Outlier sums for differential gene expression analysis

We propose a method for detecting genes that, in a disease group, exhibit unusually high gene expression in some but not all samples. This can be particularly useful in cancer studies, where mutations that can amplify or turn off gene expression often occur in only a minority of samples. In real and simulated examples, the new method often exhibits lower false discovery rates than simple t-statistic thresholding. We also compare our approach to the recent cancer profile outlier analysis proposal of Tomlins and others (2005).     

MOST: detecting cancer differential gene expression

We propose a new statistics for the detection of differentially expressed genes when the genes are activated only in a subset of the samples. Statistics designed for this unconventional circumstance has proved to be valuable for most cancer studies, where oncogenes are activated for a small number of disease samples. Previous efforts made in this direction include cancer outlier profile analysis (Tomlins and others, 2005), outlier sum (Tibshirani and Hastie, 2007), and outlier robust t-statistics (Wu, 2007). We propose a new statistics called maximum ordered subset t-statistics (MOST) which seems to be natural when the number of activated samples is unknown. We compare MOST to other statistics and find that the proposed method often has more power then its competitors.     

GTI: a novel algorithm for identifying outlier gene expression profiles from integrated microarray datasets

Background

Meta-analysis of gene expression microarray datasets presents significant challenges for statistical analysis. We developed and validated a new bioinformatic method for the identification of genes upregulated in subsets of samples of a given tumour type (‘outlier genes’), a hallmark of potential oncogenes.

Methodology

A new statistical method (the gene tissue index, GTI) was developed by modifying and adapting algorithms originally developed for statistical problems in economics. We compared the potential of the GTI to detect outlier genes in meta-datasets with four previously defined statistical methods, COPA, the OS statistic, the t-test and ORT, using simulated data. We demonstrated that the GTI performed equally well to existing methods in a single study simulation. Next, we evaluated the performance of the GTI in the analysis of combined Affymetrix gene expression data from several published studies covering 392 normal samples of tissue from the central nervous system, 74 astrocytomas, and 353 glioblastomas. According to the results, the GTI was better able than most of the previous methods to identify known oncogenic outlier genes. In addition, the GTI identified 29 novel outlier genes in glioblastomas, including TYMS and CDKN2A. The over-expression of these genes was validated in vivo by immunohistochemical staining data from clinical glioblastoma samples. Immunohistochemical data were available for 65% (19 of 29) of these genes, and 17 of these 19 genes (90%) showed a typical outlier staining pattern. Furthermore, raltitrexed, a specific inhibitor of TYMS used in the therapy of tumour types other than glioblastoma, also effectively blocked cell proliferation in glioblastoma cell lines, thus highlighting this outlier gene candidate as a potential therapeutic target.

Conclusions/Significance

Taken together, these results support the GTI as a novel approach to identify potential oncogene outliers and drug targets. The algorithm is implemented in an R package (Text S1).     

An Integrated Approach for Identifying Wrongly Labelled Samples When Performing Classification in Microarray Data

Background

Using hybrid approach for gene selection and classification is common as results obtained are generally better than performing the two tasks independently. Yet, for some microarray datasets, both classification accuracy and stability of gene sets obtained still have rooms for improvement. This may be due to the presence of samples with wrong class labels (i.e. outliers). Outlier detection algorithms proposed so far are either not suitable for microarray data, or only solve the outlier detection problem on their own.

Results

We tackle the outlier detection problem based on a previously proposed Multiple-Filter-Multiple-Wrapper (MFMW) model, which was demonstrated to yield promising results when compared to other hybrid approaches (Leung and Hung, 2010). To incorporate outlier detection and overcome limitations of the existing MFMW model, three new features are introduced in our proposed MFMW-outlier approach: 1) an unbiased external Leave-One-Out Cross-Validation framework is developed to replace internal cross-validation in the previous MFMW model; 2) wrongly labeled samples are identified within the MFMW-outlier model; and 3) a stable set of genes is selected using an L1-norm SVM that removes any redundant genes present. Six binary-class microarray datasets were tested. Comparing with outlier detection studies on the same datasets, MFMW-outlier could detect all the outliers found in the original paper (for which the data was provided for analysis), and the genes selected after outlier removal were proven to have biological relevance. We also compared MFMW-outlier with PRAPIV (Zhang et al., 2006) based on same synthetic datasets. MFMW-outlier gave better average precision and recall values on three different settings. Lastly, artificially flipped microarray datasets were created by removing our detected outliers and flipping some of the remaining samples'' labels. Almost all the ‘wrong’ (artificially flipped) samples were detected, suggesting that MFMW-outlier was sufficiently powerful to detect outliers in high-dimensional microarray datasets.     

