Volume 11, Issue 3

Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.

In this paper a correction of SGoF multitesting method for dependent tests is introduced. The correction is based in the beta-binomial model, and therefore the new method is called Beta-Binomial SGoF (or BB-SGoF). Main properties of the new method are established, and its practical implementation is discussed. BB-SGoF is illustrated through the analysis of two different real data sets on gene/protein expression levels. The performance of the method is investigated through simulations too. One of the main conclusions of the paper is that SGoF strategy may have much power even in the presence of possible dependences among the tests.

Genetic association studies require that the genotype data from a given person can be correctly linked to the phenotype data from the same person. However, sample misidentification errors sometimes happen, whereby the link becomes invalid for some of the subjects in a study. This can have substantial consequences in terms of power to detect truly associated variants. In family-based studies, Mendelian inconsistencies can be used to detect sample misidentification. Genome-wide association studies (GWAS), however, typically use unrelated individuals, making error detection more problematic.Here we present a method for identifying potential sample misidentifications in GWAS and other genetic association studies building on ideas from forensic sciences. A widely used ad-hoc method for error detection is to check if the sex of an individual matches its X-linked genotype. We generalize this idea to less stringent associations between known genotypes and phenotypes, and show that if several known associations are combined, the power to detect misidentifications increases substantially. Individuals with an unlikely set of phenotypes given their genotypes are flagged as potential errors.We provide analytical and simulation results comparing the odds that the genotype and phenotype are both from the same individual for different numbers of available genotype-phenotype associations and for different information content of the associations. Our method has good sensitivity and specificity with as few as ten moderately informative genotype-phenotype associations. We apply the method to GWAS data from the Danish National Birth Cohort.

Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is often low, the usual unbiased estimator of the error variance can be unreliable. Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in recent years. Because the same microarray platform is often used for at least several experiments to study similar biological systems, there is an opportunity to improve variance estimation further by borrowing information not only across genes but also across experiments. We propose a lognormal model for error variances that involves random gene effects and random experiment effects. Based on the model, we develop an empirical Bayes estimator of the error variance for each combination of gene and experiment and call this estimator BAGE because information is Borrowed Across Genes and Experiments. A permutation strategy is used to make inference about the differential expression status of each gene. Simulation studies with data generated from different probability models and real microarray data show that our method outperforms existing approaches.

HIV patients are treated by administration of combinations of antiretroviral drugs. The very large number of such combinations makes the manual search for an effective therapy practically impossible, especially in advanced stages of the disease. Therapy selection can be supported by statistical methods that predict the outcomes of candidate therapies. However, these methods are based on clinical data sets that have highly unbalanced therapy representation.This paper presents a novel approach that considers each drug belonging to a target combination therapy as a separate task in a multi-task hierarchical Bayes setting. The drug-specific models take into account information on all therapies containing the drug, not just the target therapy. In this way, we can circumvent the problem of data sparseness pertaining to some target therapies.The computational validation shows that compared to the most commonly used approach that provides therapy information in the form of input features, our model has significantly higher predictive power for therapies with very few training samples and is at least as powerful for abundant therapies.

Measurements from microarrays and other high-throughput technologies are susceptible to non-biological artifacts like batch effects. It is known that batch effects can alter or obscure the set of significant results and biological conclusions in high-throughput studies. Here we examine the impact of batch effects on predictors built from genomic technologies. To investigate batch effects, we collected publicly available gene expression measurements with known outcomes, and estimated batches using date. Using these data we show (1) the impact of batch effects on prediction depends on the correlation between outcome and batch in the training data, and (2) removing expression measurements most affected by batch before building predictors may improve the accuracy of those predictors. These results suggest that (1) training sets should be designed to minimize correlation between batches and outcome, and (2) methods for identifying batch-affected probes should be developed to improve prediction results for studies with high correlation between batches and outcome.

Next-generation sequencing is rapidly transforming our ability to profile the transcriptional, genetic, and epigenetic states of a cell. In particular, sequencing DNA from the immunoprecipitation of protein-DNA complexes (ChIP-seq) and methylated DNA (MeDIP-seq) can reveal the locations of protein binding sites and epigenetic modifications. These approaches contain numerous biases which may significantly influence the interpretation of the resulting data. Rigorous computational methods for detecting and removing such biases are still lacking. Also, multi-sample normalization still remains an important open problem. This theoretical paper systematically characterizes the biases and properties of ChIP-seq data by comparing 62 separate publicly available datasets, using rigorous statistical models and signal processing techniques. Statistical methods for separating ChIP-seq signal from background noise, as well as correcting enrichment test statistics for sequence-dependent and sonication biases, are presented. Our method effectively separates reads into signal and background components prior to normalization, improving the signal-to-noise ratio. Moreover, most peak callers currently use a generic null model which suffers from low specificity at the sensitivity level requisite for detecting subtle, but true, ChIP enrichment. The proposed method of determining a cell type-specific null model, which accounts for cell type-specific biases, is shown to be capable of achieving a lower false discovery rate at a given significance threshold than current methods.

