Statistical tests for differential expression in cDNA microarray experiments

Extracting biological information from microarray data requires appropriate statistical methods. The simplest statistical method for detecting differential expression is the t test, which can be used to compare two conditions when there is replication of samples. With more than two conditions, analysis of variance (ANOVA) can be used, and the mixed ANOVA model is a general and powerful approach for microarray experiments with multiple factors and/or several sources of variation.     

Two-part permutation tests for DNA methylation and microarray data

Background  

One important application of microarray experiments is to identify differentially expressed genes. Often, small and negative expression levels were clipped-off to be equal to an arbitrarily chosen cutoff value before a statistical test is carried out. Then, there are two types of data: truncated values and original observations. The truncated values are not just another point on the continuum of possible values and, therefore, it is appropriate to combine two statistical tests in a two-part model rather than using standard statistical methods. A similar situation occurs when DNA methylation data are investigated. In that case, there are null values (undetectable methylation) and observed positive values. For these data, we propose a two-part permutation test.     

Experimental design for gene expression microarrays

We examine experimental design issues arising with gene expression microarray technology. Microarray experiments have multiple sources of variation, and experimental plans should ensure that effects of interest are not confounded with ancillary effects. A commonly used design is shown to violate this principle and to be generally inefficient. We explore the connection between microarray designs and classical block design and use a family of ANOVA models as a guide to choosing a design. We combine principles of good design and A-optimality to give a general set of recommendations for design with microarrays. These recommendations are illustrated in detail for one kind of experimental objective, where we also give the results of a computer search for good designs.     

Design and Analysis of Two-Phase Experiments for Gene Expression Microarrays—Part I

Summary .   Gene expression microarray experiments are intrinsically two-phase experiments. Messenger RNA (mRNA), required for the microarray experiment, must first be derived from plants or animals that are exposed to a set of treatments in a previous experiment (Phase 1). The mRNA is then used in the subsequent laboratory-based microarray experiment (Phase 2) from which gene expression is measured and ultimately analyzed. We show that obtaining a valid test for the effects of treatments on gene expression depends on the design of both the Phase 1 and Phase 2 experiments. Examples show that the multiple dye-swap design at Phase 2 is more robust than the alternating loop design in the absence of prior knowledge of the relative size of variation in the Phase 1 and Phase 2 experiments.     

Design and analysis of two-phase experiments for gene expression microarrays-part I.

Gene expression microarray experiments are intrinsically two-phase experiments. Messenger RNA (mRNA), required for the microarray experiment, must first be derived from plants or animals that are exposed to a set of treatments in a previous experiment (Phase 1). The mRNA is then used in the subsequent laboratory-based microarray experiment (Phase 2) from which gene expression is measured and ultimately analyzed. We show that obtaining a valid test for the effects of treatments on gene expression depends on the design of both the Phase 1 and Phase 2 experiments. Examples show that the multiple dye-swap design at Phase 2 is more robust than the alternating loop design in the absence of prior knowledge of the relative size of variation in the Phase 1 and Phase 2 experiments.     

Parallel multiplicity and error discovery rate (EDR) in microarray experiments

Background  

In microarray gene expression profiling experiments, differentially expressed genes (DEGs) are detected from among tens of thousands of genes on an array using statistical tests. It is important to control the number of false positives or errors that are present in the resultant DEG list. To date, more than 20 different multiple test methods have been reported that compute overall Type I error rates in microarray experiments. However, these methods share the following dilemma: they have low power in cases where only a small number of DEGs exist among a large number of total genes on the array.     

Bayesian hierarchical error model for analysis of gene expression data

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.     

Some statistical issues in microarray gene expression data

In this paper we discuss some of the statistical issues that should be considered when conducting experiments involving microarray gene expression data. We discuss statistical issues related to preprocessing the data as well as the analysis of the data. Analysis of the data is discussed in three contexts: class comparison, class prediction and class discovery. We also review the methods used in two studies that are using microarray gene expression to assess the effect of exposure to radiofrequency (RF) fields on gene expression. Our intent is to provide a guide for radiation researchers when conducting studies involving microarray gene expression data.     

