Variable Selection in Bayesian Multiple Instance Regression using Shotgun Stochastic Search.

In multiple instance learning (MIL), a bag represents a sample that has a set of instances, each of which is described by a vector of explanatory variables, but the entire bag only has one label/response. Though many methods for MIL have been developed to date, few have paid attention to interpretability of models and results. The proposed Bayesian regression model stands on two levels of hierarchy, which transparently show how explanatory variables explain and instances contribute to bag responses. Moreover, two selection problems are simultaneously addressed; the instance selection to find out the instances in each bag responsible for the bag response, and the variable selection to search for the important covariates. To explore a joint discrete space of indicator variables created for selection of both explanatory variables and instances, the shotgun stochastic search algorithm is modified to fit in the MIL context. Also, the proposed model offers a natural and rigorous way to quantify uncertainty in coefficient estimation and outcome prediction, which many modern MIL applications call for. The simulation study shows the proposed regression model can select variables and instances with high performance (AUC greater than 0.86), thus predicting responses well. The proposed method is applied to the musk data for prediction of binding strengths (labels) between molecules (bags) with different conformations (instances) and target receptors. It outperforms all existing methods, and can identify variables relevant in modeling responses.

B-cell receptor profiling before and after IVIG monotherapy in newly diagnosed idiopathic inflammatory myopathies.

OBJECTIVE: To unravel B-cell receptor (BcR) characteristics in muscle tissues and peripheral blood and gain more insight into BcR repertoire changes in peripheral blood in idiopathic inflammatory myopathies (IIMs), and study how this correlates to the clinical response to IVIG. METHODS: Nineteen treatment-naive patients with newly diagnosed IIM were prospectively treated with IVIG monotherapy. RNA-based BcR repertoire sequencing was performed in muscle biopsies collected before, and in peripheral blood (PB) collected before and nine weeks after IVIG treatment. Results were correlated to patients' clinical improvement based on the total improvement score (TIS). RESULTS: Prior to IVIG treatment, BcR clones found in muscle tissue could be retrieved in peripheral blood. Nine weeks after IVIG treatment, new patient-specific dominant BcR clones appeared in peripheral blood while pre-treatment dominant BcR clones disappeared. The cumulative frequency of all dominant BcR clones before treatment was significantly higher in individuals who responded to IVIG compared with those who did not respond to IVIG, and correlated with a higher CK. During follow-up, a decrease in the cumulative frequency of all dominant clones correlated with a higher TIS. CONCLUSION: In treatment-naive patients with newly diagnosed IIM, muscle tissue and peripheral blood share expanded BcR clones. In our study a higher cumulative frequency of dominant BcR clones in blood before treatment was associated with a higher CK and better treatment response, suggesting that response to IVIG may depend on the composition of the pre-treatment BcR repertoire.

Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability.

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.

Assessment of disability in idiopathic inflammatory myopathy: a call for linearity.

OBJECTIVES: To evaluate the clinimetric properties of the Academic Medical Centre Disability Score (ALDS) in patients with idiopathic inflammatory myopathy (IIM). METHODS: We used prospectively collected data of IIM patients who completed a phase-2 study with first-line IVIG monotherapy. The ALDS is a patient-reported questionnaire which contains 25 items relevant for disability in myositis. ALDS and all core set measures (CSMs) for myositis [including HAQ-Disability Index (HAQ-DI)] were evaluated at baseline and 9 weeks follow-up. In addition, the 2016 ACR/EULAR myositis response criteria outcome called Total Improvement Score (TIS) was evaluated at 9 weeks. We examined floor/ceiling effects, reliability and construct validity of the ALDS. To examine known-group validity, ALDS change scores over time were compared with TIS and physician impression of clinical response. RESULTS: Nineteen patients with IIM [median age 59 years, 12 (63%) female] were enrolled. At baseline, ALDS showed a median score of 65.4 (IQR 58.2-73.5), good Cronbach's alpha (α = 0.84) and a small ceiling effect (11%). Construct validity was confirmed by moderate to strong correlations between ALDS and HAQ-DI [rs = -0.57 (baseline); -0.86 (follow-up)]. ALDS change score correlated with TIS (rs = 0.70), discriminated between responders and non-responders (TIS ≥ 40; P = 0.001), between groups based on physician impression of clinical response (P = 0.03), and detected deterioration. CONCLUSION: The ALDS showed promising clinimetric properties and detected relevant changes in disability in patients with myositis. These results warrant further investigations.

