulations and a real case study were conducted under the proposed method.

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