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A Bayesian Framework for the Analysis of Microarray Expression Data: Regularized tTest and Statistical Inferences of Gene Changes
 Bioinformatics
, 2001
"... Motivation: DNA microarrays are now capable of providing genomewide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory ..."
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Motivation: DNA microarrays are now capable of providing genomewide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. Results: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model logexpression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a ttest, provide a systematic inference approach that compares favorably with simple ttest or fold methods, and partly compensate for the lack of replication. Availability: The approach is implemented in a software called CyberT accessible through a Web interface at www.genomics.uci.edu/software.html. The code is available as Open Source and is written in the freely available statistical language R. and Department of Biological Chemistry, College of Medicine, University of California, Irvine. To whom all correspondence should be addressed. Contact: pfbaldi@ics.uci.edu, tdlong@uci.edu. 1
On Differential Variability of Expression Ratios: Improving . . .
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2001
"... We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates o ..."
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Cited by 263 (7 self)
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We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates of gene expression changes are derived within a simple hierarchical model that accounts for measurement error and fluctuations in absolute gene expression levels. Significant gene expression changes are identified by deriving the posterior odds of change within a similar model. The methods are tested via simulation and are applied to a panel of Escherichia coli microarrays.
Advances in Cluster Analysis of Microarray Data
"... Clustering genes into biological meaningful groups according to their pattern of expression is a main technique of microarray data analysis, based on the assumption that similarity in gene expression implies some form of regulatory or functional similarity. We give an overview of various clusteri ..."
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Cited by 5 (0 self)
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Clustering genes into biological meaningful groups according to their pattern of expression is a main technique of microarray data analysis, based on the assumption that similarity in gene expression implies some form of regulatory or functional similarity. We give an overview of various clustering techniques, including conventional clustering methods (such as hierarchical clustering, kmeans clustering, and selforganizing maps), as well as several clustering methods specifically developed for gene expression analysis.
Competing regression models for longitudinal data
 Biometrical Journal
, 2012
"... Received zzz, revised zzz, accepted zzz The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical examp ..."
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Cited by 2 (1 self)
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Received zzz, revised zzz, accepted zzz The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider lognormal linear mixed models (LNLMM), generalized linear mixed models (GLMM) and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEEbased models may be preferable when the goal is to compare the marginal expected responses. Supplemental materials for this article are available on line.
Discriminating Between the LogNormal and LogLogistic Distributions
 Communications in Statistics  Theory and Methods
, 2010
"... Lognormal and loglogistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution funct ..."
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Lognormal and loglogistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this paper, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion have been investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions have been used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We have performed some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose two data sets have been analyzed.
Estimation of Upper Quantiles Under Model and Parameter Uncertainty
"... In this paper we assess accuracy of some commonly used estimators of upper quantiles of a right skewed distribution under both parameter and model uncertainty. In particular, for each of lognormal, loglogistic, and logdouble exponential distributions, we study the bias and mean squared error of t ..."
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In this paper we assess accuracy of some commonly used estimators of upper quantiles of a right skewed distribution under both parameter and model uncertainty. In particular, for each of lognormal, loglogistic, and logdouble exponential distributions, we study the bias and mean squared error of the maximum likelihood estimator (MLE) of the upper quantiles under both the correct and incorrect model specifications. We also consider two data dependent or adaptive estimators. The first (tail–exponential) is based on fitting an exponential distribution to the highest ten to twenty percent of the data. The second selects the best fitting likelihoodbased model and uses the MLE obtained from that model. The simulation results provide some practical guidance concerning the estimation of the upper quantiles when one is uncertain about the underlying model. We found that the consequences of assuming lognormality when the true distribution is loglogistic or logdouble exponential are not severe in moderate sample sizes. For extreme quantiles, no estimator was reliable in small samples. For large sample sizes the selection estimator performs fairly well. For small sample sizes the tailexponential method is a good alternative. Presenting it and the MLE for the lognormal enables one to assess the potential effects of model uncertainty.
Report for 2003DC40B: Analysis of Positive, Right Skewed, and Unimodal Observations There are no reported publications resulting from this project. Report Follows Estimation of Upper Quantiles Under Model and Parameter Uncertainty
"... In this paper we assess accuracy of some commonly used estimators of upper quantiles of a right skewed distribution under both parameter and model uncertainty. In particular, for each of lognormal, loglogistic, and logdouble exponential distributions, we study the bias and mean squared error of t ..."
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In this paper we assess accuracy of some commonly used estimators of upper quantiles of a right skewed distribution under both parameter and model uncertainty. In particular, for each of lognormal, loglogistic, and logdouble exponential distributions, we study the bias and mean squared error of the maximum likelihood estimator (MLE) of the upper quantiles under both the correct and incorrect model specifications. We also consider two data dependent or adaptive estimators. The first (tail–exponential) is based on fitting an exponential distribution to the highest ten to twenty percent of the data. The second selects the best fitting likelihoodbased model and uses the MLE obtained from that model. The simulation results provide some practical guidance concerning the estimation of the upper quantiles when one is uncertain about the underlying model. We found that the consequences of assuming lognormality when the true distribution is loglogistic or logdouble exponential are not severe in moderate sample sizes. For extreme quantiles, no estimator was reliable in small samples. For large sample sizes the selection estimator performs fairly well. For small sample sizes the tailexponential method is a good alternative. Presenting it and the MLE for the lognormal enables one to assess the potential effects of model uncertainty.
Pages 509–519
, 2000
"... A Bayesian framework for the analysis of microarray expression data: regularized ttest and statistical inferences of gene changes ..."
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A Bayesian framework for the analysis of microarray expression data: regularized ttest and statistical inferences of gene changes