A False Discovery Rate approach to optimal volatility forecasting model selection

Current analysis of event-related potentials (ERP) data is usually based on the a priori selection of channels and time windows of interest for studying the differences between experimental conditions in the spatio-temporal domain. In this work we put forward a new strategy designed for situations when there is not a priori information about 'when' and 'where' these differences appear in the spatio-temporal domain, simultaneously testing numerous hypotheses, which increase the risk of false positives. This issue is known as the problem of multiple comparisons and has been managed with methods that control the false discovery rate (FDR), such as permutation test and FDR methods. Although the former has been previously applied, to our knowledge, the FDR methods have not been introduced in the ERP data analysis. Here we compare the performance (on simulated and real data) of permutation test and two FDR methods (Benjamini and Hochberg (BH) and local-fdr, by Efron). All these methods have been shown to be valid for dealing with the problem of multiple comparisons in the ERP analysis, avoiding the ad hoc selection of channels and/or time windows. FDR methods are a good alternative to the common and computationally more expensive permutation test. The BH method for independent tests gave the best overall performance regarding the balance between type I and type II errors. The local-fdr method is preferable for high dimensional (multichannel) problems where most of the tests conform to the empirical null hypothesis. Differences among the methods according to assumptions, null distributions and dimensionality of the problem are also discussed.

Multiple hypothesis testing in proteomics: A strategy for experimental work.

The multiplicity problem has become increasingly important in genetic studies as the capacity for high-throughput genotyping has increased. The control of False Discovery Rate (FDR) (Benjamini and Hochberg. [1995] J. R. Stat. Soc. Ser. B 57:289-300) has been adopted to address the problems of false positive control and low power inherent in high-volume genome-wide linkage and association studies. In many genetic studies, there is often a natural stratification of the m hypotheses to be tested. Given the FDR framework and the presence of such stratification, we investigate the performance of a stratified false discovery control approach (i.e. control or estimate FDR separately for each stratum) and compare it to the aggregated method (i.e. consider all hypotheses in a single stratum). Under the fixed rejection region framework (i.e. reject all hypotheses with unadjusted p-values less than a pre-specified level and then estimate FDR), we demonstrate that the aggregated FDR is a weighted average of the stratum-specific FDRs. Under the fixed FDR framework (i.e. reject as many hypotheses as possible and meanwhile control FDR at a pre-specified level), we specify a condition necessary for the expected total number of true positives under the stratified FDR method to be equal to or greater than that obtained from the aggregated FDR method. Application to a recent Genome-Wide Association (GWA) study by Maraganore et al. ([2005] Am. J. Hum. Genet. 77:685-693) illustrates the potential advantages of control or estimation of FDR by stratum. Our analyses also show that controlling FDR at a low rate, e.g. 5% or 10%, may not be feasible for some GWA studies.

Nuclear magnetic resonance (NMR) spectroscopy-based metabonomics is of growing importance for discovery of human disease biomarkers. Identification and validation of disease biomarkers using statistical significance analysis (SSA) is critical for translation to clinical practice. SSA is performed by assessing a null hypothesis test using a derivative of the Student's t test, e.g., a Welch's t test. Choosing how to correct the significance level for rejecting null hypotheses in the case of multiple testing to maintain a constant family-wise type I error rate is a common problem in such tests. The multiple testing problem arises because the likelihood of falsely rejecting the null hypothesis, i.e., a false positive, grows as the number of tests applied to the same data set increases. Several methods have been introduced to address this problem. Bonferroni correction (BC) assumes all variables are independent and therefore sacrifices sensitivity for detecting true positives in partially dependent data sets. False discovery rate (FDR) methods are more sensitive than BC but uniformly ascribe highest stringency to lowest p value variables. Here, we introduce standard deviation step down (SDSD), which is more sensitive and appropriate than BC for partially dependent data sets. Sensitivity and type I error rate of SDSD can be adjusted based on the degree of variable dependency. SDSD generates fundamentally different profiles of critical p values compared with FDR methods potentially leading to reduced type II error rates. SDSD is increasingly sensitive for more concentrated metabolites. SDSD is demonstrated using NMR-based metabonomics data collected on three different breast cancer cell line extracts.

