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172
Assessing Gene Significance from cDNA Microarray Expression Data via Mixed Models
, 2001
"... The determination of a list of differentially expressed genes is a basic objective in many cDNA microarray experiments. We present a statistical approach that allows direct control over the percentage of false positives in such a list and, under certain reasonable assumptions, improves on existing m ..."
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Cited by 108 (3 self)
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The determination of a list of differentially expressed genes is a basic objective in many cDNA microarray experiments. We present a statistical approach that allows direct control over the percentage of false positives in such a list and, under certain reasonable assumptions, improves on existing methods with respect to the percentage of false negatives. The method accommodates a wide variety of experimental designs and can simultaneously assess significant differences between multiple types of biological samples. Two interconnected mixed linear models are central to the method and provide a flexible means to properly account for variability both across and within genes. The mixed model also provides a convenient framework for evaluating the statistical power of any particular experimental design and thus enables a researcher to a priori select an appropriate number of replicates. We also suggest some basic graphics for visualizing lists of significant genes. Analyses of published experiments studying human cancer and yeast cells illustrate the results.
Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves
 Journal of the American Statistical Association
, 1998
"... We introduce a class of models for an additive decomposition of groups of curves strati ed by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed e ects model. The models are also useful for imputation of missing data and explorat ..."
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Cited by 81 (1 self)
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We introduce a class of models for an additive decomposition of groups of curves strati ed by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed e ects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUP) from the extended mixed e ects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components, and we show that these solutions are natural cubic splines. The model parameters are estimated using a highly e cient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition. Variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed e ects models. Our methods are applied to menstrual cycle data from studies of reproductive function that measure daily urinary progesterone; the sample of progesterone curves is strati ed by cycles nested within subjects nested within conceptive and nonconceptive groups.
Improved statistical tests for differential gene expression by shrinking variance components estimates
 Biostatistics
, 2005
"... Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the JamesSteinLi ..."
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Cited by 61 (5 self)
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Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the JamesSteinLindley shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic is compared with other statistics used to test for differential expression, namely the genespecific F test (F1), the pooledvariance F statistic (F3), and a hybrid statistic (F2) that uses the average of the individual and pooled variances. The FS test shows best or nearly best power for detecting differentially expressed genes over a wide range of simulated data in which the variance components associated with individual genes are either homogeneous or heterogeneous. Thus FS provides a powerful and robust approach to test differential expression of genes that utilizes information not available in individual gene testing approaches and does not suffer from biases of the pooled variance approach.
General MultiLevel Linear Modelling for Group Analysis in FMRI
 NeuroImage
, 2003
"... This paper discusses general modelling of multisubject and/or multisession FMRI data. In particular, we show that a twolevel mixedeffects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the singlesession level) can be made equivale ..."
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Cited by 60 (8 self)
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This paper discusses general modelling of multisubject and/or multisession FMRI data. In particular, we show that a twolevel mixedeffects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the singlesession level) can be made equivalent to a single complete mixedeffects model (where parameters of interest at the group level are estimated directly from all of the original singlesessions' timeseries data) if the (co)variance at the second level is set equal to the sum of the (co)variances in the singlelevel form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis only requires values of the parameter estimates and their (co)variance from the first level, generalising the well established 'summary statistics' approach in FMRI. The simple and generalised framework allows for different prewhitening and different firstlevel regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired ttests and F tests at the group level; explicit examples of such models are given in the paper. Using numerical simulations based on typical first level covariance structures from real FMRI data we demonstrate that by taking into account lowerlevel covariances and heterogeneity a substantial increase in higherlevel Zscore is possible. 1
Geometric Ergodicity of Gibbs and Block Gibbs Samplers for a Hierarchical Random Effects Model
, 1998
"... We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is geom ..."
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Cited by 33 (8 self)
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We consider fixed scan Gibbs and block Gibbs samplers for a Bayesian hierarchical random effects model with proper conjugate priors. A drift condition given in Meyn and Tweedie (1993, Chapter 15) is used to show that these Markov chains are geometrically ergodic. Showing that a Gibbs sampler is geometrically ergodic is the first step towards establishing central limit theorems, which can be used to approximate the error associated with Monte Carlo estimates of posterior quantities of interest. Thus, our results will be of practical interest to researchers using these Gibbs samplers for Bayesian data analysis. Key words and phrases: Bayesian model, Central limit theorem, Drift condition, Markov chain, Monte Carlo, Rate of convergence, Variance Components AMS 1991 subject classifications: Primary 60J27, secondary 62F15 1 Introduction Gelfand and Smith (1990, Section 3.4) introduced the Gibbs sampler for the hierarchical oneway random effects model with proper conjugate priors. Rosen...
