High-dimensional Biology Research Articles

High dimensional biology to assess the effects of the exposure to heavy metals, plasticizers and pesticides on child neurodevelopment

High dimensional biology to assess the effects of the exposure to heavy metals, plasticizers and pesticides on child neurodevelopment

Noninvasive prediction models of intra-amniotic infection in women with preterm labor

Among women with preterm labor, those with intra-amniotic infection present the highest risk of early delivery and the most adverse outcomes. The identification of intra-amniotic infection requires amniocentesis, perceived as too invasive by women and physicians. Noninvasive methods for identifying intra-amniotic infection and/or early delivery are crucial to focus early efforts on high-risk preterm labor women while avoiding unnecessary interventions in low-risk preterm labor women. This study modeled the best performing models, integrating biochemical data with clinical and ultrasound information to predict a composite outcome of intra-amniotic infection and/or spontaneous delivery within 7 days. From 2015 to 2020, data from a cohort of women, who underwent amniocentesis to rule in or rule out intra-amniotic infection or inflammation, admitted with a diagnosis of preterm labor at <34 weeks of gestation at the Hospital Clinic and Hospital Sant Joan de Déu, Barcelona, Spain, were used. At admission, transvaginal ultrasound was performed, and maternal blood and vaginal samples were collected. Using high-dimensional biology, vaginal proteins (using multiplex immunoassay), amino acids (using high-performance liquid chromatography), and bacteria (using 16S ribosomal RNA gene amplicon sequencing) were explored to predict the composite outcome. We selected ultrasound, maternal blood, and vaginal predictors that could be tested with rapid diagnostic techniques and developed prediction models employing machine learning that was applied in a validation cohort. A cohort of 288 women with preterm labor at <34 weeks of gestation, of which 103 (35%) had a composite outcome of intra-amniotic infection and/or spontaneous delivery within 7 days, were included in this study. The sample was divided into derivation (n=116) and validation (n=172) cohorts. Of note, 4 prediction models were proposed, including ultrasound transvaginal cervical length, maternal C-reactive protein, vaginal interleukin 6 (using an automated immunoanalyzer), vaginal pH (using a pH meter), vaginal lactic acid (using a reflectometer), and vaginal Lactobacillus genus (using quantitative polymerase chain reaction), with areas under the receiving operating characteristic curve ranging from 82.2% (95% confidence interval, ±3.1%) to 85.2% (95% confidence interval, ±3.1%), sensitivities ranging from 76.1% to 85.9%, and specificities ranging from 75.2% to 85.1%. The study results have provided proof of principle of how noninvasive methods suitable for point-of-care systems can select high-risk cases among women with preterm labor and might substantially aid in clinical management and outcomes while improving the use of resources and patient experience.

Early pathways, biomarkers, and four distinct molecular subclasses of preeclampsia: The intersection of clinical, pathological, and high-dimensional biology studies

Preeclampsia is a syndromic disease of the mother, fetus, and placenta. The main limitation in early and accurate diagnosis of preeclampsia is rooted in the heterogeneity of this syndrome as reflected by diverse molecular pathways, symptoms, and clinical outcomes. Gaps in our knowledge preclude successful early diagnosis, personalized treatment, and prevention. The advent of “omics” technologies and systems biology approaches addresses this problem by identifying the molecular pathways associated with the underlying mechanisms and clinical phenotypes of preeclampsia. Here, we provide a brief overview on how the field has progressed, focusing on studies utilizing state-of-the-art transcriptomics and proteomics methods. Moreover, we summarize our systems biology studies involving maternal blood proteomics and placental transcriptomics, which identified early maternal and placental disease pathways and showed that their interaction influences the clinical presentation of preeclampsia. We also present an analysis of maternal blood proteomics data which revealed distinct molecular subclasses of preeclampsia and their molecular mechanisms. Maternal and placental disease pathways behind these subclasses are similar to those recently reported in studies on the placental transcriptome. These findings may promote the development of novel diagnostic tools for the distinct subtypes of preeclampsia syndrome, enabling early detection and personalized follow-up and tailored care of patients.

