A mixture model for estimating the local false discovery rate in DNA microarray analysis

MOTIVATION: Statistical methods based on controlling the false discovery rate (FDR) or positive false discovery rate (pFDR) are now well established in identifying differentially expressed genes in DNA microarray. Several authors have recently raised the important issue that FDR or pFDR may give misleading inference when specific genes are of interest because they average the genes under consideration with genes that show stronger evidence for differential expression. The paper proposes a flexible and robust mixture model for estimating the local FDR which quantifies how plausible each specific gene expresses differentially. RESULTS: We develop a special mixture model tailored to multiple testing by requiring the P-value distribution for the differentially expressed genes to be stochastically smaller than the P-value distribution for the non-differentially expressed genes. A smoothing mechanism is built in. The proposed model gives robust estimation of local FDR for any reasonable underlying P-value distributions. It also provides a single framework for estimating the proportion of differentially expressed genes, pFDR, negative predictive values, sensitivity and specificity. A cervical cancer study shows that the local FDR gives more specific and relevant quantification of the evidence for differential expression that can be substantially different from pFDR. AVAILABILITY: An R function implementing the proposed model is available at http://www.geocities.com/jg_liao/software     

Evaluation of DNA microarray results with quantitative gene expression platforms

We have evaluated the performance characteristics of three quantitative gene expression technologies and correlated their expression measurements to those of five commercial microarray platforms, based on the MicroArray Quality Control (MAQC) data set. The limit of detection, assay range, precision, accuracy and fold-change correlations were assessed for 997 TaqMan Gene Expression Assays, 205 Standardized RT (Sta)RT-PCR assays and 244 QuantiGene assays. TaqMan is a registered trademark of Roche Molecular Systems, Inc. We observed high correlation between quantitative gene expression values and microarray platform results and found few discordant measurements among all platforms. The main cause of variability was differences in probe sequence and thus target location. A second source of variability was the limited and variable sensitivity of the different microarray platforms for detecting weakly expressed genes, which affected interplatform and intersite reproducibility of differentially expressed genes. From this analysis, we conclude that the MAQC microarray data set has been validated by alternative quantitative gene expression platforms thus supporting the use of microarray platforms for the quantitative characterization of gene expression.     

CDS: a fold-change based statistical test for concomitant identification of distinctness and similarity in gene expression analysis

The problem of identifying differential activity such as in gene expression is a major defeat in biostatistics and bioinformatics.Equally important,however much less frequently studied,is the question of similar activity from one biological condition to another.The foldchange,or ratio,is usually considered a relevant criterion for stating difference and similarity between measurements.Importantly,no statistical method for concomitant evaluation of similarity and distinctness currently exists for biological applications.Modem microarray,digital PCR(dPCR),and Next-Generation Sequencing(NGS) technologies frequently provide a means of coefficient of variation estimation for individual measurements.Using fold-change,and by making the assumption that measurements are normally distributed with known variances,we designed a novel statistical test that allows us to detect concomitantly,thus using the same formalism,differentially and similarly expressed genes(http://cds.ihes.fr).Given two sets of gene measurements in different biological conditions,the probabilities of making type I and type II errors in stating that a gene is differentially or similarly expressed from one condition to the other can be calculated.Furthermore,a confidence interval for the fold-change can be delineated.Finally,we demonstrate that the assumption of normality can be relaxed to consider arbitrary distributions numerically.The Concomitant evaluation of Distinctness and Similarity(CDS) statistical test correctly estimates similarities and differences between measurements of gene expression.The implementation,being time and memory efficient,allows the use of the CDS test in high-throughput data analysis such as microarray,dPCR,and NGS experiments.Importantly,the CDS test can be applied to the comparison of single measurements(N:1) provided the variance(or coefficient of variation) of the signals is known,making CDS a valuable tool also in biomedical analysis where typically a single measurement per subject is available.     