Motivation: Assessment of gene expression on spotted microarrays is based on measurement of fluorescence intensity emitted by hybridized spots. Unfortunately, quantifying fluorescence intensity from hybridized spots does not always correctly reflect gene expression level. Low gene expression levels produce low fluorescence intensities which tend to be confounded with the local background while high gene expression levels produce high fluorescence intensities which rapidly reach the saturation level. Most algorithms that combine data acquired at different voltages of the photomultiplier tube (PMT) assume that a change in scanner setting transforms the intensity measurements by a multiplicative constant.Methods and Results: In this paper we introduce a new model of spot foreground intensity which integrates a PMT voltage independent scanner optical bias. This new model is used to implement a ”Combining Multiple Scan using a Two-way ANOVA” (CMS2A) method, which is based on a maximum likelihood estimation of the scanner optical bias. After having computed scanner bias, coefficients of the two-way ANOVA model are used for correcting the saturated spots intensities obtained at high PMT voltage by using their counterpart values at lower PMT voltages. The method was compared to state-of-the-art multiple scan algorithms, using data generated from the MAQC study. CMS2A produced fold-changes that were highly correlated with qPCR fold-changes. As the scanner optical bias is accurately estimated within CMS2A, this method allows also avoiding fold-change compression biases whatever the value of this optical bias.

Problems involving thousands of null hypotheses have been addressed by estimating the local false discovery rate (LFDR). A previous LFDR approach to reporting point and interval estimates of an effect-size parameter uses an estimate of the prior distribution of the parameter conditional on the alternative hypothesis. That estimated prior is often unreliable, and yet strongly influences the posterior intervals and point estimates, causing the posterior intervals to differ from fixed-parameter confidence intervals, even for arbitrarily small estimates of the LFDR. That influence of the estimated prior manifests the failure of the conditional posterior intervals, given the truth of the alternative hypothesis, to match the confidence intervals.Those problems are overcome by changing the posterior distribution conditional on the alternative hypothesis from a Bayesian posterior to a confidence posterior. Unlike the Bayesian posterior, the confidence posterior equates the posterior probability that the parameter lies in a fixed interval with the coverage rate of the coinciding confidence interval. The resulting confidence-Bayes hybrid posterior supplies interval and point estimates that shrink toward the null hypothesis value.The confidence intervals tend to be much shorter than their fixed-parameter counterparts, as illustrated with gene expression data. Simulations nonetheless confirm that the shrunken confidence intervals cover the parameter more frequently than stated. Generally applicable sufficient conditions for correct coverage are given.In addition to having those frequentist properties, the hybrid posterior can also be motivated from an objective Bayesian perspective by requiring coherence with some default prior conditional on the alternative hypothesis. That requirement generates a new class of approximate posteriors that supplement Bayes factors modified for improper priors and that dampen the influence of proper priors on the credibility intervals. While that class of posteriors intersects the class of confidence-Bayes posteriors, neither class is a subset of the other.In short, two first principles generate both classes of posteriors: a coherence principle and a relevance principle. The coherence principle requires that all effect size estimates comply with the same probability distribution. The relevance principle means effect size estimates given the truth of an alternative hypothesis cannot depend on whether that truth was known prior to observing the data or whether it was learned from the data.

Partially paired data sets often occur in microarray experiments (Kim et al., 2005; Liu, Liang and Jang, 2006). Discussions of testing with partially paired data are found in the literature (Lin and Stivers 1974; Ekbohm, 1976; Bhoj, 1978). Bhoj (1978) initially proposed a test statistic that uses a convex combination of paired and unpaired t statistics. Kim et al. (2005) later proposed the t3 statistic, which is a linear combination of paired and unpaired t statistics, and then used it to detect differentially expressed (DE) genes in colorectal cancer (CRC) cDNA microarray data. In this paper, we extend Kim et al.’s t3 statistic to the Hotelling’s T2 type statistic Tp for detecting DE gene sets of size p. We employ Efron’s empirical null principle to incorporate inter-gene correlation in the estimation of the false discovery rate. Then, the proposed Tp statistic is applied to Kim et al’s CRC data to detect the DE gene sets of sizes p=2 and p=3. Our results show that for small p, particularly for p=2 and marginally for p=3, the proposed Tp statistic compliments the univariate procedure by detecting additional DE genes that were undetected in the univariate test procedure. We also conduct a simulation study to demonstrate that Efron’s empirical null principle is robust to the departure from the normal assumption.

