Statistical methods for genetics and genomics studies

Abstract

Genomics study: the data quality from microarray analysis is highly dependent on RNA quality. Because of the lability of RNA, steps involved in tissue sampling, RNA purification, and RNA storage are known to potentially lead to the degradation of RNAs, therefore, assessment of RNA quality is essential. Existing methods for estimating the quality of RNA on microarray either suffer from subjectivity or are inefficient in performance. To overcome these drawbacks, in this dissertation, a linear regression method for assessing RNA quality for a hybridized Genechip is proposed. In particular, our approach used the probe intensities that the Affymetrix software associates with each microarray. The effectiveness and improvements of the proposed method over the existing methods are illustrated by the application of the method to the previously published 19 human Affymetrix microarray data sets for which external verification of RNA quality is available. Genetics study : although population-based association mapping may be subject to the bias caused by population stratification, alternative methods that are robust to population stratification such as family-based linkage analysis have lower mapping resolution. In this dissertation, we propose association tests for fully observed quantitative traits as well censored data in structured populations with complex genetic relatedness among the sampled individuals. Our methods correct for continuous population stratification by first deriving population structure variables and kinship matrices through random genetic marker data and then modeling the relationship between trait values, genotypic scores at a candidate marker, and genetic background variables through a semiparametric model, where the error distribution for fully observed data or the baseline survival function for censored data is modeled as a mixture of Polya trees centered around a family of parametric distributions. We also propose multivariate Bayesian statistical models with a Gaussian conditional autoregressive (CAR) framework for multi-trait association mapping in structured populations, where the effects attributable to kinship matrix is modeled via CAR and the population structure variables are included as covariates to adjust populations stratification. We compared our model to the existing structured association tests in terms of model fit, false positive rate, power, precision, and accuracy using real data sets as well as simulated data sets.