A laminar augmented cascading flexible neural forest model for classification of cancer subtypes based on gene expression data

BackgroundCorrectly classifying the subtypes of cancer is of great significance for the in-depth study of cancer pathogenesis and the realization of personalized treatment for cancer patients. In recent years, classification of cancer subtypes using deep neural networks and gene expression data has gradually become a research hotspot. However, most classifiers may face overfitting and low classification accuracy when dealing with small sample size and high-dimensional biology data.ResultsIn this paper, a laminar augmented cascading flexible neural forest (LACFNForest) model was proposed to complete the classification of cancer subtypes. This model is a cascading flexible neural forest using deep flexible neural forest (DFNForest) as the base classifier. A hierarchical broadening ensemble method was proposed, which ensures the robustness of classification results and avoids the waste of model structure and function as much as possible. We also introduced an output judgment mechanism to each layer of the forest to reduce the computational complexity of the model. The deep neural forest was extended to the densely connected deep neural forest to improve the prediction results. The experiments on RNA-seq gene expression data showed that LACFNForest has better performance in the classification of cancer subtypes compared to the conventional methods.ConclusionThe LACFNForest model effectively improves the accuracy of cancer subtype classification with good robustness. It provides a new approach for the ensemble learning of classifiers in terms of structural design.

A Brief Introduction to the Exposome and Human Health

The exposome refers to all environmental exposures (internal and specific/general external) that humans experience from conception through to death. This article examines the importance of both fundamental biological and public health perspectives within the context of the exposome, dealing with novel and well recognized concepts that include exposotype, issues of life stage/aging, and both short (epigenetic) and long-term (evolutionary) biological effects. The problem of scale, use of omics technology and database resources are also discussed. A special focus is also placed on the role of the ultraviolet light exposome in regard to the photolysis of folate and biosynthesis of vitamin D as important molecular mechanisms within human health and biology. Specifically, this includes critical nutrigenomic interactions. High-dimensional biology will permit extremely large scale initiatives in the future that will shed new light on the exposome by better characterizing a plethora of new and established biomarkers. However, smaller, delimited studies should not be ignored, as they can still help define aspects of the human exposome that remain unclear. Still, overall trends in the field are moving inexorably towards multiplexing metabolite and other omic analyses within large population studies. This article aims to reinforce the importance of exposomics via the idea, a fundamental tenet of biology, that human phenotype results from an amalgamation of genes and environment. What needs to be recognized is that phenotypes can be either adaptive or maladaptive. Within our phenome this process propagates disease or provides evolutionary advantage. In other words, the exposome is about more than simply public health.

Multi-omics analysis reveals that co-exposure to phthalates and metals disturbs urea cycle and choline metabolism

This study aimed to evaluate the response of HepaRG cells after co-exposure to phthalates and heavy metals, using a high-dimensional biology paradigm (HDB). Liver is the main metabolism site for the majority of xenobiotics. For this reason, the HepaRG cell line was used as an in vitro model, and cells were exposed to two characteristic mixtures of phthalates and heavy metals containing phthalates (DEHP, DiNP, BBzP) and metals (lead, methylmercury, total mercury) in a concentration-dependent manner. The applied chemical mixtures were selected as the most abundant pollutants in the REPRO_PL and PHIME cohorts, which were studied using the exposome-wide approach in the frame of the EU project HEALS. These studies investigated the environmental causation of neurodevelopmental disorders in neonates and across Europe. The INTEGRA computational platform was used for the calculation of the effective concentrations of the chemicals in the liver through extrapolation from human biomonitoring data and this dose (and a ten-times higher one) was applied to the hepatocyte model. Multi-omics analysis was performed to reveal the genes, proteins, and metabolites affected by the exposure to these chemical mixtures. By extension, we could detect the perturbed metabolic pathways. The generated data were analyzed using advanced bioinformatic tools following the HEALS connectivity paradigm for multi-omics pathway analysis. Co-mapped transcriptomics and proteomics data showed that co-exposure to phthalates and heavy metals leads to perturbations of the urea cycle due to differential expression levels of arginase-1 and -2, argininosuccinate synthase, carbamoyl-phosphate synthase, ornithine carbamoyltransferase, and argininosuccinate lyase. Joint pathway analysis of proteomics and metabolomics data revealed that the detected proteins and metabolites, choline phosphate cytidylyltransferase A, phospholipase D3, group XIIA secretory phospholipase A2, α-phosphatidylcholine, and the a 1,2-diacyl-sn-glycero-3-phosphocholine, are responsible for the homeostasis of the metabolic pathways phosphatidylcholine biosynthesis I, and phospholipases metabolism. The urea, phosphatidylcholine biosynthesis I and phospholipase metabolic pathways are of particular interest since they have been identified also in human samples from the REPRO_PL and PHIME cohorts using untargeted metabolomics analysis and have been associated with impaired psychomotor development in children at the age of two. In conclusion, this study provides the mechanistic evidence that co-exposure to phthalates and metals disturb biochemical processes related to mitochondrial respiration during critical developmental stages, which are clinically linked to neurodevelopmental perturbations.

