MOTIVATION: RNA expression at isoform level is biologically more informative than at gene level and can potentially reveal cellular subsets and corresponding biomarkers that are not visible at gene level. However, due to the strong 3' bias sequencing protocol, mRNA quantification for high-throughput single-cell RNA sequencing such as Chromium Single Cell 3' 10× Genomics is currently performed at the gene level. RESULTS: We have developed an isoform-level quantification method for high-throughput single-cell RNA sequencing by exploiting the concepts of transcription clusters and isoform paralogs. The method, called Scasa, compares well in simulations against competing approaches including Alevin, Cellranger, Kallisto, Salmon, Terminus and STARsolo at both isoform- and gene-level expression. The reanalysis of a CITE-Seq dataset with isoform-based Scasa reveals a subgroup of CD14 monocytes missed by gene-based methods. AVAILABILITY AND IMPLEMENTATION: Implementation of Scasa including source code, documentation, tutorials and test data supporting this study is available at Github: https://github.com/eudoraleer/scasa and Zenodo: https://doi.org/10.5281/zenodo.5712503. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Circular RNA (circRNA) is an emerging class of RNA molecules attracting researchers due to its potential for serving as markers for diagnosis, prognosis, or therapeutic targets of cancer, cardiovascular, and autoimmune diseases. Current methods for detection of circRNA from RNA sequencing (RNA-seq) focus mostly on improving mapping quality of reads supporting the back-splicing junction (BSJ) of a circRNA to eliminate false positives (FPs). We show that mapping information alone often cannot predict if a BSJ-supporting read is derived from a true circRNA or not, thus increasing the rate of FP circRNAs. RESULTS: We have developed Circall, a novel circRNA detection method from RNA-seq. Circall controls the FPs using a robust multidimensional local false discovery rate method based on the length and expression of circRNAs. It is computationally highly efficient by using a quasi-mapping algorithm for fast and accurate RNA read alignments. We applied Circall on two simulated datasets and three experimental datasets of human cell-lines. The results show that Circall achieves high sensitivity and precision in the simulated data. In the experimental datasets it performs well against current leading methods. Circall is also substantially faster than the other methods, particularly for large datasets. CONCLUSIONS: With those better performances in the detection of circRNAs and in computational time, Circall facilitates the analyses of circRNAs in large numbers of samples. Circall is implemented in C++ and R, and available for use at https://www.meb.ki.se/sites/biostatwiki/circall and https://github.com/datngu/Circall.

