Multidimensional local false discovery rate for microarray studies

MOTIVATION: The false discovery rate (fdr) is a key tool for statistical assessment of differential expression (DE) in microarray studies. Overall control of the fdr alone, however, is not sufficient to address the problem of genes with small variance, which generally suffer from a disproportionally high rate of false positives. It is desirable to have an fdr-controlling procedure that automatically accounts for gene variability. METHODS: We generalize the local fdr as a function of multiple statistics, combining a common test statistic for assessing DE with its standard error information. We use a non-parametric mixture model for DE and non-DE genes to describe the observed multi-dimensional statistics, and estimate the distribution for non-DE genes via the permutation method. We demonstrate this fdr2d approach for simulated and real microarray data. RESULTS: The fdr2d allows objective assessment of DE as a function of gene variability. We also show that the fdr2d performs better than commonly used modified test statistics. AVAILABILITY: An R-package OCplus containing functions for computing fdr2d() and other operating characteristics of microarray data is available at http://www.meb.ki.se/~yudpaw.     

False discovery rate, sensitivity and sample size for microarray studies

MOTIVATION: In microarray data studies most researchers are keenly aware of the potentially high rate of false positives and the need to control it. One key statistical shift is the move away from the well-known P-value to false discovery rate (FDR). Less discussion perhaps has been spent on the sensitivity or the associated false negative rate (FNR). The purpose of this paper is to explain in simple ways why the shift from P-value to FDR for statistical assessment of microarray data is necessary, to elucidate the determining factors of FDR and, for a two-sample comparative study, to discuss its control via sample size at the design stage. RESULTS: We use a mixture model, involving differentially expressed (DE) and non-DE genes, that captures the most common problem of finding DE genes. Factors determining FDR are (1) the proportion of truly differentially expressed genes, (2) the distribution of the true differences, (3) measurement variability and (4) sample size. Many current small microarray studies are plagued with large FDR, but controlling FDR alone can lead to unacceptably large FNR. In evaluating a design of a microarray study, sensitivity or FNR curves should be computed routinely together with FDR curves. Under certain assumptions, the FDR and FNR curves coincide, thus simplifying the choice of sample size for controlling the FDR and FNR jointly.     

Bias in the estimation of false discovery rate in microarray studies

MOTIVATION: The false discovery rate (FDR) provides a key statistical assessment for microarray studies. Its value depends on the proportion pi(0) of non-differentially expressed (non-DE) genes. In most microarray studies, many genes have small effects not easily separable from non-DE genes. As a result, current methods often overestimate pi(0) and FDR, leading to unnecessary loss of power in the overall analysis. METHODS: For the common two-sample comparison we derive a natural mixture model of the test statistic and an explicit bias formula in the standard estimation of pi(0). We suggest an improved estimation of pi(0) based on the mixture model and describe a practical likelihood-based procedure for this purpose. RESULTS: The analysis shows that a large bias occurs when pi(0) is far from 1 and when the non-centrality parameters of the distribution of the test statistic are near zero. The theoretical result also explains substantial discrepancies between non-parametric and model-based estimates of pi(0). Simulation studies indicate mixture-model estimates are less biased than standard estimates. The method is applied to breast cancer and lymphoma data examples. AVAILABILITY: An R-package OCplus containing functions to compute pi(0) based on the mixture model, the resulting FDR and other operating characteristics of microarray data, is freely available at http://www.meb.ki.se/~yudpaw CONTACT: yudi.pawitan@meb.ki.se and alexander.ploner@meb.ki.se.     

Gene discovery in neuropharmacological and behavioral studies using Affymetrix microarray data

We describe methods and software tools for doing data analysis based on Affymetrix microarray data, emphasizing often neglected issues. In our experience with neuroscience studies, experimental design and quality assessment are vital. We also describe in detail the pre-processing methods we have found useful for Affymetrix data. Finally, we summarize the statistical literature and describe some pitfalls in the post-processing analysis.     

Subtraction-coupled custom microarray analysis for gene discovery and gene expression studies in the CNS

The revolution in our knowledge about the genomes of organisms gives rise to the question, what do we do with this information? The development of techniques allowing high throughput analysis of RNA and protein expression, such as cDNA microarrays, provide for genome-wide analysis of gene expression. These analyses will help bridge the gap between systems and molecular neuroscience. This review discusses the advantages of using a subtractive hybridization technique, such as a representational difference analysis, to generate a custom cDNA microarray enriched for genes relevant to investigating complex, heterogeneous tissues such as those involved in the chemical senses. Real and hypothetical examples of these experiments are discussed. Benefits of this approach over traditional microarray techniques include having a more relevant clone set, the potential for gene discovery and the creation of a new tool to investigate similar systems. Potential pitfalls may include PCR artifacts and the need for sequencing. However, these disadvantages can be overcome so that the coupling of subtraction techniques to microarray screening can be a fruitful approach to a variety of experimental systems.     