多重检验法在基因芯片研究中鉴定差异表达基因的统计功效

鉴于基因芯片实验的造价,在基因芯片实验设计中,首要考虑的因素是需要多少重复才能检测出一个具有显著差异表达的基因。计算多重检验法要求的重复数（样本大小）或功效可为基因芯片实验设计提供重要的参考。为此,本文基于置换重抽样法构建了一种基因表达噪声混合分布模型。该方法适用各类基因表达数据,即无论是基因表达单噪声源或是多噪声源都可行。应用混合模型和多重检验法并给定统计功效。研究者能在基因芯片实验中获得所需要的最少生物学重复数：或者根据样本大小来确定测定一个显著差异表达的基因所具有的检验功效;或者根据样本大小和统计检验功效,选择最好的统计测验方法。本文以一组在老鼠中与中风有关的3000个基因的基因芯片实验所获得的数据为例,应用该方法拟和后组建了一个单分布模型（即表达单噪声源的分布模型）。根据该模型,我们计算了4种多重检验法在鉴定一个具有表达差异（D）值的基因中所需要的统计功效。结果表明。检测一个小的差异D值,4种多重检验法中B方法的统计功效最低,而BH方法最高。但是,对于鉴定一个具有最大表达差异的基因时,4种方法有相同的鉴定功效。与传统的单个检验法一样,BH方法检测一个小的变化所需要的效率不会随基因数目增加而改变,其他3种多重检验法的检测功效则随基因数目增加而降低。     

Powers of Multiple-Testing Procedures for Identification of Genes Significantly Differentially Expressed in Microarray Experiments

Because of the high operation costs involved in microarray experiments, the determination of the number of replicates required to detect a gene significantly differentially expressed in a given multiple-testing procedure is of considerable significance. Calculation of power/replicate numbers required in multiple-testing procedures provides design guidance for microarray experiments. Based on this model and by choice of a multiple-testing procedure, expression noises based on permutation resampling can be considerably minimized. The method for mixture distribution model is suitable to various microarray data types obtained from single noise sources, or from multiple noise sources. By using the biological replicate number required in microarray experiments for a given power or by determining the power required to detect a gene significantly differentially expressed, given the sample size, or the best multiple-testing method can be chosen. As an example, a single-distribution model of t-statistic was fitted to an observed microarray dataset of 3 000 genes responsive to stroke in rat, and then used to calculate powers of four popular multiple-testing procedures to detect a gene of an expression change D. The results show that the B-procedure had the lowest power to detect a gene of small change among the multiple-testing procedures, whereas the BH-procedure had the highest power. However, all multiple-testing procedures had the same power to identify a gene having the largest change. Similar to a single test, the power of the BH-procedure to detect a small change does not vary as the number of genes increases, but powers of the other three multiple-testing procedures decline as the number of genes increases.     

Rat toxicogenomic study reveals analytical consistency across microarray platforms

To validate and extend the findings of the MicroArray Quality Control (MAQC) project, a biologically relevant toxicogenomics data set was generated using 36 RNA samples from rats treated with three chemicals (aristolochic acid, riddelliine and comfrey) and each sample was hybridized to four microarray platforms. The MAQC project assessed concordance in intersite and cross-platform comparisons and the impact of gene selection methods on the reproducibility of profiling data in terms of differentially expressed genes using distinct reference RNA samples. The real-world toxicogenomic data set reported here showed high concordance in intersite and cross-platform comparisons. Further, gene lists generated by fold-change ranking were more reproducible than those obtained by t-test P value or Significance Analysis of Microarrays. Finally, gene lists generated by fold-change ranking with a nonstringent P-value cutoff showed increased consistency in Gene Ontology terms and pathways, and hence the biological impact of chemical exposure could be reliably deduced from all platforms analyzed.     

Empirical validation of the S-Score algorithm in the analysis of gene expression data

Background

Current methods of analyzing Affymetrix GeneChip^® microarray data require the estimation of probe set expression summaries, followed by application of statistical tests to determine which genes are differentially expressed. The S-Score algorithm described by Zhang and colleagues is an alternative method that allows tests of hypotheses directly from probe level data. It is based on an error model in which the detected signal is proportional to the probe pair signal for highly expressed genes, but approaches a background level (rather than 0) for genes with low levels of expression. This model is used to calculate relative change in probe pair intensities that converts probe signals into multiple measurements with equalized errors, which are summed over a probe set to form the S-Score. Assuming no expression differences between chips, the S-Score follows a standard normal distribution, allowing direct tests of hypotheses to be made. Using spike-in and dilution datasets, we validated the S-Score method against comparisons of gene expression utilizing the more recently developed methods RMA, dChip, and MAS5.