Context.The new generation of broad-band radio continuum surveys will provide large data sets with polarization information. New algorithms need to be developed to extract reliable catalogs of linearly polarized sources that can be used to characterize those sources and produce a dense rotation measure (RM) grid to probe magneto-ionized structures along the line of sight via Faraday rotation.Aims.The aim of the paper is to develop a computationally efficient and rigorously defined source-finding algorithm for linearly polarized sources.Methods.We used a calibrated data set from the LOw Frequency ARray (LOFAR) at 150 MHz centered on the nearby galaxy M 51 to search for polarized background sources. With a new imaging software, we re-imaged the field at a resolution of 18″ × 15″ and cataloged a total of about 3000 continuum sources within 2.5° of the center of M 51. We made small StokesQandUimages centered on each source brighter than 100 mJy in total intensity (201 sources) and used RM synthesis to create corresponding Faraday cubes that were analyzed individually. For each source, the noise distribution function was determined from a subset of the measurements at high Faraday depths where no polarization is expected; the peaks in polarized intensity in the Faraday spectrum were identified and thep-value of each source was calculated. Finally, the false discovery rate method was applied to the list ofp-values to produce a list of polarized sources and quantify the reliability of the detections. We also analyzed sources fainter than 100 mJy but that were reported as polarized in the literature at at least another radio frequency.Results.Of the 201 sources that were searched for polarization, six polarized sources were detected confidently (with a false discovery rate of 5%). This corresponds to a number density of one polarized source per 3.3 square degrees, or 0.3 source per square degree. Increasing the false discovery rate to 50% yields 19 sources. A majority of the sources have a morphology that is indicative of them being double-lobed radio galaxies, and the ones with literature redshift measurements have 0.5 < z < 1.0.Conclusions.We find that this method is effective in identifying polarized sources, and is well suited for LOFAR observations. In the future, we intend to develop it further and apply it to larger data sets such as the LOFAR Two-meter Survey of the whole northern sky, LOTSS, and the ongoing deep LOFAR observations of the GOODS-North field.

ObjectiveReduced pulmonary function is an important predictor of environment-related pulmonary diseases; however, evidence of an association between exposures to various metals from all possible routes and altered pulmonary function is...

Problems with analyzing and processing high-dimensional random vectors arise in a wide variety of areas. Important practical tasks are economical representation, searching for significant features, and removal of insignificant (noise) features. These tasks are fundamentally important for a wide class of practical applications, such as genetic chain analysis, encephalography, spectrography, video and audio processing, and a number of others. Current research in this area includes a wide range of papers devoted to various filtering methods based on the sparse representation of the obtained experimental data and statistical procedures for their processing. One of the most popular approaches to constructing statistical estimates of regularities in experimental data is the procedure of multiple testing of hypotheses about the significance of observations. In this paper, we consider a procedure based on the false discovery rate (FDR) measure that controls the expected percentage of false rejections of the null hypothesis. We analyze the asymptotic properties of the mean-square error estimate for this procedure and prove the statements about the asymptotic normality of this estimate. The obtained results make it possible to construct asymptotic confidence intervals for the mean-square error of the FDR method using only the observed data.

Objectives: Formation of collateral circulation is an endogenous response to atherosclerosis, and is a natural escape mechanism by re-routing blood. Inflammatory response- related genes underlie the formation of coronary collaterals. We explored the genetic basis of collateral formation in man postulating interaction networks between functional Single Nucleotide Polymorphisms (SNPs) in these inflammatory gene candidates. Methods: The contribution of 41 genes as well as the interactions among them was examined in a cohort of 226 coronary artery disease patients, genotyped for 54 candidate SNPs. Patients were classified to the extent of collateral circulation. Stepwise logistic regression analysis and a haplotype entropy procedure were applied to search for haplotype interactions among all 54 polymorphisms. Multiple testing was addressed by using the false discovery rate (FDR) method. Results: The population comprised 84 patients with and 142 without visible collaterals. Among the 41 genes, 16 pairs of SNPs were implicated in the development of collaterals with the FDR of 0.19. Nine SNPs were found to potentially have main effects on collateral formation. Two sets of coupling haplotypes that predispose to collateral formation were suggested. Conclusions: These findings suggest that collateral formation may arise from the interactions between several SNPs in inflammatory response related genes, which may represent targets in future studies of collateral formation. This may enhance developing strategies for risk stratification and therapeutic stimulation of arteriogenesis.

