Control of false discoveries in grouped hypothesis testing for eQTL data

BACKGROUND

Expression quantitative trait locus (eQTL) analysis aims to detect the genetic variants that influence the expression of one or more genes. Gene-level eQTL testing forms a natural grouped-hypothesis testing strategy with clear biological importance. Methods to control family-wise error rate or false discovery rate for group testing have been proposed earlier, but may not be powerful or easily apply to eQTL data, for which certain structured alternatives may be defensible and may enable the researcher to avoid overly conservative approaches.

RESULTS

In an empirical Bayesian setting, we propose a new method to control the false discovery rate (FDR) for grouped hypotheses. Here, each gene forms a group, with SNPs annotated to the gene corresponding to individual hypotheses. The heterogeneity of effect sizes in different groups is considered by the introduction of a random effects component. Our method, entitled Random Effects model and testing procedure for Group-level FDR control (REG-FDR), assumes a model for alternative hypotheses for the eQTL data and controls the FDR by adaptive thresholding. As a convenient alternate approach, we also propose Z-REG-FDR, an approximate version of REG-FDR, that uses only Z-statistics of association between genotype and expression for each gene-SNP pair. The performance of Z-REG-FDR is evaluated using both simulated and real data. Simulations demonstrate that Z-REG-FDR performs similarly to REG-FDR, but with much improved computational speed.

CONCLUSION

Our results demonstrate that the Z-REG-FDR method performs favorably compared to other methods in terms of statistical power and control of FDR. It can be of great practical use for grouped hypothesis testing for eQTL analysis or similar problems in statistical genomics due to its fast computation and ability to be fit using only summary data.

A TESTING BASED APPROACH TO THE DISCOVERY OF DIFFERENTIALLY CORRELATED VARIABLE SETS

Given data obtained under two sampling conditions, it is often of interest to identify variables that behave differently in one condition than in the other. We introduce a method for differential analysis of second-order behavior called Differential Correlation Mining (DCM). The DCM method identifies differentially correlated sets of variables, with the property that the average pairwise correlation between variables in a set is higher under one sample condition than the other. DCM is based on an iterative search procedure that adaptively updates the size and elements of a candidate variable set. Updates are performed via hypothesis testing of individual variables, based on the asymptotic distribution of their average differential correlation. We investigate the performance of DCM by applying it to simulated data as well as to recent experimental datasets in genomics and brain imaging.

Basal-like Breast cancer DNA copy number losses identify genes involved in genomic instability, response to therapy, and patient survival

Breast cancer is a heterogeneous disease with known expression-defined tumor subtypes. DNA copy number studies have suggested that tumors within gene expression subtypes share similar DNA Copy number aberrations (CNA) and that CNA can be used to further sub-divide expression classes. To gain further insights into the etiologies of the intrinsic subtypes, we classified tumors according to gene expression subtype and next identified subtype-associated CNA using a novel method called SWITCHdna, using a training set of 180 tumors and a validation set of 359 tumors. Fisher's exact tests, Chi-square approximations, and Wilcoxon rank-sum tests were performed to evaluate differences in CNA by subtype. To assess the functional significance of loss of a specific chromosomal region, individual genes were knocked down by shRNA and drug sensitivity, and DNA repair foci assays performed. Most tumor subtypes exhibited specific CNA. The Basal-like subtype was the most distinct with common losses of the regions containing RB1, BRCA1, INPP4B, and the greatest overall genomic instability. One Basal-like subtype-associated CNA was loss of 5q11-35, which contains at least three genes important for BRCA1-dependent DNA repair (RAD17, RAD50, and RAP80); these genes were predominantly lost as a pair, or all three simultaneously. Loss of two or three of these genes was associated with significantly increased genomic instability and poor patient survival. RNAi knockdown of RAD17, or RAD17/RAD50, in immortalized human mammary epithelial cell lines caused increased sensitivity to a PARP inhibitor and carboplatin, and inhibited BRCA1 foci formation in response to DNA damage. These data suggest a possible genetic cause for genomic instability in Basal-like breast cancers and a biological rationale for the use of DNA repair inhibitor related therapeutics in this breast cancer subtype.

