For many high-dimensional genomic and epigenomic datasets, the outcome of interest is ordinal. While these ordinal outcomes are often thought of as the observed cutpoints of some latent continuous variable, some ordinal outcomes are truly discrete and are comprised of the subjective combination of several factors. The nonlinear stereotype logistic model, which does not assume proportional odds, was developed for these 'assessed' ordinal variables. It has previously been extended to the frequentist high-dimensional feature selection setting, but the Bayesian framework provides some distinct advantages in terms of simultaneous uncertainty quantification and variable selection. Here, we review the stereotype model and Bayesian variable selection methods and demonstrate how to combine them to select genomic features associated with discrete ordinal outcomes. We compared the Bayesian and frequentist methods in terms of variable selection performance. We additionally applied the Bayesian stereotype method to an acute myeloid leukemia RNA-sequencing dataset to further demonstrate its variable selection abilities by identifying features associated with the European LeukemiaNet prognostic risk score.

Many high-throughput genomic applications involve a large set of potential covariates and a response which is frequently measured on an ordinal scale, and it is crucial to identify which variables are truly associated with the response. Effectively controlling the false discovery rate (FDR) without sacrificing power has been a major challenge in variable selection research. This study reviews two existing variable selection frameworks, model-X knockoffs and a modified version of reference distribution variable selection (RDVS), both of which utilize artificial variables as benchmarks for decision making. Model-X knockoffs constructs a 'knockoff' variable for each covariate to mimic the covariance structure, while RDVS generates only one null variable and forms a reference distribution by performing multiple runs of model fitting. Herein, we describe how different importance measures for ordinal responses can be constructed that fit into these two selection frameworks, using either penalized regression or machine learning techniques. We compared these measures in terms of the FDR and power using simulated data. Moreover, we applied these two frameworks to high-throughput methylation data for identifying features associated with the progression from normal liver tissue to hepatocellular carcinoma to further compare and contrast their performances.

BACKGROUND: Acute myeloid leukemia (AML) is a heterogeneous cancer of the blood, though specific recurring cytogenetic abnormalities in AML are strongly associated with attaining complete response after induction chemotherapy, remission duration, and survival. Therefore recurring cytogenetic abnormalities have been used to segregate patients into favorable, intermediate, and adverse prognostic risk groups. However, it is unclear how expression of genes is associated with these prognostic risk groups. We postulate that expression of genes monotonically associated with these prognostic risk groups may yield important insights into leukemogenesis. Therefore, in this paper we propose penalized Bayesian ordinal response models to predict prognostic risk group using gene expression data. We consider a double exponential prior, a spike-and-slab normal prior, a spike-and-slab double exponential prior, and a regression-based approach with variable inclusion indicators for modeling our high-dimensional ordinal response, prognostic risk group, and identify genes through hypothesis tests using Bayes factor. RESULTS: Gene expression was ascertained using Affymetrix HG-U133Plus2.0 GeneChips for 97 favorable, 259 intermediate, and 97 adverse risk AML patients. When applying our penalized Bayesian ordinal response models, genes identified for model inclusion were consistent among the four different models. Additionally, the genes included in the models were biologically plausible, as most have been previously associated with either AML or other types of cancer. CONCLUSION: These findings demonstrate that our proposed penalized Bayesian ordinal response models are useful for performing variable selection for high-dimensional genomic data and have the potential to identify genes relevantly associated with an ordinal phenotype.