The general availability of reliable and affordable genotyping technology has enabled genetic association studies to move beyond small case-control studies to large prospective studies. For prospective studies, genetic information can be integrated into the analysis via haplotypes, with focus on their association with a censored survival outcome. We develop non-iterative, regression-based methods to estimate associations between common haplotypes and a censored survival outcome in large cohort studies. Our non-iterative methods—weighted estimation and weighted haplotype combination—are both based on the Cox regression model, but differ in how the imputed haplotypes are integrated into the model. Our approaches enable haplotype imputation to be performed once as a simple data-processing step, and thus avoid implementation based on sophisticated algorithms that iterate between haplotype imputation and risk estimation. We show that non-iterative weighted estimation and weighted haplotype combination provide valid tests for genetic associations and reliable estimates of moderate associations between common haplotypes and a censored survival outcome, and are straightforward to implement in standard statistical software. We apply the methods to an analysis of HSPB7-CLCNKA haplotypes and risk of adverse outcomes in a prospective cohort study of outpatients with chronic heart failure.

Applications on inference of biological networks have raised a strong interest in the problem of graph estimation in high-dimensional Gaussian graphical models. To handle this problem, we propose a two-stage procedure which first builds a family of candidate graphs from the data, and then selects one graph among this family according to a dedicated criterion. This estimation procedure is shown to be consistent in a high-dimensional setting, and its risk is controlled by a non-asymptotic oracle-like inequality. The procedure is tested on a real data set concerning gene expression data, and its performances are assessed on the basis of a large numerical study.The procedure is implemented in the R-package GGMselect available on the CRAN.

In cancer clinical proteomics, MALDI and SELDI profiling are used to search for biomarkers of potentially curable early-stage disease. A given number of samples must be analysed in order to detect clinically relevant differences between cancers and controls, with adequate statistical power. From clinical proteomic profiling studies, expression data for each peak (protein or peptide) from two or more clinically defined groups of subjects are typically available. Typically, both exposure and confounder information on each subject are also available, and usually the samples are not from randomized subjects. Moreover, the data is usually available in replicate. At the design stage, however, covariates are not typically available and are often ignored in sample size calculations. This leads to the use of insufficient numbers of samples and reduced power when there are imbalances in the numbers of subjects between different phenotypic groups. A method is proposed for accommodating information on covariates, data imbalances and design-characteristics, such as the technical replication and the observational nature of these studies, in sample size calculations. It assumes knowledge of a joint distribution for the protein expression values and the covariates. When discretized covariates are considered, the effect of the covariates enters the calculations as a function of the proportions of subjects with specific attributes. This makes it relatively straightforward (even when pilot data on subject covariates is unavailable) to specify and to adjust for the effect of the expected heterogeneities. The new method suggests certain experimental designs which lead to the use of a smaller number of samples when planning a study. Analysis of data from the proteomic profiling of colorectal cancer reveals that fewer samples are needed when a study is balanced than when it is unbalanced, and when the IMAC30 chip-type is used. The method is implemented in the clippda package and is available in R at: http://www.bioconductor.org/help/bioc-views/release/bioc/html/clippda.html.

Most approaches for analyzing ChIP-Seq data are focused on inferring exact protein binding sites from a single library. However, frequently multiple ChIP-Seq libraries derived from differing cell lines or tissue types from the same individual may be available. In such a situation, a separate analysis for each tissue or cell line may be inefficient. Here, we describe a novel method to analyze such data that intelligently uses the joint information from multiple related ChIP-Seq libraries. We present our method as a two-stage procedure. First, separate single cell line analysis is performed for each cell line. Here, we use a novel mixture regression approach to infer the subset of genes that are most likely to be involved in protein binding in each cell line. In the second step, we combine the separate single cell line analyses using an Empirical Bayes algorithm that implicitly incorporates inter-cell line correlation. We demonstrate the usefulness of our method using both simulated data, as well as real H3K4me3 and H3K27me3 histone methylation libraries.

In many published genome-wide association studies (GWAS), the top few strongly associated variants are often located in or near known genes. This observation raises the more general hypothesis that variants nominally associated with a phenotype are more likely to overlap genes than those not associated with a phenotype. We developed a simple approach – named GENe OVerlap Analysis (GENOVA) – to formally test this hypothesis. This approach includes two steps. First, we define largely independent groups of highly correlated SNPs (or “clumps”) and classify each clump as intersecting a gene or not. Second, we determine how strongly associated each clump is with the phenotype and use logistic regression to formally test the hypothesis that clumps associated with the phenotype are more likely to intersect genes. Simulations suggest that the power of GENOVA is affected by at least three factors: GWAS sample size, the gene boundaries used to define gene-intersecting clumps and the P-value threshold used to define phenotype-associated clumps. We applied GENOVA to results from three recent GWAS meta-analyses of height, body mass index (BMI) and waist-hip ratio (WHR) conducted by the GIANT consortium. SNPs associated with variation in height were 1.44-fold more likely to be in or near genes than SNPs not associated with height (P = 5x10-28). A weaker association was observed for BMI (1.09-fold, P = 0.008) and WHR (1.09-fold, P = 0.014). GENOVA is implemented in C++ and is freely available at https://genepi.qimr.edu.au/staff/manuelF/genova/main.html.