Shrinkage Estimation Method for Mapping Multiple Quantitative Trait Loci

In this article, shrinkage estimation method for multiple-marker analysis and for mapping multiple quantitative trait loci (QTL) was reviewed. For multiple-marker analysis, Xu (Genetics, 2003, 163:789-801) developed a Bayesian shrinkage estimation (BSE) method. The key to the success of this method is to allow each marker effect have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, a large number of markers can be handled although most of them may have negligible effects. Under epistatic genetic model, however, the running time is very long. To overcome this problem, a novel method of incorporating the idea described above into maximum likelihood, known as penalized likelihood method, was proposed. A simulated study showed that this method can handle a model with multiple effects, which are ten times larger than the sample size. For multiple QTL analysis, two modified versions for the BSE method were introduced: one is the fixed-interval method and another is the variable-interval method. The former deals with markers with intermediate density, and the latter can handle markers with extremely high density as well as model with epistatic effects. For the detection of epistatic effects, penalized likelihood method and the variable-interval approach of the BSE method are available.     

A latent variable approach to study gene-environment interactions in the presence of multiple correlated exposures

Many existing cohort studies initially designed to investigate disease risk as a function of environmental exposures have collected genomic data in recent years with the objective of testing for gene-environment interaction (G × E) effects. In environmental epidemiology, interest in G × E arises primarily after a significant effect of the environmental exposure has been documented. Cohort studies often collect rich exposure data; as a result, assessing G × E effects in the presence of multiple exposure markers further increases the burden of multiple testing, an issue already present in both genetic and environment health studies. Latent variable (LV) models have been used in environmental epidemiology to reduce dimensionality of the exposure data, gain power by reducing multiplicity issues via condensing exposure data, and avoid collinearity problems due to presence of multiple correlated exposures. We extend the LV framework to characterize gene-environment interaction in presence of multiple correlated exposures and genotype categories. Further, similar to what has been done in case-control G × E studies, we use the assumption of gene-environment (G-E) independence to boost the power of tests for interaction. The consequences of making this assumption, or the issue of how to explicitly model G-E association has not been previously investigated in LV models. We postulate a hierarchy of assumptions about the LV model regarding the different forms of G-E dependence and show that making such assumptions may influence inferential results on the G, E, and G × E parameters. We implement a class of shrinkage estimators to data adaptively trade-off between the most restrictive to most flexible form of G-E dependence assumption and note that such class of compromise estimators can serve as a benchmark of model adequacy in LV models. We demonstrate the methods with an example from the Early Life Exposures in Mexico City to Neuro-Toxicants Study of lead exposure, iron metabolism genes, and birth weight.     

Sparse sufficient dimension reduction

Existing sufficient dimension reduction methods suffer fromthe fact that each dimension reduction component is a linearcombination of all the original predictors, so that it is difficultto interpret the resulting estimates. We propose a unified estimationstrategy, which combines a regression-type formulation of sufficientdimension reduction methods and shrinkage estimation, to producesparse and accurate solutions. The method can be applied tomost existing sufficient dimension reduction methods such assliced inverse regression, sliced average variance estimationand principal Hessian directions. We demonstrate the effectivenessof the proposed method by both simulations and real data analysis.     

Bayesian Hierarchical Modeling and Selection of Differentially Expressed Genes for the EST Data

Summary Expressed sequence tag (EST) sequencing is a one‐pass sequencing reading of cloned cDNAs derived from a certain tissue. The frequency of unique tags among different unbiased cDNA libraries is used to infer the relative expression level of each tag. In this article, we propose a hierarchical multinomial model with a nonlinear Dirichlet prior for the EST data with multiple libraries and multiple types of tissues. A novel hierarchical prior is developed and the properties of the proposed prior are examined. An efficient Markov chain Monte Carlo algorithm is developed for carrying out the posterior computation. We also propose a new selection criterion for detecting which genes are differentially expressed between two tissue types. Our new method with the new gene selection criterion is demonstrated via several simulations to have low false negative and false positive rates. A real EST data set is used to motivate and illustrate the proposed method.