MOTIVATION: Estimation of isoform-level gene expression from RNA-seq data depends on simplifying assumptions, such as uniform read distribution, that are easily violated in real data. Such violations typically lead to biased estimates. Most existing methods provide bias correction step(s), which is based on biological considerations-such as GC content-and applied in single samples separately. The main problem is that not all biases are known. RESULTS: We have developed a novel method called XAEM based on a more flexible and robust statistical model. Existing methods are essentially based on a linear model Xβ, where the design matrix X is known and is computed based on the simplifying assumptions. In contrast XAEM considers Xβ as a bilinear model with both X and β unknown. Joint estimation of X and β is made possible by a simultaneous analysis of multi-sample RNA-seq data. Compared to existing methods, XAEM automatically performs empirical correction of potentially unknown biases. We use an alternating expectation-maximization (AEM) algorithm, alternating between estimation of X and β. For speed XAEM utilizes quasi-mapping for read alignment, thus leading to a fast algorithm. Overall XAEM performs favorably compared to recent advanced methods. For simulated datasets, XAEM obtains higher accuracy for multiple-isoform genes. In a differential-expression analysis of a real single-cell RNA-seq dataset, XAEM achieves substantially better rediscovery rates in independent validation sets. AVAILABILITY AND IMPLEMENTATION: The method and pipeline are implemented as a tool and freely available for use at http://fafner.meb.ki.se/biostatwiki/xaem/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Both single-cell RNA sequencing (scRNA-seq) and DNA sequencing (scDNA-seq) have been applied for cell-level genomic profiling. For mutation profiling, the latter seems more natural. However, the task is highly challenging due to the limited input materials from only two copies of DNA molecules, while whole-genome amplification generates biases and other technical noises. ScRNA-seq starts with a higher input amount, so generally has better data quality. There exists various methods for mutation detection from DNA sequencing, it is not clear whether these methods work for scRNA-seq data. RESULTS: Mutation detection methods developed for either bulk-cell sequencing data or scDNA-seq data do not work well for the scRNA-seq data, as they produce substantial numbers of false positives. We develop a novel and robust statistical method-called SCmut-to identify specific cells that harbor mutations discovered in bulk-cell data. Statistically SCmut controls the false positives using the 2D local false discovery rate method. We apply SCmut to several scRNA-seq datasets. In scRNA-seq breast cancer datasets SCmut identifies a number of highly confident cell-level mutations that are recurrent in many cells and consistent in different samples. In a scRNA-seq glioblastoma dataset, we discover a recurrent cell-level mutation in the PDGFRA gene that is highly correlated with a well-known in-frame deletion in the gene. To conclude, this study contributes a novel method to discover cell-level mutation information from scRNA-seq that can facilitate investigation of cell-to-cell heterogeneity. AVAILABILITY AND IMPLEMENTATION: The source codes and bioinformatics pipeline of SCmut are available at https://github.com/nghiavtr/SCmut. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Motivation: RNA sequencing of single cells enables characterization of transcriptional heterogeneity in seemingly homogeneous cell populations. Single-cell sequencing has been applied in a wide range of researches fields. However, few studies have focus on characterization of isoform-level expression patterns at the single-cell level. In this study, we propose and apply a novel method, ISOform-Patterns (ISOP), based on mixture modeling, to characterize the expression patterns of isoform pairs from the same gene in single-cell isoform-level expression data. Results: We define six principal patterns of isoform expression relationships and describe a method for differential-pattern analysis. We demonstrate ISOP through analysis of single-cell RNA-sequencing data from a breast cancer cell line, with replication in three independent datasets. We assigned the pattern types to each of 16 562 isoform-pairs from 4929 genes. Among those, 26% of the discovered patterns were significant (P<0.05), while remaining patterns are possibly effects of transcriptional bursting, drop-out and stochastic biological heterogeneity. Furthermore, 32% of genes discovered through differential-pattern analysis were not detected by differential-expression analysis. Finally, the effects of drop-out events and expression levels of isoforms on ISOP's performances were investigated through simulated datasets. To conclude, ISOP provides a novel approach for characterization of isoform-level preference, commitment and heterogeneity in single-cell RNA-sequencing data. Availability and implementation: The ISOP method has been implemented as a R package and is available at https://github.com/nghiavtr/ISOP under a GPL-3 license. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Single-cell RNA-sequencing technology allows detection of gene expression at the single-cell level. One typical feature of the data is a bimodality in the cellular distribution even for highly expressed genes, primarily caused by a proportion of non-expressing cells. The standard and the over-dispersed gamma-Poisson models that are commonly used in bulk-cell RNA-sequencing are not able to capture this property. RESULTS: We introduce a beta-Poisson mixture model that can capture the bimodality of the single-cell gene expression distribution. We further integrate the model into the generalized linear model framework in order to perform differential expression analyses. The whole analytical procedure is called BPSC. The results from several real single-cell RNA-seq datasets indicate that ∼90% of the transcripts are well characterized by the beta-Poisson model; the model-fit from BPSC is better than the fit of the standard gamma-Poisson model in > 80% of the transcripts. Moreover, in differential expression analyses of simulated and real datasets, BPSC performs well against edgeR, a conventional method widely used in bulk-cell RNA-sequencing data, and against scde and MAST, two recent methods specifically designed for single-cell RNA-seq data. AVAILABILITY AND IMPLEMENTATION: An R package BPSC for model fitting and differential expression analyses of single-cell RNA-seq data is available under GPL-3 license at https://github.com/nghiavtr/BPSC CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