BCDForest: a boosting cascade deep forest model towards the classification of cancer subtypes based on gene expression data

BackgroundThe classification of cancer subtypes is of great importance to cancer disease diagnosis and therapy. Many supervised learning approaches have been applied to cancer subtype classification in the past few years, especially of deep learning based approaches. Recently, the deep forest model has been proposed as an alternative of deep neural networks to learn hyper-representations by using cascade ensemble decision trees. It has been proved that the deep forest model has competitive or even better performance than deep neural networks in some extent. However, the standard deep forest model may face overfitting and ensemble diversity challenges when dealing with small sample size and high-dimensional biology data.ResultsIn this paper, we propose a deep learning model, so-called BCDForest, to address cancer subtype classification on small-scale biology datasets, which can be viewed as a modification of the standard deep forest model. The BCDForest distinguishes from the standard deep forest model with the following two main contributions: First, a named multi-class-grained scanning method is proposed to train multiple binary classifiers to encourage diversity of ensemble. Meanwhile, the fitting quality of each classifier is considered in representation learning. Second, we propose a boosting strategy to emphasize more important features in cascade forests, thus to propagate the benefits of discriminative features among cascade layers to improve the classification performance. Systematic comparison experiments on both microarray and RNA-Seq gene expression datasets demonstrate that our method consistently outperforms the state-of-the-art methods in application of cancer subtype classification.ConclusionsThe multi-class-grained scanning and boosting strategy in our model provide an effective solution to ease the overfitting challenge and improve the robustness of deep forest model working on small-scale data. Our model provides a useful approach to the classification of cancer subtypes by using deep learning on high-dimensional and small-scale biology data.

Integrating High-Dimensional Transcriptomics and Image Analysis Tools into Early Safety Screening: Proof of Concept for a New Early Drug Development Strategy.

During drug discovery and development, the early identification of adverse effects is expected to reduce costly late-stage failures of candidate drugs. As risk/safety assessment takes place rather late during the development process and due to the limited ability of animal models to predict the human situation, modern unbiased high-dimensional biology readouts are sought, such as molecular signatures predictive for in vivo response using high-throughput cell-based assays. In this theoretical proof of concept, we provide findings of an in-depth exploration of a single chemical core structure. Via transcriptional profiling, we identified a subset of close analogues that commonly downregulate multiple tubulin genes across cellular contexts, suggesting possible spindle poison effects. Confirmation via a qualified toxicity assay (in vitro micronucleus test) and the identification of a characteristic aggregate-formation phenotype via exploratory high-content imaging validated the initial findings. SAR analysis triggered the synthesis of a new set of compounds and allowed us to extend the series showing the genotoxic effect. We demonstrate the potential to flag toxicity issues by utilizing data from exploratory experiments that are typically generated for target evaluation purposes during early drug discovery. We share our thoughts on how this approach may be incorporated into drug development strategies.

Amniotic Fluid: The Use of High-Dimensional Biology to Understand Fetal Well-Being

Our aim was to review the use of high-dimensional biology techniques, specifically transcriptomics, proteomics, and metabolomics, in amniotic fluid to elucidate the mechanisms behind preterm birth or assessment of fetal development. We performed a comprehensive MEDLINE literature search on the use of transcriptomic, proteomic, and metabolomic technologies for amniotic fluid analysis. All abstracts were reviewed for pertinence to preterm birth or fetal maturation in human subjects. Nineteen articles qualified for inclusion. Most articles described the discovery of biomarker candidates, but few larger, multicenter replication or validation studies have been done. We conclude that the use of high-dimensional systems biology techniques to analyze amniotic fluid has significant potential to elucidate the mechanisms of preterm birth and fetal maturation. However, further multicenter collaborative efforts are needed to replicate and validate candidate biomarkers before they can become useful tools for clinical practice. Ideally, amniotic fluid biomarkers should be translated to a noninvasive test performed in maternal serum or urine.