Random-effects (RE) models are commonly applied to account for heterogeneity in effect sizes in gene expression meta-analysis. The degree of heterogeneity may differ due to inconsistencies in sample quality. High heterogeneity can arise in meta-analyses containing poor quality samples. We applied sample-quality weights to adjust the study heterogeneity in the DerSimonian and Laird (DSL) and two-step DSL (DSLR2) RE models and the Bayesian random-effects (BRE) models with unweighted and weighted data, Gibbs and Metropolis-Hasting (MH) sampling algorithms, weighted common effect, and weighted between-study variance. We evaluated the performance of the models through simulations and illustrated application of the methods using Alzheimer’s gene expression datasets. Sample quality adjusting within study variance ( w P 6 ) models provided an appropriate reduction of differentially expressed (DE) genes compared to other weighted functions in classical RE models. The BRE model with a uniform(0,1) prior was appropriate for detecting DE genes as compared to the models with other prior distributions. The precision of DE gene detection in the heterogeneous data was increased with the DSLR2 w P 6 weighted model compared to the DSL w P 6 weighted model. Among the BRE weighted models, the w P 6 weighted- and unweighted-data models and both Gibbs- and MH-based models performed similarly. The w P 6 weighted common-effect model performed similarly to the unweighted model in the homogeneous data, but performed worse in the heterogeneous data. The w P 6 weighted data were appropriate for detecting DE genes with high precision, while the w P 6 weighted between-study variance models were appropriate for detecting DE genes with high overall accuracy. Without the weight, when the number of genes in microarray increased, the DSLR2 performed stably, while the overall accuracy of the BRE model was reduced. When applying the weighted models in the Alzheimer’s gene expression data, the number of DE genes decreased in all metadata sets with the DSLR2 w P 6 weighted and the w P 6 weighted between study variance models. Four hundred and forty-six DE genes identified by the w P 6 weighted between study variance model could be potentially down-regulated genes that may contribute to good classification of Alzheimer’s samples. The application of sample quality weights can increase precision and accuracy of the classical RE and BRE models; however, the performance of the models varied depending on data features, levels of sample quality, and adjustment of parameter estimates.

Combining effect sizes from individual studies using random-effects meta-analysis models are commonly applied in high-dimensional gene expression data. However, unknown study heterogeneity can arise from inconsistencies in sample quality and experimental conditions. High heterogeneity of effect sizes can reduce statistical power of the models. In this study, we describe three hypothesis-testing frameworks for meta-analysis of microarray data, and review several existing meta-analytic techniques that have been used in the genomic setting. These include P-value-based methods, rank-based methods and effect-size-based methods. We then discuss limitations of some of these methods and describe random-effects-based methods in detail. We introduce two methods for estimating the inter-study variance in random-effects meta-analytic models and another method for identifying heterogeneous genes for gene expression data. We compared various methods with the standard and existing meta-analytic techniques in the genomic framework. We demonstrate our results through a series of simulations and application in Alzheimer's gene expression data.

MOTIVATION: Batch effects are due to probe-specific systematic variation between groups of samples (batches) resulting from experimental features that are not of biological interest. Principal component analysis (PCA) is commonly used as a visual tool to determine whether batch effects exist after applying a global normalization method. However, PCA yields linear combinations of the variables that contribute maximum variance and thus will not necessarily detect batch effects if they are not the largest source of variability in the data. RESULTS: We present an extension of PCA to quantify the existence of batch effects, called guided PCA (gPCA). We describe a test statistic that uses gPCA to test whether a batch effect exists. We apply our proposed test statistic derived using gPCA to simulated data and to two copy number variation case studies: the first study consisted of 614 samples from a breast cancer family study using Illumina Human 660 bead-chip arrays, whereas the second case study consisted of 703 samples from a family blood pressure study that used Affymetrix SNP Array 6.0. We demonstrate that our statistic has good statistical properties and is able to identify significant batch effects in two copy number variation case studies. CONCLUSION: We developed a new statistic that uses gPCA to identify whether batch effects exist in high-throughput genomic data. Although our examples pertain to copy number data, gPCA is general and can be used on other data types as well. AVAILABILITY AND IMPLEMENTATION: The gPCA R package (Available via CRAN) provides functionality and data to perform the methods in this article. CONTACT: [email protected]