It is common and advised practice in biomedical research to validate experimental or observational findings in a population different from the one where the findings were initially assessed. This practice increases the generalizability of the results and decreases the likelihood of reporting false-positive findings. Validation becomes critical when dealing with high-throughput experiments, where the large number of tests increases the chance to observe false-positive results. In this article, we review common approaches to determine statistical thresholds for validation and describe the factors influencing the proportion of significant findings from a 'training' sample that are replicated in a 'validation' sample. We refer to this proportion as rediscovery rate (RDR). In high-throughput studies, the RDR is a function of false-positive rate and power in both the training and validation samples. We illustrate the application of the RDR using simulated data and real data examples from metabolomics experiments. We further describe an online tool to calculate the RDR using t-statistics. We foresee two main applications. First, if the validation study has not yet been collected, the RDR can be used to decide the optimal combination between the proportion of findings taken to validation and the size of the validation study. Secondly, if a validation study has already been done, the RDR estimated using the training data can be compared with the observed RDR from the validation data; hence, the success of the validation study can be assessed.

MOTIVATION: Genome and transcriptome analyses can be used to explore cancers comprehensively, and it is increasingly common to have multiple omics data measured from each individual. Furthermore, there are rich functional data such as predicted impact of mutations on protein coding and gene/protein networks. However, integration of the complex information across the different omics and functional data is still challenging. Clinical validation, particularly based on patient outcomes such as survival, is important for assessing the relevance of the integrated information and for comparing different procedures. RESULTS: An analysis pipeline is built for integrating genomic and transcriptomic alterations from whole-exome and RNA sequence data and functional data from protein function prediction and gene interaction networks. The method accumulates evidence for the functional implications of mutated potential driver genes found within and across patients. A driver-gene score (DGscore) is developed to capture the cumulative effect of such genes. To contribute to the score, a gene has to be frequently mutated, with high or moderate mutational impact at protein level, exhibiting an extreme expression and functionally linked to many differentially expressed neighbors in the functional gene network. The pipeline is applied to 60 matched tumor and normal samples of the same patient from The Cancer Genome Atlas breast-cancer project. In clinical validation, patients with high DGscores have worse survival than those with low scores (P = 0.001). Furthermore, the DGscore outperforms the established expression-based signatures MammaPrint and PAM50 in predicting patient survival. In conclusion, integration of mutation, expression and functional data allows identification of clinically relevant potential driver genes in cancer. AVAILABILITY AND IMPLEMENTATION: The documented pipeline including annotated sample scripts can be found in http://fafner.meb.ki.se/biostatwiki/driver-genes/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: RNA-sequencing technologies provide a powerful tool for expression analysis at gene and isoform level, but accurate estimation of isoform abundance is still a challenge. Standard assumption of uniform read intensity would yield biased estimates when the read intensity is in fact non-uniform. The problem is that, without strong assumptions, the read intensity pattern is not identifiable from data observed in a single sample. RESULTS: We develop a joint statistical model that accounts for non-uniform isoform-specific read distribution and gene isoform expression estimation. The main challenge is in dealing with the large number of isoform-specific read distributions, which potentially are as many as the number of splice variants in the genome. A statistical regularization via a smoothing penalty is imposed to control the estimation. Also, for identifiability reasons, the method uses information across samples from the same region. We develop a fast and robust computational procedure based on the iterated-weighted least-squares algorithm, and apply it to simulated data and two real RNA-Seq datasets with reverse transcription-polymerase chain reaction validation. Empirical tests show that our model performs better than existing methods in terms of increasing precision in isoform-level estimation. AVAILABILITY AND IMPLEMENTATION: We have implemented our method in an R package called Sequgio as a pipeline for fast processing of RNA-Seq data.