Identification of differentially expressed genes and false discovery rate in microarray studies

PURPOSE OF REVIEW: To highlight the development in microarray data analysis for the identification of differentially expressed genes, particularly via control of false discovery rate. RECENT FINDINGS: The emergence of high-throughput technology such as microarrays raises two fundamental statistical issues: multiplicity and sensitivity. We focus on the biological problem of identifying differentially expressed genes. First, multiplicity arises due to testing tens of thousands of hypotheses, rendering the standard P value meaningless. Second, known optimal single-test procedures such as the t-test perform poorly in the context of highly multiple tests. The standard approach of dealing with multiplicity is too conservative in the microarray context. The false discovery rate concept is fast becoming the key statistical assessment tool replacing the P value. We review the false discovery rate approach and argue that it is more sensible for microarray data. We also discuss some methods to take into account additional information from the microarrays to improve the false discovery rate. SUMMARY: There is growing consensus on how to analyse microarray data using the false discovery rate framework in place of the classical P value. Further research is needed on the preprocessing of the raw data, such as the normalization step and filtering, and on finding the most sensitive test procedure.     

Query-driven module discovery in microarray data

MOTIVATION: Existing (bi)clustering methods for microarray data analysis often do not answer the specific questions of interest to a biologist. Such specific questions could be derived from other information sources, including expert prior knowledge. More specifically, given a set of seed genes which are believed to have a common function, we would like to recruit genes with similar expression profiles as the seed genes in a significant subset of experimental conditions. RESULTS: We introduce QDB, a novel Bayesian query-driven biclustering framework in which the prior distributions allow introducing knowledge from a set of seed genes (query) to guide the pattern search. In two well-known yeast compendia, we grow highly functionally enriched biclusters from small sets of seed genes using a resolution sweep approach. In addition, relevant conditions are identified and modularity of the biclusters is demonstrated, including the discovery of overlapping modules. Finally, our method deals with missing values naturally, performs well on artificial data from a recent biclustering benchmark study and has a number of conceptual advantages when compared to existing approaches for focused module search.     

Kernel-based distance metric learning for microarray data classification

Background  

The most fundamental task using gene expression data in clinical oncology is to classify tissue samples according to their gene expression levels. Compared with traditional pattern classifications, gene expression-based data classification is typically characterized by high dimensionality and small sample size, which make the task quite challenging.     

A new method for gene discovery in large-scale microarray data

Microarrays are an effective tool for monitoring genome-wide gene expression levels. In current microarray analyses, the majority of genes on arrays are frequently eliminated for further analysis because the changes in their expression levels (ratios) are considered to be not significant. This strategy risks failure to discover whole sets of genes related to a quantitative trait of interest, which is generally controlled by several loci that make various contributions. Here, we describe a high-throughput gene discovery method based on correspondence analysis with a new index for expression ratios [arctan (1/ratio)] and three artificial marker genes. This method allows us to quickly analyze the whole microarray dataset and discover up-/down-regulated genes related to a trait of interest. We employed an example dataset to show the theoretical advantage of this method. We then used the method to identify 88 cancer-related genes from a published microarray data from patients with breast cancer. This method also allows us to predict the phenotype of a given sample from the gene expression profile. This method can be easily performed and the result is also visible in 3D viewing software that we have developed.     

Covariate adjustment in the analysis of microarray data from clinical studies

There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for follow-up validation studies. We develop two approaches to the analysis of microarray data in non-randomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic (ROC) curve for the analysis of gene expression data. The ideas are illustrated using data from a prostate cancer molecular profiling study.     

Comparison of microarray designs for class comparison and class discovery

MOTIVATION: Two-color microarray experiments in which an aliquot derived from a common RNA sample is placed on each array are called reference designs. Traditionally, microarray experiments have used reference designs, but designs without a reference have recently been proposed as alternatives. RESULTS: We develop a statistical model that distinguishes the different levels of variation typically present in cancer data, including biological variation among RNA samples, experimental error and variation attributable to phenotype. Within the context of this model, we examine the reference design and two designs which do not use a reference, the balanced block design and the loop design, focusing particularly on efficiency of estimates and the performance of cluster analysis. We calculate the relative efficiency of designs when there are a fixed number of arrays available, and when there are a fixed number of samples available. Monte Carlo simulation is used to compare the designs when the objective is class discovery based on cluster analysis of the samples. The number of discrepancies between the estimated clusters and the true clusters were significantly smaller for the reference design than for the loop design. The efficiency of the reference design relative to the loop and block designs depends on the relation between inter- and intra-sample variance. These results suggest that if cluster analysis is a major goal of the experiment, then a reference design is preferable. If identification of differentially expressed genes is the main concern, then design selection may involve a consideration of several factors.     