Extensive methodological research has been conducted to improve gene expression summary methods. However, in addition to quantitative gene expression summaries, most platforms, including all those examined in the MicroArray Quality Control project, provide a qualitative detection call result for each gene on the platform. These detection call algorithms are intended to render an assessment of whether or not each transcript is reliably measured. In this paper, we review uses of these qualitative detection call results in the analysis of microarray data. We also review the detection call algorithms for two widely used gene expression microarray platforms, Affymetrix GeneChips and Illumina BeadArrays, and more clearly formalize the mathematical notation for the Illumina BeadArray detection call algorithm. Both algorithms result in a P-value which is then used for determining the qualitative detection calls. We examined the performance of these detection call algorithms and default parameters by applying the methods to two spike-in datasets. We show that the default parameters for qualitative detection calls yield few absent calls for high spike-in concentrations. When genes of interest are expected to be present at very low concentrations, spike-in datasets can be useful for appropriately adjusting the tuning parameters for qualitative detection calls.

BACKGROUND: Recent research examining cross-platform correlation of gene expression intensities has yielded mixed results. In this study, we demonstrate use of a correction factor for estimating cross-platform correlations. RESULTS: In this paper, three technical replicate microarrays were hybridized to each of three platforms. The three platforms were then analyzed to assess both intra- and cross-platform reproducibility. We present various methods for examining intra-platform reproducibility. We also examine cross-platform reproducibility using Pearson's correlation. Additionally, we previously developed a correction factor for Pearson's correlation which is applicable when X and Y are measured with error. Herein we demonstrate that correcting for measurement error by estimating the "disattenuated" correlation substantially improves cross-platform correlations. CONCLUSION: When estimating cross-platform correlation, it is essential to thoroughly evaluate intra-platform reproducibility as a first step. In addition, since measurement error is present in microarray gene expression data, methods to correct for attenuation are useful in decreasing the bias in cross-platform correlation estimates.

UNLABELLED: This paper describes a stand-alone application for estimating the 3' to 5' ratio by fitting a mixed effects model to the interior pixel intensities of perfect match probes for selected control probe sets from an Affymetrix *.DAT file. The effectiveness of this method was demonstrated previously by an application of the method to two microarray datasets for which external verification of RNA quality was known. This application provides a more objective assessment of sample quality in that both a point estimate and 95% confidence interval about the 3' to 5' ratio are provided. AVAILABILITY: The software and installation instructions are freely available for download at http://www.people.vcu.edu/~kjarcher/Research/Data.htm

SUMMARY: SScore is an R package that facilitates the comparison of gene expression between Affymetrix GeneChips using the S-score algorithm. The S-score algorithm uses probe level data directly to assess differences in gene expression, without requiring a preliminary separate step of probe set expression summary estimation. Therefore, the algorithm avoids introduction of error associated with the expression summary estimation process and has been demonstrated to improve the accuracy of identifying differentially expressed genes. The S-score produces accurate results even when few or no replicates are available. AVAILABILITY: The R package SScore is available from Bioconductor at http://www.bioconductor.org

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

BACKGROUND: The usefulness of log2 transformation for cDNA microarray data has led to its widespread application to Affymetrix data. For Affymetrix data, where absolute intensities are indicative of number of transcripts, there is a systematic relationship between variance and magnitude of measurements. Application of the log2 transformation expands the scale of genes with low intensities while compressing the scale of genes with higher intensities thus reversing the mean by variance relationship. The usefulness of these transformations needs to be examined. RESULTS: Using an Affymetrix GeneChip dataset, problems associated with applying the log2 transformation to absolute intensity data are demonstrated. Use of the spread-versus-level plot to identify an appropriate variance stabilizing transformation is presented. For the data presented, the spread-versus-level plot identified a power transformation that successfully stabilized the variance of probe set summaries. CONCLUSION: The spread-versus-level plot is helpful to identify transformations for variance stabilization. This is robust against outliers and avoids assumption of models and maximizations.