Our main interest in supervised classification of gene expression data is to infer whether the expressions can discriminate biological characteristics of samples. With thousands of gene expressions to consider, a gene selection has been advocated to decrease classification by including only the discriminating genes. We propose to make the gene selection based on partial least squares and logistic regression random-effects (RE) estimates before the selected genes are evaluated in classification models. We compare the selection with that based on the two-sample t-statistics, a current practice, and modified t-statistics. The results indicate that gene selection based on logistic regression RE estimates is recommended in a general situation, while the selection based on the PLS estimates is recommended when the number of samples is low. Gene selection based on the modified t-statistics performs well when the genes exhibit moderate-to-high variability with moderate group separation. Respecting the characteristics of the data is a key aspect to consider in gene selection.

MOTIVATION: Comparison of read depths from next-generation sequencing between cancer and normal cells makes the estimation of copy number alteration (CNA) possible, even at very low coverage. However, estimating CNA from patients' tumour samples poses considerable challenges due to infiltration with normal cells and aneuploid cancer genomes. Here we provide a method that corrects contamination with normal cells and adjusts for genomes of different sizes so that the actual copy number of each region can be estimated. RESULTS: The procedure consists of several steps. First, we identify the multi-modality of the distribution of smoothed ratios. Then we use the estimates of the mean (modes) to identify underlying ploidy and the contamination level, and finally we perform the correction. The results indicate that the method works properly to estimate genomic regions with gains and losses in a range of simulated data as well as in two datasets from lung cancer patients. It also proves a powerful tool when analysing publicly available data from two cell lines (HCC1143 and COLO829). AVAILABILITY: An R package, called CNAnorm, is available at http://www.precancer.leeds.ac.uk/cnanorm or from Bioconductor. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Analysing next-generation sequencing (NGS) data for copy number variations (CNVs) detection is a relatively new and challenging field, with no accepted standard protocols or quality control measures so far. There are by now several algorithms developed for each of the four broad methods for CNV detection using NGS, namely the depth of coverage (DOC), read-pair, split-read and assembly-based methods. However, because of the complexity of the genome and the short read lengths from NGS technology, there are still many challenges associated with the analysis of NGS data for CNVs, no matter which method or algorithm is used. RESULTS: In this review, we describe and discuss areas of potential biases in CNV detection for each of the four methods. In particular, we focus on issues pertaining to (i) mappability, (ii) GC-content bias, (iii) quality control measures of reads and (iv) difficulty in identifying duplications. To gain insights to some of the issues discussed, we also download real data from the 1000 Genomes Project and analyse its DOC data. We show examples of how reads in repeated regions can affect CNV detection, demonstrate current GC-correction algorithms, investigate sensitivity of DOC algorithm before and after quality control of reads and discuss reasons for which duplications are harder to detect than deletions.

BACKGROUND: Gene-set enrichment analyses (GEA or GSEA) are commonly used for biological characterization of an experimental gene-set. This is done by finding known functional categories, such as pathways or Gene Ontology terms, that are over-represented in the experimental set; the assessment is based on an overlap statistic. Rich biological information in terms of gene interaction network is now widely available, but this topological information is not used by GEA, so there is a need for methods that exploit this type of information in high-throughput data analysis. RESULTS: We developed a method of network enrichment analysis (NEA) that extends the overlap statistic in GEA to network links between genes in the experimental set and those in the functional categories. For the crucial step in statistical inference, we developed a fast network randomization algorithm in order to obtain the distribution of any network statistic under the null hypothesis of no association between an experimental gene-set and a functional category. We illustrate the NEA method using gene and protein expression data from a lung cancer study. CONCLUSIONS: The results indicate that the NEA method is more powerful than the traditional GEA, primarily because the relationships between gene sets were more strongly captured by network connectivity rather than by simple overlaps.