The Joint Null Criterion for Multiple Hypothesis Tests

Simultaneously performing many hypothesis tests is a problem commonly encountered in high-dimensional biology. In this setting, a large set of p-values is calculated from many related features measured simultaneously. Classical statistics provides a criterion for defining what a “correct” p-value is when performing a single hypothesis test. We show here that even when each p-value is marginally correct under this single hypothesis criterion, it may be the case that the joint behavior of the entire set of p-values is problematic. On the other hand, there are cases where each p-value is marginally incorrect, yet the joint distribution of the set of p-values is satisfactory. Here, we propose a criterion defining a well behaved set of simultaneously calculated p-values that provides precise control of common error rates and we introduce diagnostic procedures for assessing whether the criterion is satisfied with simulations. Multiple testing p-values that satisfy our new criterion avoid potentially large study specific errors, but also satisfy the usual assumptions for strong control of false discovery rates and family-wise error rates. We utilize the new criterion and proposed diagnostics to investigate two common issues in high-dimensional multiple testing for genomics: dependent multiple hypothesis tests and pooled versus test-specific null distributions.

Shrinkage Estimation of Effect Sizes as an Alternative to Hypothesis Testing Followed by Estimation in High-Dimensional Biology: Applications to Differential Gene Expression

Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a hard-threshold estimator of the expression ratio that is not known to perform well in terms of mean-squared error, the sum of estimator variance and squared estimator bias. On the basis of two distinct simulation studies and data from different microarray studies, we systematically compared the performance of several estimators representing both current practice and shrinkage. We find that the threshold-based estimators usually perform worse than the maximum-likelihood estimator (MLE) and they often perform far worse as quantified by estimated mean-squared risk. By contrast, the shrinkage estimators tend to perform as well as or better than the MLE and never much worse than the MLE, as expected from what is known about shrinkage. However, a Bayesian measure of performance based on the prior information that few genes are differentially expressed indicates that hard-threshold estimators perform about as well as the local false discovery rate (FDR), the best of the shrinkage estimators studied. Based on the ability of the latter to leverage information across genes, we conclude that the use of the local-FDR estimator of the fold change instead of informal or threshold-based combinations of statistical tests and non-shrinkage estimators can be expected to substantially improve the reliability of gene prioritization at very little risk of doing so less reliably. Since the proposed replacement of post-selection estimates with shrunken estimates applies as well to other types of high-dimensional data, it could also improve the analysis of SNP data from genome-wide association studies.

How accurate are the extremely small [formula omitted]-values used in genomic research: An evaluation of numerical libraries

In the fields of genomics and high-dimensional biology (HDB), massive multiple testing prompts the use of extremely small significance levels. Because tail areas of statistical distributions are needed for hypothesis testing, the accuracy of these areas is important to confidently make scientific judgments. Previous work on accuracy was primarily focused on evaluating professionally written statistical software, like SAS, on the Statistical Reference Datasets (StRD) provided by the National Institute of Standards and Technology (NIST) and on the accuracy of tail areas in statistical distributions. The goal of this paper is to provide guidance to investigators, who are developing their own custom scientific software built upon numerical libraries written by others. Specifically, we evaluate the accuracy of small tail areas from cumulative distribution functions (CDF) of the Chi-square and t -distribution by comparing several open-source, free, or commercially licensed numerical libraries in Java, C, and R to widely accepted standards of comparison like ELV and DCDFLIB. In our evaluation, the C libraries and R functions are consistently accurate up to six significant digits. Amongst the evaluated Java libraries, Colt is the most accurate. These languages and libraries are popular choices among programmers developing scientific software, so the results herein can be useful to programmers in choosing libraries for CDF accuracy.