Results

The S-score showed excellent sensitivity and specificity in detecting low-level gene expression changes. Rank ordering of S-Score values more accurately reflected known fold-change values compared to other algorithms.

Conclusion

The S-score method, utilizing probe level data directly, offers significant advantages over comparisons using only probe set expression summaries.     

Thresholding rules for recovering a sparse signal from microarray experiments

We consider array experiments that compare expression levels of a high number of genes in two cell lines with few repetitions and with no subject effect. We develop a statistical model that illustrates under which assumptions thresholding is optimal in the analysis of such microarray data. The results of our model explain the success of the empirical rule of two-fold change. We illustrate a thresholding procedure that is adaptive to the noise level of the experiment, the amount of genes analyzed, and the amount of genes that truly change expression level. This procedure, in a world of perfect knowledge on noise distribution, would allow reconstruction of a sparse signal, minimizing the false discovery rate. Given the amount of information actually available, the thresholding rule described provides a reasonable estimator for the change in expression of any gene in two compared cell lines.     

How many differentially expressed genes: A perspective from the comparison of genotypic and phenotypic distances

Identifying differentially expressed genes is critical in microarray data analysis. Many methods have been developed by combining p-value, fold-change, and various statistical models to determine these genes. When using these methods, it is necessary to set up various pre-determined cutoff values. However, many of these cutoff values are somewhat arbitrary and may not have clear connections to biology. In this study, a genetic distance method based on gene expression level was developed to analyze eight sets of microarray data extracted from the GEO database. Since the genes used in distance calculation have been ranked by fold-change, the genetic distance becomes more stable when adding more genes in the calculation, indicating there is an optimal set of genes which are sufficient to characterize the stable difference between samples. This set of genes is differentially expressed genes representing both the genotypic and phenotypic differences between samples.     

Statistical analysis of a small set of time-ordered gene expression data using linear splines

MOTIVATION: Recently, the temporal response of genes to changes in their environment has been investigated using cDNA microarray technology by measuring the gene expression levels at a small number of time points. Conventional techniques for time series analysis are not suitable for such a short series of time-ordered data. The analysis of gene expression data has therefore usually been limited to a fold-change analysis, instead of a systematic statistical approach. METHODS: We use the maximum likelihood method together with Akaike's Information Criterion to fit linear splines to a small set of time-ordered gene expression data in order to infer statistically meaningful information from the measurements. The significance of measured gene expression data is assessed using Student's t-test. RESULTS: Previous gene expression measurements of the cyanobacterium Synechocystis sp. PCC6803 were reanalyzed using linear splines. The temporal response was identified of many genes that had been missed by a fold-change analysis. Based on our statistical analysis, we found that about four gene expression measurements or more are needed at each time point.     

Rosetta error model for gene expression analysis

MOTIVATION: In microarray gene expression studies, the number of replicated microarrays is usually small because of cost and sample availability, resulting in unreliable variance estimation and thus unreliable statistical hypothesis tests. The unreliable variance estimation is further complicated by the fact that the technology-specific variance is intrinsically intensity-dependent. RESULTS: The Rosetta error model captures the variance-intensity relationship for various types of microarray technologies, such as single-color arrays and two-color arrays. This error model conservatively estimates intensity error and uses this value to stabilize the variance estimation. We present two commonly used error models: the intensity error-model for single-color microarrays and the ratio error model for two-color microarrays or ratios built from two single-color arrays. We present examples to demonstrate the strength of our error models in improving statistical power of microarray data analysis, particularly, in increasing expression detection sensitivity and specificity when the number of replicates is limited.     

Differential gene expression in disease: a comparison between high-throughput studies and the literature

Background

Differential gene expression is important to understand the biological differences between healthy and diseased states. Two common sources of differential gene expression data are microarray studies and the biomedical literature.

Methods

With the aid of text mining and gene expression analysis we have examined the comparative properties of these two sources of differential gene expression data.

Results

The literature shows a preference for reporting genes associated to higher fold changes in microarray data, rather than genes that are simply significantly differentially expressed. Thus, the resemblance between the literature and microarray data increases when the fold-change threshold for microarray data is increased. Moreover, the literature has a reporting preference for differentially expressed genes that (1) are overexpressed rather than underexpressed; (2) are overexpressed in multiple diseases; and (3) are popular in the biomedical literature at large. Additionally, the degree to which diseases are similar depends on whether microarray data or the literature is used to compare them. Finally, vaguely-qualified reports of differential expression magnitudes in the literature have only small correlation with microarray fold-change data.