MOTIVATION: With the expansion of whole-genome studies, there is rapid evolution of genotyping platforms. This leads to practical issues such as upgrading of genotyping equipment which often results in research groups having data from different platforms for the same samples. While having more data can potentially yield more accurate copy-number estimates, combining such data is not straightforward as different platforms show different degrees of attenuation of the true copy-number or different noise characteristics and marker panels. Currently, there is still a relative lack of procedures for combining information from different platforms. RESULTS: We develop a method, called MPSS, based on a correlated random-effect model for the unobserved patterns and extend the robust smooth segmentation approach to the multiple-platform scenario. We also propose an objective criterion for discrete segmentation required for downstream analyses. For each identified segment, the software reports a P-value to indicate the likelihood of the segment being a true CNV. From the analyses of real and simulated data, we show that MPSS has better operating characteristics when compared to single-platform methods, and have substantially higher sensitivity compared to an existing multiplatform method. AVAILABILITY: The methods are implemented in an R package MPSS, and the source is available from http://www.meb.ki.se/~yudpaw.

BACKGROUND: Principal component analysis (PCA) has gained popularity as a method for the analysis of high-dimensional genomic data. However, it is often difficult to interpret the results because the principal components are linear combinations of all variables, and the coefficients (loadings) are typically nonzero. These nonzero values also reflect poor estimation of the true vector loadings; for example, for gene expression data, biologically we expect only a portion of the genes to be expressed in any tissue, and an even smaller fraction to be involved in a particular process. Sparse PCA methods have recently been introduced for reducing the number of nonzero coefficients, but these existing methods are not satisfactory for high-dimensional data applications because they still give too many nonzero coefficients. RESULTS: Here we propose a new PCA method that uses two innovations to produce an extremely sparse loading vector: (i) a random-effect model on the loadings that leads to an unbounded penalty at the origin and (ii) shrinkage of the singular values obtained from the singular value decomposition of the data matrix. We develop a stable computing algorithm by modifying nonlinear iterative partial least square (NIPALS) algorithm, and illustrate the method with an analysis of the NCI cancer dataset that contains 21,225 genes. CONCLUSIONS: The new method has better performance than several existing methods, particularly in the estimation of the loading vectors.

BACKGROUND: Algorithms and software for CNV detection have been developed, but they detect the CNV regions sample-by-sample with individual-specific breakpoints, while common CNV regions are likely to occur at the same genomic locations across different individuals in a homogenous population. Current algorithms to detect common CNV regions do not account for the varying reliability of the individual CNVs, typically reported as confidence scores by SNP-based CNV detection algorithms. General methodologies for identifying these recurrent regions, especially those directed at SNP arrays, are still needed. RESULTS: In this paper, we describe two new approaches for identifying common CNV regions based on (i) the frequency of occurrence of reliable CNVs, where reliability is determined by high confidence scores, and (ii) a weighted frequency of occurrence of CNVs, where the weights are determined by the confidence scores. In addition, motivated by the fact that we often observe partially overlapping CNV regions as a mixture of two or more distinct subregions, regions identified using the two approaches can be fine-tuned to smaller sub-regions using a clustering algorithm. We compared the performance of the methods with sequencing-based results in terms of discordance rates, rates of departure from Hardy-Weinberg equilibrium (HWE) and average frequency and size of the identified regions. The discordance rates as well as the rates of departure from HWE decrease when we select CNVs with higher confidence scores. We also performed comparisons with two previously published methods, STAC and GISTIC, and showed that the methods we consider are better at identifying low-frequency but high-confidence CNV regions. CONCLUSIONS: The proposed methods for identifying common CNV regions in multiple individuals perform well compared to existing methods. The identified common regions can be used for downstream analyses such as group comparisons in association studies.