Arrow Plot: a new graphical tool for selecting up and down regulated genes and genes differentially expressed on sample subgroups

ABSTRACT: BACKGROUND: A common task in analyzing microarray data is to determine which genes are differentially expressed across two (or more) kind of tissue samples or samples submitted under experimental conditions. Several statistical methods have been proposed to accomplish this goal, generally based on measures of distance between classes. It is well known that biological samples are heterogeneous because of factors such as molecular subtypes or genetic background that are often unknown to the experimenter. For instance, in experiments which involve molecular classification of tumors it is important to identify significant subtypes of cancer. Bimodal or multimodal distributions often reflect the presence of subsamples mixtures. Consequently, there can be genes differentially expressed on sample subgroups which are missed if usual statistical approaches are used. In this paper we propose a new graphical tool which not only identifies genes with up and down regulations, but also genes with differential expression in different subclasses, that are usually missed if current statistical methods are used. This tool is based on two measures of distance between samples, namely the overlapping coefficient (OVL) between two densities and the area under the receiver operating characteristic (ROC) curve. The methodology proposed here was implemented in the open-source R software. RESULTS: This method was applied to a publicly available dataset, as well as to a simulated dataset. We compared our results with the ones obtained using some of the standard methods for detecting differentially expressed genes, namely Welch t-statistic, fold change (FC), rank products (RP), average difference (AD), weighted average difference (WAD), moderated t-statistic (modT), intensity-based moderated t-statistic (ibmT), significance analysis of microarrays (samT) and area under the ROC curve (AUC). On both datasets all differentially expressed genes with bimodal or multimodal distributions were not selected by all standard selection procedures. We also compared our results with (i) area between ROC curve and rising area (ABCR) and (ii) the test for not proper ROC curves (TNRC). We found our methodology more comprehensive, because it detects both bimodal and multimodal distributions and different variances can be considered on both samples. Another advantage of our method is that we can analyze graphically the behavior of different kinds of differentially expressed genes. CONCLUSION: Our results indicate that the arrow plot represents a new flexible and useful tool for the analysis of gene expression profiles from microarrays.     

An Iterative Leave-One-Out Approach to Outlier Detection in RNA-Seq Data

The discrete data structure and large sequencing depth of RNA sequencing (RNA-seq) experiments can often generate outlier read counts in one or more RNA samples within a homogeneous group. Thus, how to identify and manage outlier observations in RNA-seq data is an emerging topic of interest. One of the main objectives in these research efforts is to develop statistical methodology that effectively balances the impact of outlier observations and achieves maximal power for statistical testing. To reach that goal, strengthening the accuracy of outlier detection is an important precursor. Current outlier detection algorithms for RNA-seq data are executed within a testing framework and may be sensitive to sparse data and heavy-tailed distributions. Therefore, we propose a univariate algorithm that utilizes a probabilistic approach to measure the deviation between an observation and the distribution generating the remaining data and implement it within in an iterative leave-one-out design strategy. Analyses of real and simulated RNA-seq data show that the proposed methodology has higher outlier detection rates for both non-normalized and normalized negative binomial distributed data.     

Comparing parasite numbers between samples of hosts

The comparison of parasite numbers or intensities between different samples of hosts is a common and important question in most parasitological studies. The main question is whether the values in one sample tend to be higher (or lower) than the values of the other sample. We argue that it is more appropriate to test a null hypothesis about the probability that an individual host from one sample has a higher value than individual hosts from a second sample rather than testing hypotheses about means or medians. We present a recently proposed statistical test especially designed to test hypotheses about that probability. This novel test is more appropriate than other statistical tests, such as Student's t-test, the Mann-Whitney U-test, or a bootstrap test based on Welch's t-statistic, regularly used by parasitologists.     