Introduction Racial disparities in breast cancer (BrCa) mortality are well documented. We previously reported that African American (AA) women with estrogen receptor-positive (ER+) BrCa have a 4-fold higher rate of death compared to non-Hispanic whites (white) after controlling for stage at diagnosis and treatment initiation. This suggests that racial differences in tumor biology may contribute to the survival disparity. In preliminary work we found that AA BrCa cases have higher serum levels of C-reactive protein (CRP) compared to whites, and that increased CRP was associated with worse survival, suggesting that increased systemic inflammation in AA women drives aggressive tumor biology and contributes to the racial disparity in survival. The goal of this study is to identify specific inflammatory pathways that may be involved. Experimental Procedures Pre-treatment blood samples from women with stage I-III ER+ BrCa (AA, n=40; white, n=55) and from healthy controls (AA, n=51; white, n=38) were analyzed with the Olink® targeted proteomic assay, which measures 92 inflammatory proteins. Normalized data was log2 transformed, and generalized linear models compared the normalized intensities with covariates of interest. The fit of the model was tested with empirical Bayes methods. All p-values are corrected for multiple testing with the false discovery rate (FDR) method of Benjamini and Hochberg. Findings After adjustment for site of enrollment, plasma levels of 13 inflammatory cytokines showed a log2 fold-change (log2FC) ≥ 1.0 for AA compared to white women, i.e. at least a two-fold increase in the mean value on a linear scale (Table). The racial difference was evident among both cases and controls, and remained after adjusting for body mass index (BMI). There were no differences between AA cases and controls, indicating that cytokine elevation in AA BrCa patients is not an effect of the tumor. Several of the cytokines are known to promote tumor progression and aggressive biological features in breast tumors. ProteinLog2FCProteinLog2FCCXCL52.42**CCL81.13***CXCL12.06***EIF4EBP11.12**STAMBP1.91*CCL201.10**CXCL111.89**TNF141.06*CCL31.45**TGF beta1.04**CXCL61.40**CCL71.03***CCL131.16**FDR corrected p-values: * < 0.05, **< 0.01, ***< 0.001 Conclusion Systemic elevation of biologically relevant inflammatory cytokines in AA women with ER+ BrCa does not appear to be an effect of the tumor. This inflammatory phenotype may activate inflammatory programs in ER+ breast tumors that develop in AA women, leading to disproportionately aggressive tumor biology and worse outcomes. Supported by grants U54CA203000; U54CA2022995; and U54CA2022997 from the National Institutes of Health. Citation Format: Oana C. Danciu, George Chlipala, Zeynep Madak-Erdogan, Hariyali Patel, Landan Banks, Ayesha Zaidi, Ashlie Santaliz-Casiano, Lauren Schulte, Lauren Weller, Deanna Taiym, Natalie Pulliam, Elona Liko Hazizi, Elonia Martin, Anita Fareeduddin, Archana Bargaje, Carlos Garcia, Scott Hegerty, Sarah Friedewald, Seema Khan, J Julie Kim, William Gradishar, Garth Rauscher, Jonna Frasor, Kent F. Hoskins. Racial differences in circulating inflammatory cytokines and breast cancer disparities [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 1176.

ABSTRACTIn many scientific fields, it is interesting and important to determine whether an observed data stream comes from a prespecified model or not, particularly when the number of data streams is of large scale, where multiple hypotheses testing is necessary. In this article, we consider large-scale model checking under certain dependence among different data streams observed at the same time. We propose a false discovery rate (FDR) control procedure to check those unusual data streams. Specifically, we derive an approximation of false discovery and construct a point estimate of FDR. Theoretical results show that, under some mild assumptions, our proposed estimate of FDR is simultaneously conservatively consistent with the true FDR, and hence it is an asymptotically strong control procedure. Simulation comparisons with some competing procedures show that our proposed FDR procedure behaves better in general settings. Application of our proposed FDR procedure is illustrated by the StarPlus fMRI data.

Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all significant hypotheses. The FDR is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests. In this work, we introduce a modified version of the FDR called the “positive false discovery rate” (pFDR). We discuss the advantages and disadvantages of the pFDR and investigate its statistical properties. When assuming the test statistics follow a mixture distribution, we show that the pFDR can be written as a Bayesian posterior probability and can be connected to classification theory. These properties remain asymptotically true under fairly general conditions, even under certain forms of dependence. Also, a new quantity called the “q-value” is introduced and investigated, which is a natural “Bayesian posterior p-value,” or rather the pFDR analogue of the p-value. 1. Introduction. When testing a single hypothesis, one is usually concerned with controlling the false positive rate while maximizing the probability of detecting an effect when one really exists. In statistical terms, we maximize the power conditional on the Type I error rate being at or below some level. The field of multiple hypothesis testing tries to extend this basic paradigm to the situation where several hypotheses are tested simultaneously. One must define an appropriate compound error measure according to the rate of false positives one is willing to encounter. Then a procedure is developed that allows one to control the error rate at a desired level, while maintaining the power of each test as much as possible. The most commonly controlled quantity when testing multiple hypotheses is the family wise error rate (FWER), which is the probability of yielding one or more false positives out of all hypotheses tested. The most familiar example of this is the Bonferroni method. If there are m hypothesis tests, each test is controlled so that the probability of a false positive is less than or equal to α/m for some chosen value of α. It then follows that the overall FWER is less than or equal to α .M any

Model selection is an omnipresent problem in signal processing applications. The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are the most commonly used solutions to this problem. These criteria have been found to have satisfactory performance in many cases and had a dominant role in the model selection literature since their introduction several decades ago, despite numerous attempts to dethrone them. Model selection can be viewed as a multiple hypothesis testing problem. This simple observation makes it possible to use for model selection a number of powerful hypothesis testing procedures that control the false discovery rate (FDR) or the familywise error rate (FER). This is precisely what we do in this paper in which we follow the lead of the proposers of the said procedures and introduce two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">general</i> rules for model selection based on FDR and FER, respectively. We show in a numerical performance study that the FDR and FER rules are serious competitors of AIC and BIC with significant performance gains in more demanding cases, essentially at the same computational effort.