BACKGROUND: Joint analysis of transcriptomic and proteomic data taken from the same samples has the potential to elucidate complex biological mechanisms. Most current methods that integrate these datasets allow for the computation of the correlation between a gene and protein but only after a one-to-one matching of genes and proteins is done. However, genes and proteins are connected via biological pathways and their relationship is not necessarily one-to-one. In this paper, we investigate the use of Correlated Factor Analysis (CFA) for modeling the correlation of genome-scale gene and protein data. Unlike existing approaches, CFA considers all possible gene-protein pairs and utilizes all gene and protein information in its modeling framework. The Generalized Singular Value Decomposition (gSVD) is another method which takes into account all available transcriptomic and proteomic data. Comparison is made between CFA and gSVD. RESULTS: Our simulation study indicates that the CFA estimates can consistently capture the dominant patterns of correlation between two sets of measurements; in contrast, the gSVD estimates cannot do that. Applied to real cancer data, the list of co-regulated genes and proteins identified by CFA has biologically meaningful interpretation, where both the gene and protein expressions are pointing to the same processes. Among the GO terms for which the genes and proteins are most correlated, we observed blood vessel morphogenesis and development. CONCLUSION: We demonstrate that CFA is a useful tool for gene-protein data integration and modeling, where the main question is in finding which patterns of gene expression are most correlated with protein expression.

MOTIVATION: In searching for differentially expressed (DE) genes in microarray data, we often observe a fraction of the genes to have unequal variability between groups. This is not an issue in large samples, where a valid test exists that uses individual variances separately. The problem arises in the small-sample setting, where the approximately valid Welch test lacks sensitivity, while the more sensitive moderated t-test assumes equal variance. METHODS: We introduce a moderated Welch test (MWT) that allows unequal variance between groups. It is based on (i) weighting of pooled and unpooled standard errors and (ii) improved estimation of the gene-level variance that exploits the information from across the genes. RESULTS: When a non-trivial proportion of genes has unequal variability, false discovery rate (FDR) estimates based on the standard t and moderated t-tests are often too optimistic, while the standard Welch test has low sensitivity. The MWT is shown to (i) perform better than the standard t, the standard Welch and the moderated t-tests when the variances are unequal between groups and (ii) perform similarly to the moderated t, and better than the standard t and Welch tests when the group variances are equal. These results mean that MWT is more reliable than other existing tests over wider range of data conditions. AVAILABILITY: R package to perform MWT is available at http://www.meb.ki.se/~yudpaw

BACKGROUND: It is well known that the normalization step of microarray data makes a difference in the downstream analysis. All normalization methods rely on certain assumptions, so differences in results can be traced to different sensitivities to violation of the assumptions. Illustrating the lack of robustness, in a striking spike-in experiment all existing normalization methods fail because of an imbalance between up- and down-regulated genes. This means it is still important to develop a normalization method that is robust against violation of the standard assumptions RESULTS: We develop a new algorithm based on identification of the least-variant set (LVS) of genes across the arrays. The array-to-array variation is evaluated in the robust linear model fit of pre-normalized probe-level data. The genes are then used as a reference set for a non-linear normalization. The method is applicable to any existing expression summaries, such as MAS5 or RMA. CONCLUSION: We show that LVS normalization outperforms other normalization methods when the standard assumptions are not satisfied. In the complex spike-in study, LVS performs similarly to the ideal (in practice unknown) housekeeping-gene normalization. An R package called lvs is available in http://www.meb.ki.se/~yudpaw.

MOTIVATION: Array comparative genomic hybridization (aCGH) provides a genome-wide technique to screen for copy number alteration. The existing segmentation approaches for analyzing aCGH data are based on modeling data as a series of discrete segments with unknown boundaries and unknown heights. Although the biological process of copy number alteration is discrete, in reality a variety of biological and experimental factors can cause the signal to deviate from a stepwise function. To take this into account, we propose a smooth segmentation (smoothseg) approach. METHODS: To achieve a robust segmentation, we use a doubly heavy-tailed random-effect model. The first heavy-tailed structure on the errors deals with outliers in the observations, and the second deals with possible jumps in the underlying pattern associated with different segments. We develop a fast and reliable computational procedure based on the iterative weighted least-squares algorithm with band-limited matrix inversion. RESULTS: Using simulated and real data sets, we demonstrate how smoothseg can aid in identification of regions with genomic alteration and in classification of samples. For the real data sets, smoothseg leads to smaller false discovery rate and classification error rate than the circular binary segmentation (CBS) algorithm. In a realistic simulation setting, smoothseg is better than wavelet smoothing and CBS in identification of regions with genomic alterations and better than CBS in classification of samples. For comparative analyses, we demonstrate that segmenting the t-statistics performs better than segmenting the data. AVAILABILITY: The R package smoothseg to perform smooth segmentation is available from http://www.meb.ki.se/~yudpaw.