Conclusions

Reporting biases of differential gene expression in the literature can be affecting our appreciation of disease biology and of the degree of similarity that actually exists between different diseases.

     

Local-pooled-error test for identifying differentially expressed genes with a small number of replicated microarrays

MOTIVATION: In microarray studies gene discovery based on fold-change values is often misleading because error variability for each gene is heterogeneous under different biological conditions and intensity ranges. Several statistical testing methods for differential gene expression have been suggested, but some of these approaches are underpowered and result in high false positive rates because within-gene variance estimates are based on a small number of replicated arrays. RESULTS: We propose to use local-pooled-error (LPE) estimates and robust statistical tests for evaluating significance of each gene's differential expression. Our LPE estimation is based on pooling errors within genes and between replicate arrays for genes in which expression values are similar. We have applied our LPE method to compare gene expression in na?ve and activated CD8+ T-cells. Our results show that the LPE method effectively identifies significant differential-expression patterns with a small number of replicated arrays. AVAILABILITY: The methodology is implemented with S-PLUS and R functions available at http://hesweb1.med.virginia.edu/bioinformatics     

Proof of the Concept to Use a Malignant B Cell Line Drug Screen Strategy for Identification and Weight of Melphalan Resistance Genes in Multiple Myeloma

In a conceptual study of drug resistance we have used a preclinical model of malignant B-cell lines by combining drug induced growth inhibition and gene expression profiling. In the current report a melphalan resistance profile of 19 genes were weighted by microarray data from the MRC Myeloma IX trial and time to progression following high dose melphalan, to generate an individual melphalan resistance index. The resistance index was subsequently validated in the HOVON65/GMMG-HD4 trial data set to prove the concept. Biologically, the assigned resistance indices were differentially distributed among translocations and cyclin D expression classes. Clinically, the 25% most melphalan resistant, the intermediate 50% and the 25% most sensitive patients had a median progression free survival of 18, 32 and 28 months, respectively (log-rank P-value  = 0.05). Furthermore, the median overall survival was 45 months for the resistant group and not reached for the intermediate and sensitive groups (log-rank P-value  = 0.003) following 38 months median observation. In a multivariate analysis, correcting for age, sex and ISS-staging, we found a high resistance index to be an independent variable associated with inferior progression free survival and overall survival. This study provides clinical proof of concept to use in vitro drug screen for identification of melphalan resistance gene signatures for future functional analysis.     

Mouse strain specific gene expression differences for illumina microarray expression profiling in embryos

ABSTRACT: BACKGROUND: In the field of mouse genetics the advent of technologies like microarray based expression profiling dramatically increased data availability and sensitivity, yet these advanced methods are often vulnerable to the unavoidable heterogeneity of in vivo material and might therefore reflect differentially expressed genes between mouse strains of no relevance to a targeted experiment. The aim of this study was not to elaborate on the usefulness of microarray analysis in general, but to expand our knowledge regarding this potential "background noise" for the widely used Illumina microarray platform surpassing existing data which focused primarily on the adult sensory and nervous system, by analyzing patterns of gene expression at different embryonic stages using wild type strains and modern transgenic models of often non-isogenic backgrounds. RESULTS: Wild type embryos of 11 mouse strains commonly used in transgenic and molecular genetic studies at three developmental time points were subjected to Illumina microarray expression profiling in a strain-by-strain comparison. Our data robustly reflects known gene expression patterns during mid-gestation development. Decreasing diversity of the input tissue and/or increasing strain diversity raised the sensitivity of the array towards the genetic background. Consistent strain sensitivity of some probes was attributed to genetic polymorphisms or probe design related artifacts. CONCLUSION: Our study provides an extensive reference list of gene expression profiling background noise of value to anyone in the field of developmental biology and transgenic research performing microarray expression profiling with the widely used Illumina microarray platform. Probes identified as strain specific background noise further allow for microarray expression profiling on its own to be a valuable tool for establishing genealogies of mouse inbred strains.