GPHMM: an integrated hidden Markov model for identification of copy number alteration and loss of heterozygosity in complex tumor samples using whole genome SNP arrays

There is an increasing interest in using single nucleotide polymorphism (SNP) genotyping arrays for profiling chromosomal rearrangements in tumors, as they allow simultaneous detection of copy number and loss of heterozygosity with high resolution. Critical issues such as signal baseline shift due to aneuploidy, normal cell contamination, and the presence of GC content bias have been reported to dramatically alter SNP array signals and complicate accurate identification of aberrations in cancer genomes. To address these issues, we propose a novel Global Parameter Hidden Markov Model (GPHMM) to unravel tangled genotyping data generated from tumor samples. In contrast to other HMM methods, a distinct feature of GPHMM is that the issues mentioned above are quantitatively modeled by global parameters and integrated within the statistical framework. We developed an efficient EM algorithm for parameter estimation. We evaluated performance on three data sets and show that GPHMM can correctly identify chromosomal aberrations in tumor samples containing as few as 10% cancer cells. Furthermore, we demonstrated that the estimation of global parameters in GPHMM provides information about the biological characteristics of tumor samples and the quality of genotyping signal from SNP array experiments, which is helpful for data quality control and outlier detection in cohort studies.     

Detection of outlier residues for improving interface prediction in protein heterocomplexes

Sequence-based understanding and identification of protein binding interfaces is a challenging research topic due to the complexity in protein systems and the imbalanced distribution between interface and noninterface residues. This paper presents an outlier detection idea to address the redundancy problem in protein interaction data. The cleaned training data are then used for improving the prediction performance. We use three novel measures to describe the extent a residue is considered as an outlier in comparison to the other residues: the distance of a residue instance from the center instance of all residue instances of the same class label (Dist), the probability of the class label of the residue instance (PCL), and the importance of within-class and between-class (IWB) residue instances. Outlier scores are computed by integrating the three factors; instances with a sufficiently large score are treated as outliers and removed. The data sets without outliers are taken as input for a support vector machine (SVM) ensemble. The proposed SVM ensemble trained on input data without outliers performs better than that with outliers. Our method is also more accurate than many literature methods on benchmark data sets. From our empirical studies, we found that some outlier interface residues are truly near to noninterface regions, and some outlier noninterface residues are close to interface regions.     

Spatial detection of outlier loci with Moran eigenvector maps

The spatial signature of microevolutionary processes structuring genetic variation may play an important role in the detection of loci under selection. However, the spatial location of samples has not yet been used to quantify this. Here, we present a new two‐step method of spatial outlier detection at the individual and deme levels using the power spectrum of Moran eigenvector maps (MEM). The MEM power spectrum quantifies how the variation in a variable, such as the frequency of an allele at a SNP locus, is distributed across a range of spatial scales defined by MEM spatial eigenvectors. The first step (Moran spectral outlier detection: MSOD) uses genetic and spatial information to identify outlier loci by their unusual power spectrum. The second step uses Moran spectral randomization (MSR) to test the association between outlier loci and environmental predictors, accounting for spatial autocorrelation. Using simulated data from two published papers, we tested this two‐step method in different scenarios of landscape configuration, selection strength, dispersal capacity and sampling design. Under scenarios that included spatial structure, MSOD alone was sufficient to detect outlier loci at the individual and deme levels without the need for incorporating environmental predictors. Follow‐up with MSR generally reduced (already low) false‐positive rates, though in some cases led to a reduction in power. The results were surprisingly robust to differences in sample size and sampling design. Our method represents a new tool for detecting potential loci under selection with individual‐based and population‐based sampling by leveraging spatial information that has hitherto been neglected.     