BACKGROUND: Many procedures for finding differentially expressed genes in microarray data are based on classical or modified t-statistics. Due to multiple testing considerations, the false discovery rate (FDR) is the key tool for assessing the significance of these test statistics. Two recent papers have generalized two aspects: Storey et al. (2005) have introduced a likelihood ratio test statistic for two-sample situations that has desirable theoretical properties (optimal discovery procedure, ODP), but uses standard FDR assessment; Ploner et al. (2006) have introduced a multivariate local FDR that allows incorporation of standard error information, but uses the standard t-statistic (fdr2d). The relationship and relative performance of these methods in two-sample comparisons is currently unknown. METHODS: Using simulated and real datasets, we compare the ODP and fdr2d procedures. We also introduce a new procedure called S2d that combines the ODP test statistic with the extended FDR assessment of fdr2d. RESULTS: For both simulated and real datasets, fdr2d performs better than ODP. As expected, both methods perform better than a standard t-statistic with standard local FDR. The new procedure S2d performs as well as fdr2d on simulated data, but performs better on the real data sets. CONCLUSION: The ODP can be improved by including the standard error information as in fdr2d. This means that the optimality enjoyed in theory by ODP does not hold for the estimated version that has to be used in practice. The new procedure S2d has a slight advantage over fdr2d, which has to be balanced against a significantly higher computational effort and a less intuititive test statistic.

MOTIVATION: Wide-scale correlations between genes are commonly observed in gene expression data, due to both biological and technical reasons. These correlations increase the variability of the standard estimate of the false discovery rate (FDR). We highlight the false discovery proportion (FDP, instead of the FDR) as the suitable quantity for assessing differential expression in microarray data, demonstrate the deleterious effects of correlation on FDP estimation and propose an improved estimation method that accounts for the correlations. METHODS: We analyse the variation pattern of the distribution of test statistics under permutation using the singular value decomposition. The results suggest a latent FDR model that accounts for the effects of correlation, and is statistically closer to the FDP. We develop a procedure for estimating the latent FDR (ELF) based on a Poisson regression model. RESULTS: For simulated data based on the correlation structure of real datasets, we find that ELF performs substantially better than the standard FDR approach in estimating the FDP. We illustrate the use of ELF in the analysis of breast cancer and lymphoma data. AVAILABILITY: R code to perform ELF is available in http://www.meb.ki.se/~yudpaw.

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.

MOTIVATION: There is a well-recognized potential of protein expression profiling using the surface-enhanced laser desorption and ionization technology for discovering biomarkers that can be applied in clinical diagnosis, prognosis and therapy prediction. The pre-processing of the raw data, however, is still problematic. METHODS: We focus on the peak detection step, where the standard method is marked by poor specificity. Currently, scientists need to inspect individual spectra visually and laboriously in order to verify that spectral peaks identified by the standard method are real. Motivated by this multi-spectral process, we investigate an analytical approach-called RS for 'regions of significance'-that reduces the data to a single spectrum of F-statistics capturing significant variability between spectra. To account for multiple testing, we use a false discovery rate criterion for identifying potentially interesting proteins. RESULTS: We show that RS has better operating characteristics than several existing methods and demonstrate routine applications on a number of large datasets.

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.

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: [email protected] and [email protected].