Aims: CD36 , an important gene involved in cholesterol and fatty acid metabolism,, has been associated with many metabolic-related traits, including diabetes, hypertension, and obesity in different populations. However, the association of this gene with metabolic syndrome (MS) has not been well-studied. We aimed to investigate the association of CD36 with the risk of MS and longitudinal changes of its components in among participants of the Rural Chinese Cohort Study (RCCS). Materials and Methods: The RCCS enrolled 20,194 participants aged 2 18 years old between July of 2007 and August of 2008. A total of 17,265 participants (response rate 85.5%) were examined in the follow-up survey between July of 2013 and October of 2014. During the six years, 729 new incident cases of MS were ascertained. We conducted a nested case-control study within the RCCS. Specifically, 408 MS randomly cases and 408 one-to-one matched controls were included in the current study. In addition to follow-up time, non-MS controls were matched to MS cases on age, gender, marital status, and residence village. Human genomic DNA was extracted using a standard method from blood samples collected at the baseline. After quality control, 4 single nucleotide polymorphisms (SNPs) within the CD36 were successfully genotyped. MS was defined according to the 2009 criteria proposed by IDF and AHA/NHLBI. Multivariate conditional logistic regression was used to determine additive associations of SNPs and SNP-haplotype with MS adjusting for body mass index (BMI), smoking, drinking, and physical activity at baseline. Multivariate linear regression models were conducted among the control group to examine association of SNPs and SNP-haplotypes with MS components, controlling for age, gender, BMI, smoking, drinking and physical activity. Multiple testing was corrected by false positive discovery rate (FDR) method. Results: Two SNPs, rs7755 and rs1049673, were associated with risk for MS. Per minor allele increase in rs7755 and rs1049673 was associated with 2.29 (95% confidence interval [CI]: 1.24-4.24, p =0.008) and 2.30 (95% CI: 1.24-4.26, p =0.008) times higher odds of MS, respectively. In addition, rs1194197 was associated with changes of triglycerides level (β=0.151, p =0.014), and rs7755 (β=-0.065, p =0.028) and rs1049673 (β=-0.067, p =0.025) were associated with changes of high density lipoprotein cholesterol in the control group. One haplotype of the four SNPs, AGAG, was associated with the change of waist circumference (β=-1.773, p =0.048). Conclusions: We identified important SNPs and SNP-haplotypes of the CD36 associated with MS and changes of MS components in a Han Chinese population.

Circadian genes and prostate cancer risk: Results from the EPICAP study

We examined the associations of common variants in ENaC genes with BP changes and hypertension incidence in a longitudinal family study. A total of 2755 Han Chinese participants of the Genetic Epidemiology Network of Salt Sensitivity (GenSalt) baseline examination were eligible for the current study. The average of nine BP measurements obtained using a random-zero sphygmomanometer at the baseline and each of two follow-up visits were used for the current analysis. The associations of 43 tag-SNPs in ENaC genes with BP changes and hypertension incidence were assessed using mixed models to account for the correlations of repeated measures among individuals and within families. A genotype by time interaction term was used to model differences in BP change according to genotype over time. The false discovery rate (FDR) method was used to adjust for multiple testing. During an average of 7.4 years follow-up, systolic BP (SBP) and diastolic BP (DBP) increased, and approximately 33% of participants developed hypertension. Multiple variants in ENaC genes were significantly associated with longitudinal changes in SBP after adjustment for multiple testing, including SCNN1A SNP rs11064153 ( P interaction = 5.8х10 -4 ; FDR-Q = 0.01); SCNN1G SNPs rs4299163 ( P interaction = 0.011; FDR-Q = 0.05) and rs4401050 ( P interaction = 0.001; FDR-Q = 0.01); and SCNN1B SNP rs1004749 ( P interaction = 0.006; FDR-Q = 0.03). Similar but not significant trends were observed for the associations between both rs11064153 and rs4401050 and DBP changes ( P interaction = 0.024 and 0.005, respectively; FDR-Q = 0.41 and 0.17, respectively) and between rs11604153 and hypertension incidence ( P = 0.017; FDR-Q = 0.19). Our findings indicate that ENaC genes may contribute to longitudinal BP changes in the Han Chinese population. Replication of these findings is warranted.