Outlier Detection using Projection Quantile Regression for Mass Spectrometry Data with Low Replication

ABSTRACT: BACKGROUND: Mass spectrometry (MS) data are often generated from various biological or chemical experiments and there may exist outlying observations, which are extreme due to technical reasons. The determination of outlying observations is important in the analysis of replicated MS data because elaborate pre-processing is essential for successful analysis with reliable results and manual outlier detection as one of pre-processing steps is time-consuming. The heterogeneity of variability and low replication are often obstacles to successful analysis, including outlier detection. Existing approaches, which assume constant variability, can generate many false positives (outliers) and/or false negatives non-outliers). Thus, a more powerful and accurate approach is needed to account for the heterogeneity of variability and low replication. FINDINGS: We proposed an outlier detection algorithm using projection and quantile regression in MS data from multiple experiments. The performance of the algorithm and program was demonstrated by using both simulated and real-life data. The projection approach with linear, nonlinear, or nonparametric quantile regression was appropriate in heterogeneous high-throughput data with low replication. CONCLUSION: Various quantile regression approaches combined with projection were proposed for detecting outliers. The choice among linear, nonlinear, and nonparametric regressions is dependent on the degree of heterogeneity of the data. The proposed approach was illustrated with MS data with two or more replicates.     

Coordinate-independent mapping of structural and functional data by objective relational transformation (ORT)

Neuroscience has produced an enormous amount of structural and functional data. Powerful database systems are required to make these data accessible for computational approaches such as higher-order analyses and simulations. Available databases for key data such as anatomical and functional connectivity between cortical areas, however, are still hampered by methodological problems. These problems arise predominantly from the parcellation problem, the use of incongruent parcellation schemes by different authors. We here present a coordinate-independent mathematical method to overcome this problem: objective relational transformation (ORT). Based on new classifications for brain data and on methods from theoretical computer science, ORT represents a formally defined, transparent transformation method for reproducible, coordinate-independent mapping of brain data to freely chosen parcellation schemes. We describe the methodology of ORT and discuss its strengths and limitations. Using two practical examples, we show that ORT in conjunction with connectivity databases like CoCoMac (http://www.cocomac.org) is an important tool for analyses of cortical organization and structure-function relationships.     

Outlier Analysis Defines Zinc Finger Gene Family DNA Methylation in Tumors and Saliva of Head and Neck Cancer Patients

Head and Neck Squamous Cell Carcinoma (HNSCC) is the fifth most common cancer, annually affecting over half a million people worldwide. Presently, there are no accepted biomarkers for clinical detection and surveillance of HNSCC. In this work, a comprehensive genome-wide analysis of epigenetic alterations in primary HNSCC tumors was employed in conjunction with cancer-specific outlier statistics to define novel biomarker genes which are differentially methylated in HNSCC. The 37 identified biomarker candidates were top-scoring outlier genes with prominent differential methylation in tumors, but with no signal in normal tissues. These putative candidates were validated in independent HNSCC cohorts from our institution and TCGA (The Cancer Genome Atlas). Using the top candidates, ZNF14, ZNF160, and ZNF420, an assay was developed for detection of HNSCC cancer in primary tissue and saliva samples with 100% specificity when compared to normal control samples. Given the high detection specificity, the analysis of ZNF DNA methylation in combination with other DNA methylation biomarkers may be useful in the clinical setting for HNSCC detection and surveillance, particularly in high-risk patients. Several additional candidates identified through this work can be further investigated toward future development of a multi-gene panel of biomarkers for the surveillance and detection of HNSCC.     

Simple outlier detection for a multi-environmental field trial

The aim of plant breeding trials is often to identify crop variety that are well adapt to target environments. These varieties are identified through genomic prediction from the analysis of multi-environmental field trial (MET) using linear mixed models. The occurrence of outliers in MET is common and known to adversely impact the accuracy of genomic prediction yet the detection of outliers are often neglected. A number of reasons stand for this—first, complex data such as a MET give rise to distinct levels of residuals (eg, at a trial level or individual observation level). This complexity offers additional challenges for an outlier detection method. Second, many linear mixed model software packages that cater for complex variance structures needed in the analysis of MET are not well streamlined for diagnostics by practitioners. We demonstrate outlier detection methods that are simple to implement in any linear mixed model software packages and computationally fast. Although these methods are not optimal methods in outlier detection, they offer practical value for ease of application in the analysis pipeline of regularly collected data. These are demonstrated using simulation based on two real bread wheat yield METs. In particular, models that consider analysis of yield trials either independently or jointly (thus borrowing strength across trials) are considered. Case studies are presented to highlight benefit of joint analysis for outlier detection.     