BACKGROUND: There are currently a number of competing techniques for low-level processing of oligonucleotide array data. The choice of technique has a profound effect on subsequent statistical analyses, but there is no method to assess whether a particular technique is appropriate for a specific data set, without reference to external data. RESULTS: We analyzed coregulation between genes in order to detect insufficient normalization between arrays, where coregulation is measured in terms of statistical correlation. In a large collection of genes, a random pair of genes should have on average zero correlation, hence allowing a correlation test. For all data sets that we evaluated, and the three most commonly used low-level processing procedures including MAS5, RMA and MBEI, the housekeeping-gene normalization failed the test. For a real clinical data set, RMA and MBEI showed significant correlation for absent genes. We also found that a second round of normalization on the probe set level improved normalization significantly throughout. CONCLUSION: Previous evaluation of low-level processing in the literature has been limited to artificial spike-in and mixture data sets. In the absence of a known gold-standard, the correlation criterion allows us to assess the appropriateness of low-level processing of a specific data set and the success of normalization for subsets of genes.

A non-Gaussian smoothing (NGS) technique is developed for filtering low count transmission (TR) data to be used for attenuation correction (AC) of positron emission tomography (PET) studies. The method is based on a statistical technique known as the generalized linear mixed model that allows an inverse link function that avoids the inversion of the observed transmission data. The NGS technique has been implemented in the sinogram domain in one-dimensional mode as angle-by-angle computation. To make it adaptive as a function of the TR count statistics we also develop and validate an objective procedure to choose an optimal smoothing parameter. The technique is assessed using experimental phantoms, simulating PET whole-body studies, and applied to real patient data. Different experimental conditions, in terms of TR scan time (from 1 h to 1 min), covering a wide range of TR counting statistic are considered. The method is evaluated, in terms of mean squared error (MSE), by comparing pixel by pixel the distribution for high counts statistics TR scan (1 h) with the corresponding counts distribution for low count statistics TR scans (e.g., 1 min). The smoothing parameter selection is shown to have high efficiency, meaning that it tends to choose values close to the unknown best value. Furthermore, the counts distribution of emission (EM) images, reconstructed with AC generated using low count TR data (1 min), are within 5% of the corresponding EM images reconstructed with AC generated using the high count statistics TR data (1 h). An application to a real patient whole-body PET study shows the promise of the technique for routine use.

The problem of negative artifacts in emission tomography reconstructions computed by filtered backprojection (FBP) is of practical concern particularly in low count studies. Statistical reconstruction methods based on maximum likelihood (ML) are automatically constrained to be non-negative but their excessive computational overhead (orders of magnitude greater than FBP) has limited their use in operational settings. Motivated by the statistical character of the negativity artifact, the authors develop a simple post-processing technique that iteratively adjusts negative values by cancellation with positive values in a surrounding local neighborhood. The compute time of this approach is roughly equivalent to 2 applications of FBP. The approach was evaluated by numerical simulation in 1- and 2-dimensional (2D) settings. In 2D, the source distributions included the Hoffman, the Shepp and Vardi, and a digitized version of the Jaszczak cold spheres phantoms. The authors' studies compared smoothed versions of FBP, the post-processed FBP, and ML implemented by the expectation-maximization algorithm. The root mean square (RMS) error between the true and estimated source distribution was used to evaluate performance; in 2D, additional region-of-interest-based measures of reconstruction accuracy were also employed. In making comparisons between the different methods, the amount of smoothing applied to each reconstruction method was adapted to minimize the RMS error-this was found to be critical.

At present, the choice of bandwidth in emission computed tomography (ECT) reconstruction is done by subjective means. The authors develop an automated objective selection technique for linear reconstruction algorithms such as filtered backprojection. The approach is based on the method of unbiased risk estimation. A set of 2-D validation studies using computer simulated and physical phantom data from the Hoffman et al. (1990) brain phantom are carried out. These 2-D studies incorporate measured corrections for object attenuation and lack of uniformity in detector sensitivity. It is found that the unbiased risk approach works very well. Over a range of count rates and brain slice source distributions, the root mean square (RMS) error of the fully automated reconstruction, with the data-dependent choice of bandwidth, is around 5% greater than the RMS error for the reconstruction with an ideal choice of the bandwidth.