Volume 13, Issue 2

In association mapping of quantitative traits, the F -test based on an assumed genetic model is a basic statistical tool for testing association of each candidate locus with the trait of interest. However, the true underlying genetic model is often unknown, and using an incorrect model may cause serious loss of power. For case-control studies, it is known that the combination of several tests that are optimal for different models is robust to model misspecification. In this paper, we extend the test combination approach to quantitative trait association. We first derive the exact correlations among transformed test statistics and discuss interesting special cases. We then propose and evaluate a multivariate normality based approximation to the joint distribution of test statistics, such that the marginal distributions and pairwise correlations among test statistics are accounted for. Through simulations, we show that the sizes of the resulting approximate combined tests are accurate for practical purposes under a variety of situations. We find that the combination of the tests from the additive model and the genotypic model performs well, because it demonstrates both robustness to incorrect models and satisfactory power. A mouse lipoprotein data set is used to demonstrate the method.

Through integration of genomic data from multiple sources, we may obtain a more accurate and complete picture of the molecular mechanisms underlying tumorigenesis. We discuss the integration of DNA copy number and mRNA gene expression data from an observational integrative genomics study involving cancer patients. The two molecular levels involved are linked through the central dogma of molecular biology. DNA copy number aberrations abound in the cancer cell. Here we investigate how these aberrations affect gene expression levels within a pathway using observational integrative genomics data of cancer patients. In particular, we aim to identify differential edges between regulatory networks of two groups involving these molecular levels. Motivated by the rate equations, the regulatory mechanism between DNA copy number aberrations and gene expression levels within a pathway is modeled by a simultaneous-equations model, for the one- and two-group case. The latter facilitates the identification of differential interactions between the two groups. Model parameters are estimated by penalized least squares using the lasso ( L 1 ) penalty to obtain a sparse pathway topology. Simulations show that the inclusion of DNA copy number data benefits the discovery of gene-gene interactions. In addition, the simulations reveal that cis -effects tend to be over-estimated in a univariate (single gene) analysis. In the application to real data from integrative oncogenomic studies we show that inclusion of prior information on the regulatory network architecture benefits the reproducibility of all edges. Furthermore, analyses of the TP53 and TGFb signaling pathways between ER+ and ER- samples from an integrative genomics breast cancer study identify reproducible differential regulatory patterns that corroborate with existing literature.

Complex traits result from an interplay between genes and environment. A better understanding of their joint effects can help refine understanding of the epidemiology of the trait. Various tests have been proposed to assess the statistical interaction between genes and the environment ( G × E ) in case-parent trio data. However, these tests can lose power when the form of G × E departs from that for which the test was developed. To address this limitation, we propose a data-smoothing approach to estimate and test G × E between a single nucleotide polymorphism and a continuous environmental covariate. For estimating G × E , we fit a generalized additive model using penalized likelihood. The resulting point- and interval-estimates of G × E lead to a graphical display, which can serve as a visualization tool for exploring the form of interaction. For testing G × E , we propose a permutation approach, which accounts for the extra uncertainty introduced by the smoothing process. We investigate the statistical properties of the proposed methods through simulation. We also illustrate the use of the approach with an example data set. We conclude that the approach is useful for exploring novel interactions in data-rich settings.

A tiling array yields a series of abundance measurements across the genome using evenly spaced probes. These data can be used for detecting sequences that exhibit a particular behavior. Scanning window statistics are often employed for testing each probe while accounting for local correlation and smoothing noisy measurements. However, window testing may yield false probe discoveries around the sequences and false non-discoveries within the sequences, resulting in biased predicted intervals. We propose to avoid this problem by stipulating that a sequence of interest can appear at most once within a defined region, such as a gene; thus, only one window statistic is considered per region. This substantially reduces the number of tests and hence, is potentially more powerful. We compare this approach to a genome-wise scan that does not require pre-defined search regions, but considers clumps of adjacent probe discoveries. Simulations show that the gene-wise search maintains the nominal FDR level, while the genome-wise scan yields FDR that exceeds the nominal level for low interval effects, and achieves slightly less power. Using arrays to map introns in yeast, we identified 71% of the previously published introns, detected nine previously undiscovered introns, and observed no false intron discoveries by either method.

In this study, we propose a novel statistical framework for detecting progressive changes in molecular traits as response to a pathogenic stimulus. In particular, we propose to employ Bayesian hierarchical models to analyse changes in mean level, variance and correlation of metabolic traits in relation to covariates. To illustrate our approach we investigate changes in urinary metabolic traits in response to cadmium exposure, a toxic environmental pollutant. With the application of the proposed approach, previously unreported variations in the metabolism of urinary metabolites in relation to urinary cadmium were identified. Our analysis highlights the potential effect of urinary cadmium on the variance and correlation of a number of metabolites involved in the metabolism of choline as well as changes in urinary alanine. The results illustrate the potential of the proposed approach to investigate the gradual effect of pathogenic stimulus in molecular traits.

RNA-seq studies allow for the quantification of transcript expression by aligning millions of short reads to a reference genome. However, transcripts share much of their sequence, so that many reads map to more than one place and their origin remains uncertain. This problem can be dealt using mixtures of distributions and transcript expression reduces to estimating the weights of the mixture. In this paper, variational Bayesian (VB) techniques are used in order to approximate the posterior distribution of transcript expression. VB has previously been shown to be more computationally efficient for this problem than Markov chain Monte Carlo. VB methodology can precisely estimate the posterior means, but leads to variance underestimation. For this reason, a novel approach is introduced which integrates the latent allocation variables out of the VB approximation. It is shown that this modification leads to a better marginal likelihood bound and improved estimate of the posterior variance. A set of simulation studies and application to real RNA-seq datasets highlight the improved performance of the proposed method.

We have developed a modified Patient Rule-Induction Method (PRIM) as an alternative strategy for analyzing representative samples of non-experimental human data to estimate and test the role of genomic variations as predictors of disease risk in etiologically heterogeneous sub-samples. A computational limit of the proposed strategy is encountered when the number of genomic variations (predictor variables) under study is large (>500) because permutations are used to generate a null distribution to test the significance of a term (defined by values of particular variables) that characterizes a sub-sample of individuals through the peeling and pasting processes. As an alternative, in this paper we introduce a theoretical strategy that facilitates the quick calculation of Type I and Type II errors in the evaluation of terms in the peeling and pasting processes carried out in the execution of a PRIM analysis that are under-estimated and non-existent, respectively, when a permutation-based hypothesis test is employed. The resultant savings in computational time makes possible the consideration of larger numbers of genomic variations (an example genome-wide association study is given) in the selection of statistically significant terms in the formulation of PRIM prediction models.