Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the effect scaling has on the posterior mean through its relationship to penalization. Several model selection strategies, some frequentist and some Bayesian in nature, are developed and studied theoretically. We demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification, and show this is achieved using the posterior from a rescaled spike and slab model. We also show how to verify a procedure's ability to reduce model uncertainty in finite samples using a specialized forward selection strategy. Using this tool, we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty.Comment: Published at http://dx.doi.org/10.1214/009053604000001147 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mutations in dystrophin cause Duchenne muscular dystrophy (DMD), but absent dystrophin does not invariably cause necrosis in all muscles, life stages and species. Using DNA microarray, we established a molecular signature of dystrophinopathy in the mdx mouse, with evidence that secondary mechanisms are key contributors to pathogenesis. We used variability controls, adequate replicates and stringent analytic tools, including significance analysis of microarrays to estimate and manage false positive rates. In leg muscle, we identified 242 differentially expressed genes, >75% of which have not been previously reported as altered in human or animal dystrophies. Data provide evidence for coordinated activity of numerous components of a chronic inflammatory response, including cytokine and chemokine signaling, leukocyte adhesion and diapedesis, invasive cell type-specific markers, and complement system activation. Selective chemokine upregulation was confirmed by RT-PCR and immunoblot, and may be a key determinant of the nature of the inflammatory response in dystrophic muscle. Up-regulation of secreted phosphoprotein 1 (minopontin, osteopontin) mRNA and protein in dystrophic muscle identified a novel linkage between inflammatory cells and repair processes. Extracellular matrix genes were up-regulated in mdx to levels similar to those in DMD. Since, unlike DMD, mdx exhibits little fibrosis, data suggest that collagen regulation at post-transcriptional stages mediates extensive fibrosis in DMD. Taken together, these data identify a relatively neglected aspect of DMD, suggest new treatment avenues, and highlight the value of genome-wide profiling in study of complex disease processes.

Skeletal muscle fibers are defined by patterned covariation of key traits that determine contractile and metabolic characteristics. Although the functional properties of most skeletal muscles result from their proportional content of a few conserved muscle fiber types, some, typically craniofacial, muscles exhibit fiber types that appear to lie outside the common phenotypic range. We analyzed gene expression profiles of three putative muscle classes, limb, masticatory, and extraocular muscle (EOM), in adult mice by high-density oligonucleotide arrays. Pairwise comparisons using conservative acceptance criteria identified expression differences in 287 genes between EOM and limb and͞or masticatory muscles. Use of significance analysis of microarrays methodology identified up to 400 genes as having an EOM-specific expression pattern. Genes differentially expressed in EOM reflect key aspects of muscle biology, including transcriptional regulation, sarcomeric organization, excitation-contraction coupling, intermediary metabolism, and immune response. These patterned differences in gene expression define EOM as a distinct muscle class and may explain the unique response of these muscles in neuromuscular diseases.

Hemant ISHWARAN and J. Sunil RAODNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while sacri cing power. The drawback of this approach is that more subtle expression differences will be missed that might give investigators more insight into the genetic environment necessary for a disease process to take hold. We introduce a new method for detecting differentially expressed genes based on a high-dimensional model selection technique, Bayesian ANOVA for microarrays (BAM), which strikes a balance between false rejections and false nonrejections. The basis of the new approach involves a weighted average of generalized ridge regression estimates that provides the bene ts of using shrinkage estimation combined with model averaging. A simple graphical tool based on the amount of shrinkage is developed to visualize the trade-off between low false-discovery rates and nding more genes. Simulations are used to illustrate BAM's performance, and the method is applied to a large database of colon cancer gene expression data. Our working hypothesis in the colon cancer analysis is that large differential expressions may not be the only ones contributing to metastasis-in fact, moderate changes in expression of genes may be involved in modifying the genetic environment to a suf cient extent for metastasis to occur. A functional biological analysis of gene effects found by BAM, but not other false-discovery-based approaches, lends support to this hypothesis.

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS517 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

No abstract

No abstract

Crooked tail (Cd) mice bear a gain-of-function mutation in Lrp6, a co-receptor for canonical WNT signaling, and are a model of neural tube defects (NTDs), preventable with dietary folic acid (FA) supplementation. Whether the FA response reflects a direct influence of FA on LRP6 function was tested with prenatal supplementation in LRP6-deficient embryos. The enriched FA (10 ppm) diet reduced the occurrence of birth defects among all litters compared with the control (2 ppm FA) diet, but did so by increasing early lethality of Lrp6(-/-) embryos while actually increasing NTDs among nulls alive at embryonic days 10-13 (E10-13). Proliferation in cranial neural folds was reduced in homozygous Lrp6(-/-) mutants versus wild-type embryos at E10, and FA supplementation increased proliferation in wild-type but not mutant neuroepithelia. Canonical WNT activity was reduced in LRP6-deficient midbrain-hindbrain at E9.5, demonstrated in vivo by a TCF/LEF-reporter transgene. FA levels in media modulated the canonical WNT response in NIH3T3 cells, suggesting that although FA was required for optimal WNT signaling, even modest FA elevations attenuated LRP5/6-dependent canonical WNT responses. Gene expression analysis in embryos and adults showed striking interactions between targeted Lrp6 deficiency and FA supplementation, especially for mitochondrial function, folate and methionine metabolism, WNT signaling and cytoskeletal regulation that together implicate relevant signaling and metabolic pathways supporting cell proliferation, morphology and differentiation. We propose that FA supplementation rescues Lrp6(Cd/Cd) fetuses by normalizing hyperactive WNT activity, whereas in LRP6-deficient embryos, added FA further attenuates reduced WNT activity, thereby compromising development.