Importance of randomization in microarray experimental designs with Illumina platforms

Measurements of gene expression from microarray experiments are highly dependent on experimental design. Systematic noise can be introduced into the data at numerous steps. On Illumina BeadChips, multiple samples are assayed in an ordered series of arrays. Two experiments were performed using the same samples but different hybridization designs. An experiment confounding genotype with BeadChip and treatment with array position was compared to another experiment in which these factors were randomized to BeadChip and array position. An ordinal effect of array position on intensity values was observed in both experiments. We demonstrate that there is increased rate of false-positive results in the confounded design and that attempts to correct for confounded effects by statistical modeling reduce power of detection for true differential expression. Simple analysis models without post hoc corrections provide the best results possible for a given experimental design. Normalization improved differential expression testing in both experiments but randomization was the most important factor for establishing accurate results. We conclude that lack of randomization cannot be corrected by normalization or by analytical methods. Proper randomization is essential for successful microarray experiments.     

DNA microarray data imputation and significance analysis of differential expression

MOTIVATION: Significance analysis of differential expression in DNA microarray data is an important task. Much of the current research is focused on developing improved tests and software tools. The task is difficult not only owing to the high dimensionality of the data (number of genes), but also because of the often non-negligible presence of missing values. There is thus a great need to reliably impute these missing values prior to the statistical analyses. Many imputation methods have been developed for DNA microarray data, but their impact on statistical analyses has not been well studied. In this work we examine how missing values and their imputation affect significance analysis of differential expression. RESULTS: We develop a new imputation method (LinCmb) that is superior to the widely used methods in terms of normalized root mean squared error. Its estimates are the convex combinations of the estimates of existing methods. We find that LinCmb adapts to the structure of the data: If the data are heterogeneous or if there are few missing values, LinCmb puts more weight on local imputation methods; if the data are homogeneous or if there are many missing values, LinCmb puts more weight on global imputation methods. Thus, LinCmb is a useful tool to understand the merits of different imputation methods. We also demonstrate that missing values affect significance analysis. Two datasets, different amounts of missing values, different imputation methods, the standard t-test and the regularized t-test and ANOVA are employed in the simulations. We conclude that good imputation alleviates the impact of missing values and should be an integral part of microarray data analysis. The most competitive methods are LinCmb, GMC and BPCA. Popular imputation schemes such as SVD, row mean, and KNN all exhibit high variance and poor performance. The regularized t-test is less affected by missing values than the standard t-test. AVAILABILITY: Matlab code is available on request from the authors.     

Microarray standard data set and figures of merit for comparing data processing methods and experiment designs

MOTIVATION: There is a very large and growing level of effort toward improving the platforms, experiment designs, and data analysis methods for microarray expression profiling. Along with a growing richness in the approaches there is a growing confusion among most scientists as to how to make objective comparisons and choices between them for different applications. There is a need for a standard framework for the microarray community to compare and improve analytical and statistical methods. RESULTS: We report on a microarray data set comprising 204 in-situ synthesized oligonucleotide arrays, each hybridized with two-color cDNA samples derived from 20 different human tissues and cell lines. Design of the approximately 24 000 60mer oligonucleotides that report approximately 2500 known genes on the arrays, and design of the hybridization experiments, were carried out in a way that supports the performance assessment of alternative data processing approaches and of alternative experiment and array designs. We also propose standard figures of merit for success in detecting individual differential expression changes or expression levels, and for detecting similarities and differences in expression patterns across genes and experiments. We expect this data set and the proposed figures of merit will provide a standard framework for much of the microarray community to compare and improve many analytical and statistical methods relevant to microarray data analysis, including image processing, normalization, error modeling, combining of multiple reporters per gene, use of replicate experiments, and sample referencing schemes in measurements based on expression change. AVAILABILITY/SUPPLEMENTARY INFORMATION: Expression data and supplementary information are available at http://www.rii.com/publications/2003/HE_SDS.htm     

Statistical methods for analyzing microarray feature data with replications.

Expression levels in oligonucleotide microarray experiments depend on a potentially large number of factors, for example, treatment conditions, different probes, different arrays, and so on. To dissect the effects of these factors on expression levels, fixed-effects ANOVA methods have previously been proposed. Because we are not necessarily interested in estimating the specific effects of different probes and arrays, we propose to treat these as random effects. Then we only need to estimate their means and variances but not the effect of each of their levels; that is, we can work with a much reduced number of parameters and, consequently, higher precision for estimating expression levels. Thus, we developed a mixed-effects ANOVA model with some random and some fixed effects. It automatically accounts for local normalization between different arrays and for background correction. The method was applied to each of the 6,584 genes investigated in a microarray experiment on two mouse cell lines, PA6/S and PA6/8, where PA6/S enhances proliferation of Pre B cells in vitro but PA6/8 does not. To detect a set of differentially expressed genes (multiple testing problem), we applied the method of controlling the false discovery rate (FDR), which successfully identified 207 genes with significantly different expression levels.     