Reprioritizing genetic associations in hit regions using LASSO-based resample model averaging

Significance testing one SNP at a time has proven useful for identifying genomic regions that harbor variants affecting human disease. But after an initial genome scan has identified a “hit region” of association, single-locus approaches can falter. Local linkage disequilibrium (LD) can make both the number of underlying true signals and their identities ambiguous. Simultaneous modeling of multiple loci should help. However, it is typically applied ad hoc: conditioning on the top SNPs, with limited exploration of the model space and no assessment of how sensitive model choice was to sampling variability. Formal alternatives exist but are seldom used. Bayesian variable selection is coherent but requires specifying a full joint model, including priors on parameters and the model space. Penalized regression methods (e.g., LASSO) appear promising but require calibration, and, once calibrated, lead to a choice of SNPs that can be misleadingly decisive. We present a general method for characterizing uncertainty in model choice that is tailored to reprioritizing SNPs within a hit region under strong LD. Our method, LASSO local automatic regularization resample model averaging (LLARRMA), combines LASSO shrinkage with resample model averaging and multiple imputation, estimating for each SNP the probability that it would be included in a multi-SNP model in alternative realizations of the data. We apply LLARRMA to simulations based on case-control genome-wide association studies data, and find that when there are several causal loci and strong LD, LLARRMA identifies a set of candidates that is enriched for true signals relative to single locus analysis and to the recently proposed method of Stability Selection. Genet. Epidemiol. 36:451–462, 2012. © 2012 Wiley Periodicals, Inc.

Mining Non-Redundant High Order Correlations in Binary Data

Many approaches have been proposed to find correlations in binary data. Usually, these methods focus on pair-wise correlations. In biology applications, it is important to find correlations that involve more than just two features. Moreover, a set of strongly correlated features should be non-redundant in the sense that the correlation is strong only when all the interacting features are considered together. Removing any feature will greatly reduce the correlation.In this paper, we explore the problem of finding non-redundant high order correlations in binary data. The high order correlations are formalized using multi-information, a generalization of pairwise mutual information. To reduce the redundancy, we require any subset of a strongly correlated feature subset to be weakly correlated. Such feature subsets are referred to as Non-redundant Interacting Feature Subsets (NIFS). Finding all NIFSs is computationally challenging, because in addition to enumerating feature combinations, we also need to check all their subsets for redundancy. We study several properties of NIFSs and show that these properties are useful in developing efficient algorithms. We further develop two sets of upper and lower bounds on the correlations, which can be incorporated in the algorithm to prune the search space. A simple and effective pruning strategy based on pair-wise mutual information is also developed to further prune the search space. The efficiency and effectiveness of our approach are demonstrated through extensive experiments on synthetic and real-life datasets.

Gene expression profiles do not consistently predict the clinical treatment response in locally advanced breast cancer

Neoadjuvant treatment offers an opportunity to correlate molecular variables to treatment response and to explore mechanisms of drug resistance in vivo. Here, we present a statistical analysis of large-scale gene expression patterns and their relationship to response following neoadjuvant chemotherapy in locally advanced breast cancers. We analyzed cDNA expression data from 81 tumors from two patient series, one treated with doxorubicin alone (51) and the other treated with 5-fluorouracil and mitomycin (30), and both were previously studied for correlations between TP53 status and response to therapy. We observed a low frequency of progressive disease within the luminal A subtype from both series (2 of 36 versus 13 of 45 patients; P = 0.0089) and a high frequency of progressive disease among patients with luminal B type tumors treated with doxorubicin (5 of 8 patients; P = 0.0078); however, aside from these two observations, no other consistent associations between response to chemotherapy and tumor subtype were observed. These specific associations could possibly be explained by covariance with TP53 mutation status, which also correlated with tumor subtype. Using supervised analysis, we could not uncover a gene profile that could reliably (>70% accuracy and specificity) predict response to either treatment regimen. [Mol Cancer Ther 2006;5(11):2914–8]

The molecular portraits of breast tumors are conserved across microarray platforms

BACKGROUND

Validation of a novel gene expression signature in independent data sets is a critical step in the development of a clinically useful test for cancer patient risk-stratification. However, validation is often unconvincing because the size of the test set is typically small. To overcome this problem we used publicly available breast cancer gene expression data sets and a novel approach to data fusion, in order to validate a new breast tumor intrinsic list.