A secreted protein microarray platform for extracellular protein interaction discovery

Characterization of the extracellular protein interactome has lagged far behind that of intracellular proteins, where mass spectrometry and yeast two-hybrid technologies have excelled. Improved methods for identifying receptor-ligand and extracellular matrix protein interactions will greatly accelerate biological discovery in cell signaling and cellular communication. These technologies must be able to identify low-affinity binding events that are often observed between membrane-bound coreceptor molecules during cell-cell or cell-extracellular matrix contact. Here we demonstrate that functional protein microarrays are particularly well-suited for high-throughput screening of extracellular protein interactions. To evaluate the performance of the platform, we screened a set of 89 immunoglobulin (Ig)-type receptors against a highly diverse extracellular protein microarray with 686 genes represented. To enhance detection of low-affinity interactions, we developed a rapid method to assemble bait Fc fusion proteins into multivalent complexes using protein A microbeads. Based on these screens, we developed a statistical methodology for hit calling and identification of nonspecific interactions on protein microarrays. We found that the Ig receptor interactions identified using our methodology are highly specific and display minimal off-target binding, resulting in a 70% true-positive to false-positive hit ratio. We anticipate that these methods will be useful for a wide variety of functional protein microarray users.     

Toxicogenomics in drug discovery: from preclinical studies to clinical trials

Gene expression analysis applied to toxicology studies, also referred to as toxicogenomics, is rapidly being embraced by the pharmaceutical industry as a useful tool to identify safer drugs in a quicker, more cost-effective manner. Studies have already demonstrated the benefits of applying gene expression profiling towards drug safety evaluation, both for identifying mechanisms underlying toxicity, as well as for providing a means to identify safety liabilities early in the drug discovery process. Furthermore, toxicogenomics has the potential to better identify and assess adverse drug reactions of new drug candidates or marketed products in humans. While much still remains to be learned about the relevance and the application of gene expression changes in human toxicology, the next few years should see gene expression technologies applied to more stages and more programs of the drug discovery and development process. This review will focus on how toxicogenomics can or has been applied in drug discovery and development, and will discuss some of the challenges that still remain.     

Binary state pattern clustering: a digital paradigm for class and biomarker discovery in gene microarray studies of cancer.

Class and biomarker discovery continue to be among the preeminent goals in gene microarray studies of cancer. We have developed a new data mining technique, which we call Binary State Pattern Clustering (BSPC) that is specifically adapted for these purposes, with cancer and other categorical datasets. BSPC is capable of uncovering statistically significant sample subclasses and associated marker genes in a completely unsupervised manner. This is accomplished through the application of a digital paradigm, where the expression level of each potential marker gene is treated as being representative of its discrete functional state. Multiple genes that divide samples into states along the same boundaries form a kind of gene-cluster that has an associated sample-cluster. BSPC is an extremely fast deterministic algorithm that scales well to large datasets. Here we describe results of its application to three publicly available oligonucleotide microarray datasets. Using an alpha-level of 0.05, clusters reproducing many of the known sample classifications were identified along with associated biomarkers. In addition, a number of simulations were conducted using shuffled versions of each of the original datasets, noise-added datasets, as well as completely artificial datasets. The robustness of BSPC was compared to that of three other publicly available clustering methods: ISIS, CTWC and SAMBA. The simulations demonstrate BSPC's substantially greater noise tolerance and confirm the accuracy of our calculations of statistical significance.     

Adjustments and measures of differential expression for microarray data

MOTIVATION: Existing analyses of microarray data often incorporate an obscure data normalization procedure applied prior to data analysis. For example, ratios of microarray channels intensities are normalized to have common mean over the set of genes. We made an attempt to understand the meaning of such procedures from the modeling point of view, and to formulate the model assumptions that underlie them. Given a considerable diversity of data adjustment procedures, the question of their performance, comparison and ranking for various microarray experiments was of interest. RESULTS: A two-step statistical procedure is proposed: data transformation (adjustment for slide-specific effect) followed by a statistical test applied to transformed data. Various methods of analysis for differential expression are compared using simulations and real data on colon cancer cell lines. We found that robust categorical adjustments outperform the ones based on a precisely defined stochastic model, including some commonly used procedures.     

