Analysis of oligonucleotide array experiments with repeated measures using mixed models

BACKGROUND: Two or more factor mixed factorial experiments are becoming increasingly common in microarray data analysis. In this case study, the two factors are presence (Patients with Alzheimer's disease) or absence (Control) of the disease, and brain regions including olfactory bulb (OB) or cerebellum (CER). In the design considered in this manuscript, OB and CER are repeated measurements from the same subject and, hence, are correlated. It is critical to identify sources of variability in the analysis of oligonucleotide array experiments with repeated measures and correlations among data points have to be considered. In addition, multiple testing problems are more complicated in experiments with multi-level treatments or treatment combinations. RESULTS: In this study we adopted a linear mixed model to analyze oligonucleotide array experiments with repeated measures. We first construct a generalized F test to select differentially expressed genes. The Benjamini and Hochberg (BH) procedure of controlling false discovery rate (FDR) at 5% was applied to the P values of the generalized F test. For those genes with significant generalized F test, we then categorize them based on whether the interaction terms were significant or not at the α-level (α(new )= 0.0033) determined by the FDR procedure. Since simple effects may be examined for the genes with significant interaction effect, we adopt the protected Fisher's least significant difference test (LSD) procedure at the level of α(new )to control the family-wise error rate (FWER) for each gene examined. CONCLUSIONS: A linear mixed model is appropriate for analysis of oligonucleotide array experiments with repeated measures. We constructed a generalized F test to select differentially expressed genes, and then applied a specific sequence of tests to identify factorial effects. This sequence of tests applied was designed to control for gene based FWER

Identification of gene expression patterns using planned linear contrasts

BACKGROUND: In gene networks, the timing of significant changes in the expression level of each gene may be the most critical information in time course expression profiles. With the same timing of the initial change, genes which share similar patterns of expression for any number of sampling intervals from the beginning should be considered co-expressed at certain level(s) in the gene networks. In addition, multiple testing problems are complicated in experiments with multi-level treatments when thousands of genes are involved. RESULTS: To address these issues, we first performed an ANOVA F test to identify significantly regulated genes. The Benjamini and Hochberg (BH) procedure of controlling false discovery rate (FDR) at 5% was applied to the P values of the F test. We then categorized the genes with a significant F test into 4 classes based on the timing of their initial responses by sequentially testing a complete set of orthogonal contrasts, the reverse Helmert series. For genes within each class, specific sequences of contrasts were performed to characterize their general \u27fluctuation\u27 shapes of expression along the subsequent sampling time points. To be consistent with the BH procedure, each contrast was examined using a stepwise Studentized Maximum Modulus test to control the gene based maximum family-wise error rate (MFWER) at the level of alphanew determined by the BH procedure. We demonstrated our method on the analysis of microarray data from murine olfactory sensory epithelia at five different time points after target ablation. CONCLUSION: In this manuscript, we used planned linear contrasts to analyze time-course microarray experiments. This analysis allowed us to characterize gene expression patterns based on the temporal order in the data, the timing of a gene\u27s initial response, and the general shapes of gene expression patterns along the subsequent sampling time points. Our method is particularly suitable for analysis of microarray experiments in which it is often difficult to take sufficiently frequent measurements and/or the sampling intervals are non-uniform

Identification of gene expression patterns using planned linear contrasts

BACKGROUND: In gene networks, the timing of significant changes in the expression level of each gene may be the most critical information in time course expression profiles. With the same timing of the initial change, genes which share similar patterns of expression for any number of sampling intervals from the beginning should be considered co-expressed at certain level(s) in the gene networks. In addition, multiple testing problems are complicated in experiments with multi-level treatments when thousands of genes are involved. RESULTS: To address these issues, we first performed an ANOVA F test to identify significantly regulated genes. The Benjamini and Hochberg (BH) procedure of controlling false discovery rate (FDR) at 5% was applied to the P values of the F test. We then categorized the genes with a significant F test into 4 classes based on the timing of their initial responses by sequentially testing a complete set of orthogonal contrasts, the reverse Helmert series. For genes within each class, specific sequences of contrasts were performed to characterize their general \u27fluctuation\u27 shapes of expression along the subsequent sampling time points. To be consistent with the BH procedure, each contrast was examined using a stepwise Studentized Maximum Modulus test to control the gene based maximum family-wise error rate (MFWER) at the level of alphanew determined by the BH procedure. We demonstrated our method on the analysis of microarray data from murine olfactory sensory epithelia at five different time points after target ablation. CONCLUSION: In this manuscript, we used planned linear contrasts to analyze time-course microarray experiments. This analysis allowed us to characterize gene expression patterns based on the temporal order in the data, the timing of a gene\u27s initial response, and the general shapes of gene expression patterns along the subsequent sampling time points. Our method is particularly suitable for analysis of microarray experiments in which it is often difficult to take sufficiently frequent measurements and/or the sampling intervals are non-uniform