Geoadditive Models
, 2000
"... this paper is a recent article on modelbased geostatistics by Diggle, Tawn and Moyeed (1998) where pure kriging (i.e. no covariates) is the focus. Our paper inherits some of its aspects: modelbased and with mixed model connections. In particular the comment by Bowman (1998) in the ensuing discussi ..."
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Cited by 33 (1 self)
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this paper is a recent article on modelbased geostatistics by Diggle, Tawn and Moyeed (1998) where pure kriging (i.e. no covariates) is the focus. Our paper inherits some of its aspects: modelbased and with mixed model connections. In particular the comment by Bowman (1998) in the ensuing discussion suggested that additive modelling would be a worthwhile extension. This paper essentially follows this suggestion. However, this paper is not the first to combine the notions of geostatistics and additive modelling. References known to us are Kelsall and Diggle (1998), Durban Reguera (1998) and Durban, Hackett, Currie and Newton (2000). Nevertheless, we believe that our approach has a number of attractive features (see (1)(4) above), not all shared by these references. Section 2 describes the motivating application and data in detail. Section 3 shows how one can express additive models as a mixed model, while Section 4 does the same for kriging and merges the two into the geoadditive model. Issues concerning the amount of smoothing are discussed in Section 5 and inferential aspects are treated in Section 6. Our analysis of the Upper Cape Cod reproductive data is presented in Section 7. Section 8 discusses extension to the generalised context.We close the paper with some disussion in Section 9. 2 Description of the application and data
Multilevel linear modelling for FMRI group analysis using Bayesian inference
 Neuroimage
, 2004
"... Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects varia ..."
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Cited by 33 (6 self)
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Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and toplevel regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an informationtheoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.
Assortment: An AttributeBased Approach
 Carnegie Mellon University
, 2000
"... Most supermarket categories are cluttered with items or SKUs (stockkeeping units) that differ very little at the attribute level. Previous research has found that reductions (up to 54%) in the number of lowselling SKUs need not affect perceptions of variety, and therefore sales, significantly. In ..."
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Cited by 20 (1 self)
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Most supermarket categories are cluttered with items or SKUs (stockkeeping units) that differ very little at the attribute level. Previous research has found that reductions (up to 54%) in the number of lowselling SKUs need not affect perceptions of variety, and therefore sales, significantly. In this research, we analyze data from a natural experiment conducted by an online grocer in which 94% of the categories experienced dramatic cuts in the number of SKUs offered, particularly lowselling SKUs. We find sales were indeed affected dramatically, with sales increasing an average of 11% across the 42 categories examined. Sales rose in more than twothirds of these categories, with nearly half experiencing an increase of 10% or more; 75% of households increased their overall expenditures after the cut in SKUs. In turn, we examined how different types of SKU reductions  defined by how the cuts affect the available attributes or features of a category (e.g., the number of brands)  af...
Likelihood Ratio Tests in Linear Mixed Models With One Variance Component
, 2003
"... this paper but the results were practically indistinguishable, indicating that our choice of grid provides an accurate approximation ..."
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Cited by 20 (3 self)
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this paper but the results were practically indistinguishable, indicating that our choice of grid provides an accurate approximation
Analysis of variance components in gene expression data
, 2004
"... Motivation: A microarray experiment is a multistep process, and each step is a potential source of variation. There are two major sources of variation: biological variation and technical variation. This study presents a variancecomponents approach to investigating animaltoanimal, betweenarray, ..."
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Cited by 13 (0 self)
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Motivation: A microarray experiment is a multistep process, and each step is a potential source of variation. There are two major sources of variation: biological variation and technical variation. This study presents a variancecomponents approach to investigating animaltoanimal, betweenarray, withinarray and daytoday variations for two data sets. The first data set involved estimation of technical variances for pooled control and pooled treated RNA samples. The variance components included betweenarray, and two nested withinarray variances: betweensection (the upper and lowersections of the array are replicates) and withinsection (two adjacent spots of the same gene are printed within each section). The second experiment was conducted on four different weeks. Each week there were reference and test samples