An ensemble method for gene discovery based on DNA microarray data

The advent of DNA microarray technology has offered the promise of casting new insights onto deciphering secrets of life by monitoring activities of thousands of genes simultaneously. Current analyses of microarray data focus on precise classification of biological types, for example, tumor versus normal tissues. A further scientific challenging task is to extract disease-relevant genes from the bewildering amounts of raw data, which is one of the most critical themes in the post-genomic era, but it is generally ignored due to lack of an efficient approach. In this paper, we present a novel ensemble method for gene extraction that can be tailored to fulfill multiple biological tasks including (i) precise classification of biological types; (ii) disease gene mining; and (iii) target-driven gene networking. We also give a numerical application for(i) and (ii) using a public microarrary data set and set aside a separate paper to address (iii).     

An ensemble method for gene discovery based on DNA microarray data

DNA microarrays are now able to measure the expressions of thousands of genes simultaneously. These measurements or gene profiling provides a snapshot?of life that maps to a cross section of ge-netic activities in a four-dimension space of time and the biological entity. Although recent microarray ex-periments[1, 2] hold the promise of the innovative tech-nology to cast new insights onto discovery of secrets of life, development of powerful and efficient analysis strategies for microarray dat…     

An a posteriori strategy for enhancing gene discovery in anonymous cDNA microarray experiments

MOTIVATION: Because of the high cost of sequencing, the bulk of gene discovery is performed using anonymous cDNA microarrays. Though the clones on such arrays are easier and cheaper to construct and utilize than unigene and oligonucleotide arrays, they are there in proportion to their corresponding gene expression activity in the tissue being examined. The associated redundancy will be there in any pool of possibly interesting differentially expressed clones identified in a microarray experiment for subsequent sequencing and investigation. An a posteriori sampling strategy is proposed to enhance gene discovery by reducing the impact of the redundancy in the identified pool. RESULTS: The proposed strategy exploits the fact that individual genes that are highly expressed in a tissue are more likely to be present as a number of spots in an anonymous library and, as a direct consequence, are also likely to give higher fluorescence intensity responses when present in a probe in a cDNA microarray experiment. Consequently, spots that respond with low intensities will have a lower redundancy and so should be sequenced in preference to those with the highest intensities. The proposed method, which formalizes how the fluorescence intensity of a spot should be assessed, is validated using actual microarray data, where the sequences of all the clones in the identified pool had been previously determined. For such validations, the concept of a repeat plot is introduced. It is also utilized to visualize and examine different measures for the characterization of fluorescence intensity. In addition, as confirmatory evidence, sequencing from the lowest to the highest intensities in a pool, with all the sequences known, is compared graphically with their random sequencing. The results establish that, in general, the opportunity for gene discovery is enhanced by avoiding the pooling of different biological libraries (because their construction will have involved different hybridization episodes) and concentrating on the clones with lower fluorescence intensities.     

Cluster stability scores for microarray data in cancer studies

Background  

A potential benefit of profiling of tissue samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Hierarchical clustering has been the primary analytical tool used to define disease subtypes from microarray experiments in cancer settings. Assessing cluster reliability poses a major complication in analyzing output from clustering procedures. While most work has focused on estimating the number of clusters in a dataset, the question of stability of individual-level clusters has not been addressed.     

Reproducibility-optimized test statistic for ranking genes in microarray studies

A principal goal of microarray studies is to identify the genes showing differential expression under distinct conditions. In such studies, the selection of an optimal test statistic is a crucial challenge, which depends on the type and amount of data under analysis. While previous studies on simulated or spike-in datasets do not provide practical guidance on how to choose the best method for a given real dataset, we introduce an enhanced reproducibility-optimization procedure, which enables the selection of a suitable gene- anking statistic directly from the data. In comparison with existing ranking methods, the reproducibilityoptimized statistic shows good performance consistently under various simulated conditions and on Affymetrix spike-in dataset. Further, the feasibility of the novel statistic is confirmed in a practical research setting using data from an in-house cDNA microarray study of asthma-related gene expression changes. These results suggest that the procedure facilitates the selection of an appropriate test statistic for a given dataset without relying on a priori assumptions, which may bias the findings and their interpretation. Moreover, the general reproducibilityoptimization procedure is not limited to detecting differential expression only but could be extended to a wide range of other applications as well.