Statistical implications of pooling RNA samples for microarray experiments

BACKGROUND: Microarray technology has become a very important tool for studying gene expression profiles under various conditions. Biologists often pool RNA samples extracted from different subjects onto a single microarray chip to help defray the cost of microarray experiments as well as to correct for the technical difficulty in getting sufficient RNA from a single subject. However, the statistical, technical and financial implications of pooling have not been explicitly investigated. RESULTS: Modeling the resulting gene expression from sample pooling as a mixture of individual responses, we derived expressions for the experimental error and provided both upper and lower bounds for its value in terms of the variability among individuals and the number of RNA samples pooled. Using virtual pooling of data from real experiments and computer simulations, we investigated the statistical properties of RNA sample pooling. Our study reveals that pooling biological samples appropriately is statistically valid and efficient for microarray experiments. Furthermore, optimal pooling design(s) can be found to meet statistical requirements while minimizing total cost. CONCLUSIONS: Appropriate RNA pooling can provide equivalent power and improve efficiency and cost-effectiveness for microarray experiments with a modest increase in total number of subjects. Pooling schemes in terms of replicates of subjects and arrays can be compared before experiments are conducted

ASA Study on Modular Instruction - Position Paper

28 pages, 1 article*ASA Study on Modular Instruction - Position Paper* (Wood, Constance L.) 28 page

Large Sample Results for Kolmogorov-Smirnov Statistics for Discrete Distributions

9 pages, 1 article*Large Sample Results for Kolmogorov-Smirnov Statistics for Discrete Distributions* (Wood, Constance L.; Altavela, Michele M.) 9 page

Lumpectomy Plus Tamoxifen With or Without Irradiation in Women Age 70 Years or Older With Early Breast Cancer: Long-Term Follow-Up of CALGB 9343

To determine whether there is a benefit to adjuvant radiation therapy after breast-conserving surgery and tamoxifen in women age ≥ 70 years with early-stage breast cancer

The Ninth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Baryon Oscillation Spectroscopic Survey

The Sloan Digital Sky Survey III (SDSS-III) presents the first spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS). This ninth data release (DR9) of the SDSS project includes 535,995 new galaxy spectra (median z=0.52), 102,100 new quasar spectra (median z=2.32), and 90,897 new stellar spectra, along with the data presented in previous data releases. These spectra were obtained with the new BOSS spectrograph and were taken between 2009 December and 2011 July. In addition, the stellar parameters pipeline, which determines radial velocities, surface temperatures, surface gravities, and metallicities of stars, has been updated and refined with improvements in temperature estimates for stars with T_eff<5000 K and in metallicity estimates for stars with [Fe/H]>-0.5. DR9 includes new stellar parameters for all stars presented in DR8, including stars from SDSS-I and II, as well as those observed as part of the SDSS-III Sloan Extension for Galactic Understanding and Exploration-2 (SEGUE-2). The astrometry error introduced in the DR8 imaging catalogs has been corrected in the DR9 data products. The next data release for SDSS-III will be in Summer 2013, which will present the first data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) along with another year of data from BOSS, followed by the final SDSS-III data release in December 2014.Comment: 9 figures; 2 tables. Submitted to ApJS. DR9 is available at http://www.sdss3.org/dr

Hundreds of variants clustered in genomic loci and biological pathways affect human height

Most common human traits and diseases have a polygenic pattern of inheritance: DNA sequence variants at many genetic loci influence the phenotype. Genome-wide association (GWA) studies have identified more than 600 variants associated with human traits, but these typically explain small fractions of phenotypic variation, raising questions about the use of further studies. Here, using 183,727 individuals, we show that hundreds of genetic variants, in at least 180 loci, influence adult height, a highly heritable and classic polygenic trait. The large number of loci reveals patterns with important implications for genetic studies of common human diseases and traits. First, the 180 loci are not random, but instead are enriched for genes that are connected in biological pathways (P = 0.016) and that underlie skeletal growth defects (P < 0.001). Second, the likely causal gene is often located near the most strongly associated variant: in 13 of 21 loci containing a known skeletal growth gene, that gene was closest to the associated variant. Third, at least 19 loci have multiple independently associated variants, suggesting that allelic heterogeneity is a frequent feature of polygenic traits, that comprehensive explorations of already-discovered loci should discover additional variants and that an appreciable fraction of associated loci may have been identified. Fourth, associated variants are enriched for likely functional effects on genes, being over-represented among variants that alter amino-acid structure of proteins and expression levels of nearby genes. Our data explain approximately 10% of the phenotypic variation in height, and we estimate that unidentified common variants of similar effect sizes would increase this figure to approximately 16% of phenotypic variation (approximately 20% of heritable variation). Although additional approaches are needed to dissect the genetic architecture of polygenic human traits fully, our findings indicate that GWA studies can identify large numbers of loci that implicate biologically relevant genes and pathways.