Survival Analysis Methods in Genetic Epidemiology

Mapping genes for complex human diseases is a challenging problem due to the fact that many such diseases are due to both genetic and enviromental risk factors and many also exhibit phenotypic heterogeneity, such as variable age of onset. Information on variable age of disease onset is often a good indicator for disease heterogeneity and incorporation of such information together with enviromental risk factors into genetic analysis should lead to more powerful tests for genetic analysis. Due to the problem of censoring, survival analysis methods have proved to be very useful for genetic analysis. In this paper, I review some recent methodological developments on integrating modern survival analysis methods and human genetics in order to rigorously incorporate both age of onset and enviromental covariates data into aggregation analysis, segregation analysis, linkage analysis, association analysis and gene risk characterization. I also briefly discuss the issue of ascertainment correction and survival analysis methods for high-dimensional genomic data. Finally, I outline several areas that need further methodological developments

Identification of genes associated with multiple cancers via integrative analysis

<p>Abstract</p> <p>Background</p> <p>Advancement in gene profiling techniques makes it possible to measure expressions of thousands of genes and identify genes associated with development and progression of cancer. The identified cancer-associated genes can be used for diagnosis, prognosis prediction, and treatment selection. Most existing cancer microarray studies have been focusing on the identification of genes associated with a specific type of cancer. Recent biomedical studies suggest that different cancers may share common susceptibility genes. A comprehensive description of the associations between genes and cancers requires identification of not only multiple genes associated with a specific type of cancer but also genes associated with multiple cancers.</p> <p>Results</p> <p>In this article, we propose the Mc.TGD (Multi-cancer Threshold Gradient Descent), an integrative analysis approach capable of analyzing multiple microarray studies on different cancers. The Mc.TGD is the first regularized approach to conduct "two-dimensional" selection of genes with joint effects on cancer development. Simulation studies show that the Mc.TGD can more accurately identify genes associated with multiple cancers than meta analysis based on "one-dimensional" methods. As a byproduct, identification accuracy of genes associated with only one type of cancer may also be improved. We use the Mc.TGD to analyze seven microarray studies investigating development of seven different types of cancers. We identify one gene associated with six types of cancers and four genes associated with five types of cancers. In addition, we also identify 11, 9, 18, and 17 genes associated with 4 to 1 types of cancers, respectively. We evaluate prediction performance using a Leave-One-Out cross validation approach and find that only 4 (out of 570) subjects cannot be properly predicted.</p> <p>Conclusion</p> <p>The Mc.TGD can identify a short list of genes associated with one or multiple types of cancers. The identified genes are considerably different from those identified using meta analysis or analysis of marginal effects.</p

Regularized gene selection in cancer microarray meta-analysis

<p>Abstract</p> <p>Background</p> <p>In cancer studies, it is common that multiple microarray experiments are conducted to measure the same clinical outcome and expressions of the same set of genes. An important goal of such experiments is to identify a subset of genes that can potentially serve as predictive markers for cancer development and progression. Analyses of individual experiments may lead to unreliable gene selection results because of the small sample sizes. Meta analysis can be used to pool multiple experiments, increase statistical power, and achieve more reliable gene selection. The meta analysis of cancer microarray data is challenging because of the high dimensionality of gene expressions and the differences in experimental settings amongst different experiments.</p> <p>Results</p> <p>We propose a Meta Threshold Gradient Descent Regularization (MTGDR) approach for gene selection in the meta analysis of cancer microarray data. The MTGDR has many advantages over existing approaches. It allows different experiments to have different experimental settings. It can account for the joint effects of multiple genes on cancer, and it can select the same set of cancer-associated genes across multiple experiments. Simulation studies and analyses of multiple pancreatic and liver cancer experiments demonstrate the superior performance of the MTGDR.</p> <p>Conclusion</p> <p>The MTGDR provides an effective way of analyzing multiple cancer microarray studies and selecting reliable cancer-associated genes.</p

Bayesian Statistical Methods for Genetic Association Studies with Case-Control and Cohort Design

Large-scale genetic association studies are carried out with the hope of discovering single nucleotide polymorphisms involved in the etiology of complex diseases. We propose a coalescent-based model for association mapping which potentially increases the power to detect disease-susceptibility variants in genetic association studies with case-control and cohort design. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions and we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium (LD) therein assuming a perfect phylogeny. The haplotype space is then partitioned into disjoint clusters within which the phenotype-haplotype association is assumed to be the same. The novelty of our approach consists in the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common mutation. Our approach is fully Bayesian and we develop Markov Chain Monte Carlo algorithms to sample efficiently over the space of possible partitions. We have also developed a Bayesian survival regression model for high-dimension and small sample size settings. We provide a Bayesian variable selection procedure and shrinkage tool by imposing shrinkage priors on the regression coefficients. We have developed a computationally efficient optimization algorithm to explore the posterior surface and find the maximum a posteriori estimates of the regression coefficients. We compare the performance of the proposed methods in simulation studies and using real datasets to both single-marker analyses and recently proposed multi-marker methods and show that our methods perform similarly in localizing the causal allele while yielding lower false positive rates. Moreover, our methods offer computational advantages over other multi-marker approaches

A New Class of Dantzig Selectors for Censored Linear Regression Models

The Dantzig variable selector has recently emerged as a powerful tool for fitting regularized regression models. A key advantage is that it does not pertain to a particular likelihood or objective function, as opposed to the existing penalized likelihood methods, and hence has the potential for wide applicability. To our knowledge, limited work has been done for the Dantzig selector when the outcome is subject to censoring. This paper proposes a new class of Dantzig variable selectors for linear regression models for right-censored outcomes. We first establish the finite sample error bound for the estimator and show the proposed selector is nearly optimal in the `2 sense. To improve model selection performance, we further propose an adaptive Dantzig variable selector and discuss its large sample properties, namely, consistency in model selection and asymptotic normality of the estimator. The practical utility of the proposed adaptive Dantzig selectors is verified via extensive simulations. We apply the proposed methods to a myeloma clinical trial and identify important predictive genes for patients ’ survival

Advanced Bayesian Models for High-Dimensional Biomedical Data

Alzheimer’s Disease (AD) is a neurodegenerative and firmly incurable disease, and the total number of AD patients is predicted to be 13.8 million by 2050. Our motivation comes from needs to unravel a missing link between AD and biomedical information for a better understanding of AD. With the advent of data acquisition techniques, we could obtain more biomedical data with a massive and complex structure. Classical statistical models, however, often fail to address the unique structures, which hinders rigorous analysis. A fundamental question this dissertation is asking is how to use the data in a better way. Bayesian methods for high-dimensional data have been successfully employed by using novel priors, MCMC algorithms, and hierarchical modeling. This dissertation proposes novel Bayesian approaches to address statistical challenges arising in biomedical data including brain imaging and genetic data. The first and second projects aim to quantify effects of hippocampal morphology and genetic variants on the time to conversion to AD within mild cognitive impairment (MCI) patients. We propose Bayesian survival models with functional/high-dimensional covariates. The third project discusses a Bayesian matrix decomposition method applicable to brain functional connectivity. It facilitates estimation of clinical covariates, the examination of whether functional connectivity is different among normal, MCI, and AD subjects.Doctor of Philosoph