RESULTS

A 105-tumor training set containing 26 sample pairs was used to derive a new breast tumor intrinsic gene list. This intrinsic list contained 1300 genes and a proliferation signature that was not present in previous breast intrinsic gene sets. We tested this list as a survival predictor on a data set of 311 tumors compiled from three independent microarray studies that were fused into a single data set using Distance Weighted Discrimination. When the new intrinsic gene set was used to hierarchically cluster this combined test set, tumors were grouped into LumA, LumB, Basal-like, HER2+/ER-, and Normal Breast-like tumor subtypes that we demonstrated in previous datasets. These subtypes were associated with significant differences in Relapse-Free and Overall Survival. Multivariate Cox analysis of the combined test set showed that the intrinsic subtype classifications added significant prognostic information that was independent of standard clinical predictors. From the combined test set, we developed an objective and unchanging classifier based upon five intrinsic subtype mean expression profiles (i.e. centroids), which is designed for single sample predictions (SSP). The SSP approach was applied to two additional independent data sets and consistently predicted survival in both systemically treated and untreated patient groups.

CONCLUSION

This study validates the "breast tumor intrinsic" subtype classification as an objective means of tumor classification that should be translated into a clinical assay for further retrospective and prospective validation. In addition, our method of combining existing data sets can be used to robustly validate the potential clinical value of any new gene expression profile.

Repeated observation of breast tumor subtypes in independent gene expression data sets

Characteristic patterns of gene expression measured by DNA microarrays have been used to classify tumors into clinically relevant subgroups. In this study, we have refined the previously defined subtypes of breast tumors that could be distinguished by their distinct patterns of gene expression. A total of 115 malignant breast tumors were analyzed by hierarchical clustering based on patterns of expression of 534 "intrinsic" genes and shown to subdivide into one basal-like, one ERBB2-overexpressing, two luminal-like, and one normal breast tissue-like subgroup. The genes used for classification were selected based on their similar expression levels between pairs of consecutive samples taken from the same tumor separated by 15 weeks of neoadjuvant treatment. Similar cluster analyses of two published, independent data sets representing different patient cohorts from different laboratories, uncovered some of the same breast cancer subtypes. In the one data set that included information on time to development of distant metastasis, subtypes were associated with significant differences in this clinical feature. By including a group of tumors from BRCA1 carriers in the analysis, we found that this genotype predisposes to the basal tumor subtype. Our results strongly support the idea that many of these breast tumor subtypes represent biologically distinct disease entities.

Mapping cortical asymmetry and complexity patterns in normal children

This study reports the first comprehensive three-dimensional (3D) maps of cortical patterns in children. Using a novel parametric mesh-based analytic technique applied to high-resolution T1-weighted MRI scans, we examined age (6-16 years) and gender differences in cortical complexity (the fractal dimension or complexity of sulcal/gyral convolutions) and asymmetry of 24 primary cortical sulci in normally developing children (N=24). Three-dimensional models of the cerebral cortex were extracted and major sulci mapped in stereotaxic space. Given the documented age-related changes in frontal lobe functions and several neuroimaging studies that have reported accompanying volumetric changes in these regions, we hypothesized that, with age, we would find continued modifications of the cerebrum in frontal cortex. We also predicted that phylogenetically older regions of the cerebrum, such as olfactory cortex, would be less variable in anatomic location across subjects and with age. Age-related increases in cortical complexity were found in both left and right inferior frontal and left superior frontal regions, possibly indicating an increase in secondary branching with age in these regions. Moreover, a significant increase in the length of the left inferior frontal sulcus and a posterior shifting of the left pre-central sulcus was associated with age. Three-dimensional asymmetry and anatomic variability maps revealed a significant left-greater-than-right asymmetry of the Sylvian fissures and superior temporal sulci, and increased variance in dorsolateral frontal and perisylvian areas relative to ventral regions of the cortex. These results suggest increases in cortical complexity and subtle modifications of sulcal topography of frontal lobe regions, likely reflecting ongoing processes such as myelination and synaptic remodeling that continue into the second decade of life. More studies in a larger sample set and/or longitudinal design are needed to address the issues of normal individual variation and sulcal development.