A note on using permutation-based false discovery rate estimates to compare different analysis methods for microarray data

MOTIVATION: False discovery rate (FDR) is defined as the expected percentage of false positives among all the claimed positives. In practice, with the true FDR unknown, an estimated FDR can serve as a criterion to evaluate the performance of various statistical methods under the condition that the estimated FDR approximates the true FDR well, or at least, it does not improperly favor or disfavor any particular method. Permutation methods have become popular to estimate FDR in genomic studies. The purpose of this paper is 2-fold. First, we investigate theoretically and empirically whether the standard permutation-based FDR estimator is biased, and if so, whether the bias inappropriately favors or disfavors any method. Second, we propose a simple modification of the standard permutation to yield a better FDR estimator, which can in turn serve as a more fair criterion to evaluate various statistical methods. RESULTS: Both simulated and real data examples are used for illustration and comparison. Three commonly used test statistics, the sample mean, SAM statistic and Student's t-statistic, are considered. The results show that the standard permutation method overestimates FDR. The overestimation is the most severe for the sample mean statistic while the least for the t-statistic with the SAM-statistic lying between the two extremes, suggesting that one has to be cautious when using the standard permutation-based FDR estimates to evaluate various statistical methods. In addition, our proposed FDR estimation method is simple and outperforms the standard method.     

Outlier SNPs show more genetic structure between two Bay of Fundy metapopulations of Atlantic salmon than do neutral SNPs

Atlantic salmon of Eastern Canada were once of considerable importance to aboriginal, recreational, and commercial fisheries, yet many populations are now in decline, particularly those of the inner Bay of Fundy (iBoF), which were recently listed as endangered. We investigated whether nonneutral SNPs could be used to assign individual Atlantic salmon accurately to either the iBoF or the outer Bay of Fundy (oBoF) metapopulations because this has been difficult with existing neutral markers. We first searched for markers under diversifying selection by genotyping eight captively bred Bay of Fundy (BoF) populations for 320 SNP loci with the Sequenom MassARRAY? system and then analysed the data set with four different F(ST) outlier detection programs. Three outlier loci were identified by both BayesFST and BayeScan whereas seven outlier loci, including the three previously mentioned, were identified by both Fdist and Arlequin. A subset of 14 nonneutral SNPs was more accurate (85% accuracy) than a subset of 67 neutral SNPs (75% accuracy) at assigning individual salmon back to their metapopulation. We then chose a subset of nine outlier SNP markers and used them to inexpensively genotype archived DNA samples from seven wild BoF populations using Invader? chemistry. Hierarchical AMOVA of these independent wild samples corroborated our previous findings of significant genetic differentiation between iBoF and oBoF salmon metapopulations. Our research shows that identifying and using outlier loci is an important step towards achieving the goal of consistently and accurately distinguishing iBoF from oBoF Atlantic salmon, which will aid in their conservation.     

Challenges and pitfalls in the characterization of anonymous outlier AFLP markers in non-model species: lessons from an ocellated lizard genome scan

In the last few years, dozens of studies have documented the detection of loci influenced by selection from genome scans in a wide range of non-model species. Many of those studies used amplified fragment length polymorphism (AFLP) markers, which became popular for being easily applicable to any organism. However, because they are anonymous markers, AFLPs impose many challenges for their isolation and identification. Most recent AFLP genome scans used capillary electrophoresis (CE), which adds even more obstacles to the isolation of bands with a specific size for sequencing. These caveats might explain the extremely low number of studies that moved from the detection of outlier AFLP markers to their actual isolation and characterization. We document our efforts to characterize a set of outlier AFLP markers from a previous genome scan with CE in ocellated lizards (Lacerta lepida). Seven outliers were successfully isolated, cloned and sequenced. Their sequences are noncoding and show internal indels or polymorphic repetitive elements (microsatellites). Three outliers were converted into codominant markers by using specific internal primers to sequence and screen population variability from undigested DNA. Amplification in closely related lizard species was also achieved, revealing remarkable interspecific conservation in outlier loci sequences. We stress the importance of following up AFLP genome scans to validate selection signatures of outlier loci, but also report the main challenges and pitfalls that may be faced during the process.     

Procedure for Detecting Outliers in a Circular Regression Model

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.