Statistical framework for phylogenomic analysis of gene family expression profiles

Microarray technology has produced massive expression data that are invaluable for investigating the genome-wide evolutionary pattern of gene expression. To this end, phylogenetic expression analysis is highly desirable. On the basis of the Brownian process, we developed a statistical framework (called the E(0) model), assuming the independent expression of evolution between lineages. Several evolutionary mechanisms are integrated to characterize the pattern of expression diversity after gene duplications, including gradual drift and dramatic shift (punctuated equilibrium). When the phylogeny of a gene family is given, we show that the likelihood function follows a multivariate normal distribution; the variance-covariance matrix is determined by the phylogenetic topology and evolutionary parameters. Maximum-likelihood methods for multiple microarray experiments are developed, and likelihood-ratio tests are designed for testing the evolutionary pattern of gene expression. To reconstruct the evolutionary trace of expression diversity after gene (or genome) duplications, we developed a Bayesian-based method and use the posterior mean as predictors. Potential applications in evolutionary genomics are discussed.     

Split-Plot Microarray Experiments

This article focuses on microarray experiments with two or more factors in which treatment combinations of the factors corresponding to the samples paired together onto arrays are not completely random. A main effect of one (or more) factor(s) is confounded with arrays (the experimental blocks). This is called a split-plot microarray experiment. We utilise an analysis of variance (ANOVA) model to assess differentially expressed genes for between-array and within-array comparisons that are generic under a split-plot microarray experiment. Instead of standard t- or F-test statistics that rely on mean square errors of the ANOVA model, we use a robust method, referred to as 'a pooled percentile estimator', to identify genes that are differentially expressed across different treatment conditions. We illustrate the design and analysis of split-plot microarray experiments based on a case application described by Jin et al. A brief discussion of power and sample size for split-plot microarray experiments is also presented.     

Clustering gene expression data based on predicted differential effects of GV interaction

Microarray has become a popular biotechnology in biological and medical research. However, systematic and stochastic variabilities in microarray data are expected and unavoidable, resulting in the problem that the raw measurements have inherent “noise” within microarray experiments. Currently, logarithmic ratios are usually analyzed by various clustering methods directly, which may introduce bias interpretation in identifying groups of genes or samples. In this paper, a statistical method based on mixed model approaches was proposed for microarray data cluster analysis. The underlying rationale of this method is to partition the observed total gene expression level into various variations caused by different factors using an ANOVA model, and to predict the differential effects of GV （gene by variety） interaction using the adjusted unbiased prediction （AUP） method. The predicted GV interaction effects can then be used as the inputs of cluster analysis. We illustrated the application of our method with a gene expression dataset and elucidated the utility of our approach using an external validation.     

NuGO PPS1 mouse study 1: preliminary statistical analysis

Time course experiments are aimed at characterizing the dynamic regulation of gene expression in biological systems. Data are collected at different time points to monitor the dynamic behaviour of gene expression. The NuGO PPS Mouse Study 1 investigates the development of high fat-induced insulin resistance (IR) over time in APOE*3Leiden (E3L) mice. The study consists in a series of analyses at time points, which are crucial in the development of central and peripheral IR. Affymetrix arrays have been made on critical organs. We present the results of the preliminary statistical analysis on these microarray data. We used a non-parametric approach to identify genes the expression of which changed over time, separately for three tissues: liver, muscle and white adipose tissue. We specified for each gene a basic ANOVA model, in order to check the null hypothesis that gene expression did not vary over time. We addressed the multiple tests problem calculating positive false discovery rate and q values for the F test statistics. The appropriateness of the hypothesis of homogeneous variances over time was investigated by mean of the Bartlett’s test for homoschedasticity. This is a relevant point because heteroschedasticity could be indicative of outlying behaviour of some individuals at specific time points. The necessity to use a moderated F test was evaluated. We found that a considerable part of the genes varied expression over time. For part of the genes, the variance of the response was not homogeneous over time. Response differed by tissue.