High-dimensional biology to comprehend hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is the fifth most common cancer worldwide and is the third leading cause of death from cancer. The diverse etiology, high morbidity/mortality, lack of diagnostic markers for early diagnosis and the highly variable clinical course of HCC have hindered advances in diagnosis and treatment. Microsatellite instability, chromosomal aberrations, mutations in key cell cycle genes and epigenetic changes have been reported in HCC. Availability of modern technologies advance ‘high-dimensional biology’ (HDB), a term that refers to the simultaneous study of the genetic variants (genome), transcription (mRNA; transcriptome), peptides and proteins (proteomics), and metabolites (metabolomics) for the intermediate products of metabolism of an organ, tissue or organism. The growing interest in omics-based research has enabled the simultaneous examination of thousands of genes, transcripts and proteins of interest, with high-throughput techniques and advanced analytical tools for data analysis. The use of each approach towards functional omics has lead to the classification of HCC into molecular subgroups. Here we review the use of HDB as a tool for the identification of markers for screening, diagnosis, molecular classification and the discovery of new therapeutic drug targets of HCC. With the extensive use of HDB, it may be possible in the near future, to have custom-made therapeutic regimens for HCC based on the molecular subtype, ultimately leading to an improved survival of HCC patients.

Translationale Forschung in der Geburtsmedizin: Beispiel angiogene Faktoren und Präeklampsie

Translationale Forschung im eigentlichen Wortsinn bedeutet eine Übersetzungsfunktion zwischen Grundlagenforschung und klinischer Forschung und beinhaltet den direkten Eingang der experimentellen Forschungsresultate in konkrete diagnostische und therapeutische Novitäten. Darüber hinaus muss es auch eine Rückkopplung von der Klinik in die Labore hinein geben und die dortigen Fragestellungen beeinflussen. Diese Brücke muss auch in der geburtsmedizinischen Forschung aufgebaut werden, da bislang der punktuelle Einsatz von Methoden der „high-dimensional biology“ bei einem der ungelösten Probleme der Geburtsmedizin, nämlich dem Komplex hypertensive Schwangerschaftserkrankungen/Plazentainsuffizienz, keinen wirklichen klinischen Durchbruch gebracht hat. Durch die Erforschung angiogener Faktoren scheint man jetzt aber, wenn nicht der Ursache der Präeklampsie, so doch den entscheidenden pathogenetischen Mediatoren sehr nahe gekommen zu sein. Da antiangiogene Faktoren wie sFlt1 (soluble fms-like tyrosine kinase 1) und sEng (soluble endoglin) bereits Wochen vor Manifestation einer Präeklampsie sehr stark erhöht im mütterlichen Blut messbar sind und maternale Serumkonzentrationen dieser Faktoren gut mit dem klinischen Verlauf korrelieren, ist jetzt im Risikokollektiv eine sehr gute klinische Prognose möglich. Als nächster Schritt steht die Entwicklung einer therapeutischen Intervention, die durch die pharmakologische Beeinflussung des angiogenen-antiangiogenen Gleichgewichts die präeklamptischen Symptome positiv beeinflussen kann. Die Messung angiogener Faktoren in verschiedenen klinischen Studien hat rückwirkend wichtige Informationen darüber gebracht, welche Faktoren die angiogene-antiangiogene Balance beeinflussen.

The use of high-dimensional biology (genomics, transcriptomics, proteomics, and metabolomics) to understand the preterm parturition syndrome.

High-dimensional biology (HDB) refers to the simultaneous study of the genetic variants (DNA variation), transcription (messenger RNA [mRNA]), peptides and proteins, and metabolites of an organ, tissue, or an organism in health and disease. The fundamental premise is that the evolutionary complexity of biological systems renders them difficult to comprehensively understand using only a reductionist approach. Such complexity can become tractable with the use of "omics" research. This term refers to the study of entities in aggregate. The current nomenclature of "omics" sciences includes genomics for DNA variants, transcriptomics for mRNA, proteomics for proteins, and metabolomics for intermediate products of metabolism. Another discipline relevant to medicine is pharmacogenomics. The two major advances that have made HDB possible are technological breakthroughs that allow simultaneous examination of thousands of genes, transcripts, and proteins, etc., with high-throughput techniques and analytical tools to extract information. What is conventionally considered hypothesis-driven research and discovery-driven research (through "omic" methodologies) are complementary and synergistic. Here we review data which have been derived from: 1) genomics to examine predisposing factors for preterm birth; 2) transcriptomics to determine changes in mRNA in reproductive tissues associated with preterm labour and preterm prelabour rupture of membranes; 3) proteomics to identify differentially expressed proteins in amniotic fluid of women with preterm labour; and 4) metabolomics to identify the metabolic footprints of women with preterm labour likely to deliver preterm and those who will deliver at term. The complementary nature of discovery science and HDB is emphasised.

