Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments
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Gordon K Smyth
The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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- Error-Rate and Decision-Theoretic Methods of Multiple Testing: Which Genes Have High Objective Probabilities of Differential Expression?
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- Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate
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- Calculating the Statistical Significance of Changes in Pathway Activity From Gene Expression Data
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- Reader's Reaction
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- Response to Foulkes and De Gruttola
- Software Communication
- BayesMendel: an R Environment for Mendelian Risk Prediction
- Letter to the Editor
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Articles in the same Issue
- Article
- Using Alpha Wisely: Improving Power to Detect Multiple QTL
- Relating HIV-1 Sequence Variation to Replication Capacity via Trees and Forests
- Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments
- Asymptotic Optimality of Likelihood-Based Cross-Validation
- Using Importance Sampling to Improve Simulation in Linkage Analysis
- Model-Based Assignment and Inference of Protein Backbone Nuclear Magnetic Resonances
- Error-Rate and Decision-Theoretic Methods of Multiple Testing: Which Genes Have High Objective Probabilities of Differential Expression?
- Evaluation of Multiple Models to Distinguish Closely Related Forms of Disease Using DNA Microarray Data: an Application to Multiple Myeloma
- Saturation and Quantization Reduction in Microarray Experiments using Two Scans at Different Sensitivities
- Combining Nearest Neighbor Classifiers Versus Cross-Validation Selection
- Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates
- Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate
- Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives
- Calculating the Statistical Significance of Changes in Pathway Activity From Gene Expression Data
- A Family-Based Association Test for Repeatedly Measured Quantitative Traits Adjusting for Unknown Environmental and/or Polygenic Effects
- Deletion/Substitution/Addition Algorithm in Learning with Applications in Genomics
- Classifying Gene Expression Profiles from Pairwise mRNA Comparisons
- Hierarchical Bayesian Neural Network for Gene Expression Temporal Patterns
- A Mixed Model Approach to Identify Yeast Transcriptional Regulatory Motifs via Microarray Experiments
- Mammalian Genomes Ease Location of Human DNA Functional Segments but Not Their Description
- On the Dependence Structure of Sequence Alignment Scores Calculated with Multiple Scoring Matrices
- Increasing Power for Tests of Genetic Association in the Presence of Phenotype and/or Genotype Error by Use of Double-Sampling
- A Method for Evaluating the Impact of Individual Haplotypes on Disease Incidence in Molecular Epidemiology Studies
- Statistical Methods for Identifying Conserved Residues in Multiple Sequence Alignment
- MergeMaid: R Tools for Merging and Cross-Study Validation of Gene Expression Data
- Sparse Inverse of Covariance Matrix of QTL Effects with Incomplete Marker Data
- Maximum Likelihood for Genome Phylogeny on Gene Content
- Confidence Levels for the Comparison of Microarray Experiments
- PLS Dimension Reduction for Classification with Microarray Data
- Statistical Analysis of Genomic Tag Data
- Statistical Analysis of Adsorption Models for Oligonucleotide Microarrays
- Statistical Significance Threshold Criteria For Analysis of Microarray Gene Expression Data
- A Compendium to Ensure Computational Reproducibility in High-Dimensional Classification Tasks
- Validation and Discovery in Markov Models of Genetics Data
- Making Sense of High-Throughput Protein-Protein Interaction Data
- Reader's Reaction
- Reader Reaction
- Response to Foulkes and De Gruttola
- Software Communication
- BayesMendel: an R Environment for Mendelian Risk Prediction
- Letter to the Editor
- Concerns About Unreliable Data from Spotted cDNA Microarrays Due to Cross-Hybridization and Sequence Errors