Physiological genomics special issue on animal functional genomics

this special issue of Physiological Genomics highlights 12 papers that reflect presentations made by 110 international delegates of the 2nd International Symposium on Animal Functional Genomics (2nd ISAFG) held May 16th-19th, 2006, at Michigan State University (East Lansing, MI). This was the second

Epistemological issues in omics and high-dimensional biology: give the people what they want

Gene expression microarrays have been the vanguard of new analytic approaches in high-dimensional biology. Draft sequences of several genomes coupled with new technologies allow study of the influences and responses of entire genomes rather than isolated genes. This has opened a new realm of highly dimensional biology where questions involve multiplicity at unprecedented scales: thousands of genetic polymorphisms, gene expression levels, protein measurements, genetic sequences, or any combination of these and their interactions. Such situations demand creative approaches to the processes of inference, estimation, prediction, classification, and study design. Although bench scientists intuitively grasp the need for flexibility in the inferential process, the elaboration of formal supporting statistical frameworks is just at the very start. Here, we will discuss some of the unique statistical challenges facing investigators studying high-dimensional biology, describe some approaches being developed by statistical scientists, and offer an epistemological framework for the validation of proffered statistical procedures. A key theme will be the challenge in providing methods that a statistician judges to be sound and a biologist finds informative. The shift from family-wise error rate control to false discovery rate estimation and to assessment of ranking and other forms of stability will be portrayed as illustrative of approaches to this challenge.

HDBStat!: A platform-independent software suite for statistical analysis of high dimensional biology data

BackgroundMany efforts in microarray data analysis are focused on providing tools and methods for the qualitative analysis of microarray data. HDBStat! (High-Dimensional Biology-Statistics) is a software package designed for analysis of high dimensional biology data such as microarray data. It was initially developed for the analysis of microarray gene expression data, but it can also be used for some applications in proteomics and other aspects of genomics. HDBStat! provides statisticians and biologists a flexible and easy-to-use interface to analyze complex microarray data using a variety of methods for data preprocessing, quality control analysis and hypothesis testing.ResultsResults generated from data preprocessing methods, quality control analysis and hypothesis testing methods are output in the form of Excel CSV tables, graphs and an Html report summarizing data analysis.ConclusionHDBStat! is a platform-independent software that is freely available to academic institutions and non-profit organizations. It can be downloaded from our website .

Towards sound epistemological foundations of statistical methods for high-dimensional biology.

A sound epistemological foundation for biological inquiry comes, in part, from application of valid statistical procedures. This tenet is widely appreciated by scientists studying the new realm of high-dimensional biology, or 'omic' research, which involves multiplicity at unprecedented scales. Many papers aimed at the high-dimensional biology community describe the development or application of statistical techniques. The validity of many of these is questionable, and a shared understanding about the epistemological foundations of the statistical methods themselves seems to be lacking. Here we offer a framework in which the epistemological foundation of proposed statistical methods can be evaluated.

Power and sample size estimation in high dimensional biology

Genomic scientists often test thousands of hypotheses in a single experiment. One example is a microarray experiment that seeks to determine differential gene expression among experimental groups. Planning such experiments involves a determination of sample size that will allow meaningful interpretations. Traditional power analysis methods may not be well suited to this task when thousands of hypotheses are tested in a discovery oriented basic research. We introduce the concept of expected discovery rate (EDR) and an approach that combines parametric mixture modelling with parametric bootstrapping to estimate the sample size needed for a desired accuracy of results. While the examples included are derived from microarray studies, the methods, herein, are ‘extraparadigmatic’ in the approach to study design and are applicable to most high dimensional biological situations. Pilot data from three different microarray experiments are used to extrapolate EDR as well as the related false discovery rate at different sample sizes and thresholds.