Ultrasound and MR muscle imaging in new onset idiopathic inflammatory myopathies at diagnosis and after treatment: a comparative pilot study.

OBJECTIVES: To prospectively compare ultrasound (US) and whole-body MRI for detection of muscle abnormalities compatible with idiopathic inflammatory myopathies (IIM). METHODS: Newly diagnosed IIM patients underwent US (14 muscles) and MRI (36 muscles) at diagnosis and after nine weeks monotherapy with intravenous immunoglobulin. Muscles were compatible with IIM when quantitative US echo-intensity (EI) z scores was ≥1.5, semi-quantitative US Heckmatt score was ≥2, qualitative US was abnormal, or when MRI showed oedema on T2-weighted images. At patient level, findings were classified as abnormal when quantitative US EI z scores was >1.5 (n = 3 muscles), >2.5 (n = 2 muscles) or >3.5 (n = 1 muscle), or if ≥3 muscles showed abnormalities as described above for the other diagnostic methods. RESULTS: At diagnosis, in 18 patients US of 252 muscles revealed abnormalities in 36 muscles (14%) with quantitative, in 153 (61%) with semi-quantitative and in 168 (67%) with qualitative analysis. MRI showed oedema in 476 out of 623 muscles (76%). Five patients (28%) reached abnormal classification with quantitative US, 16 (89%) with semi-quantitative and qualitative US, and all patients (100%) with MRI. Nine-week follow-up of 12 patients showed no change over time with quantitative US or MRI, and a decrease in abnormalities with semi-quantitative US (P <0.01), and qualitative US (P <0.01). CONCLUSION: At diagnosis, MRI was more sensitive than US to detect muscle abnormalities compatible with IIM. Semi-quantitative US and qualitative US detected abnormalities in the majority of the patients while evaluating fewer muscles than MRI and showed change over time after nine weeks of treatment.

RCRdiff: A fully integrated Bayesian method for differential expression analysis using raw NanoString nCounter data.

The medium-throughput mRNA abundance platform NanoString nCounter has gained great popularity in the past decade, due to its high sensitivity and technical reproducibility as well as remarkable applicability to ubiquitous formalin fixed paraffin embedded (FFPE) tissue samples. Based on RCRnorm developed for normalizing NanoString nCounter data and Bayesian LASSO for variable selection, we propose a fully integrated Bayesian method, called RCRdiff, to detect differentially expressed (DE) genes between different groups of tissue samples (eg, normal and cancer). Unlike existing methods that often require normalization performed beforehand, RCRdiff directly handles raw read counts and jointly models the behaviors of different types of internal controls along with DE and non-DE gene patterns. Doing so would avoid efficiency loss caused by ignoring estimation uncertainty from the normalization step in a sequential approach and thus can offer more reliable statistical inference. We also propose clustering-based strategies for DE gene selection, which do not require any external dataset and are free of any arbitrary cutoff. Empirical evidence of the attractiveness of RCRdiff is demonstrated via extensive simulation and data examples.

Path algorithms for fused lasso signal approximator with application to COVID-19 spread in Korea.

The fused lasso signal approximator (FLSA) is a smoothing procedure for noisy observations that uses fused lasso penalty on unobserved mean levels to find sparse signal blocks. Several path algorithms have been developed to obtain the whole solution path of the FLSA. However, it is known that the FLSA has model selection inconsistency when the underlying signals have a stair-case block, where three consecutive signal blocks are either strictly increasing or decreasing. Modified path algorithms for the FLSA have been proposed to guarantee model selection consistency regardless of the stair-case block. In this paper, we provide a comprehensive review of the path algorithms for the FLSA and prove the properties of the recently modified path algorithms' hitting times. Specifically, we reinterpret the modified path algorithm as the path algorithm for local FLSA problems and reveal the condition that the hitting time for the fusion of the modified path algorithm is not monotone in a tuning parameter. To recover the monotonicity of the solution path, we propose a pathwise adaptive FLSA having monotonicity with similar performance as the modified solution path algorithm. Finally, we apply the proposed method to the number of daily-confirmed cases of COVID-19 in Korea to identify the change points of its spread.

Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples.

The area under a receiver operating characteristic curve (AUC) is a useful tool to assess the performance of continuous-scale diagnostic tests on binary classification. In this article, we propose an empirical likelihood (EL) method to construct confidence intervals for the AUC from data collected by ranked set sampling (RSS). The proposed EL-based method enables inferences without assumptions required in existing nonparametric methods and takes advantage of the sampling efficiency of RSS. We show that for both balanced and unbalanced RSS, the EL-based point estimate is the Mann-Whitney statistic, and confidence intervals can be obtained from a scaled chi-square distribution. Simulation studies and two case studies on diabetes and chronic kidney disease data suggest that using the proposed method and RSS enables more efficient inference on the AUC.

Intravenous immunoglobulins as first-line treatment in idiopathic inflammatory myopathies: a pilot study.

OBJECTIVES: We explored efficacy and safety of IVIg as first-line treatment in patients with an idiopathic inflammatory myopathy. METHODS: In this investigator-initiated phase 2 open-label study, we included 20 adults with a newly diagnosed, biopsy-proven idiopathic inflammatory myopathy, and a disease duration of less than 9 months. Patients with IBM and prior use of immunosuppressants were excluded. The standard treatment regimen consisted of IVIg (Privigen) monotherapy for 9 weeks: a loading dose (2 g/kg body weight) and two subsequent maintenance doses (1 g/kg body weight) with a 3-week interval. The primary outcome was the number of patients with at least moderate improvement on the 2016 ACR/EULAR Total Improvement Score. Secondary outcomes included time to improvement, the number of patients requiring rescue medication and serious adverse events. RESULTS: We included patients with DM (n = 9), immune-mediated necrotizing myopathy (n = 6), non-specific myositis/overlap myositis (n = 4) and anti-synthetase syndrome (n = 1). One patient was excluded from analyses because of minimal weakness resulting in a ceiling effect. Eight patients (8/19 = 42.0%; Clopper-Pearson 95% CI: 19.6, 64.6) had at least moderate improvement by 9 weeks. Of these, six reached improvement by 3 weeks. Seven patients required rescue medication due to insufficient efficacy and prematurely ended the study. Three serious adverse events occurred, of which one was pulmonary embolism. CONCLUSION: First-line IVIg monotherapy led to at least moderate improvement in nearly half of patients with a fast clinical response in the majority of responders. TRIAL REGISTRATION: Netherlands Trial Register identifier, NTR6160.

Biomarker profiles of endothelial activation and dysfunction in rare systemic autoimmune diseases: implications for cardiovascular risk.

OBJECTIVES: Vasculopathy is an important hallmark of systemic chronic inflammatory connective tissue diseases (CICTD) and is associated with increased cardiovascular risk. We investigated disease-specific biomarker profiles associated with endothelial dysfunction, angiogenic homeostasis and (tissue) inflammation, and their relation to disease activity in rare CICTD. METHODS: A total of 38 serum proteins associated with endothelial (dys)function and inflammation were measured by multiplex-immunoassay in treatment-naive patients with localized scleroderma (LoS, 30), eosinophilic fasciitis (EF, 8) or (juvenile) dermatomyositis (34), 119 (follow-up) samples during treatment, and 65 controls. Data were analysed by unsupervised clustering, Spearman correlations, non-parametric t test and ANOVA. RESULTS: The systemic CICTD, EF and dermatomyositis, had distinct biomarker profiles, with 'signature' markers galectin-9 (dermatomyositis) and CCL4, CCL18, CXCL9, fetuin, fibronectin, galectin-1 and TSP-1 (EF). In LoS, CCL18, CXCL9 and CXCL10 were subtly increased. Furthermore, dermatomyositis and EF shared upregulation of markers related to interferon (CCL2, CXCL10), endothelial activation (VCAM-1), inhibition of angiogenesis (angiopoietin-2, sVEGFR-1) and inflammation/leucocyte chemo-attraction (CCL19, CXCL13, IL-18, YKL-40), as well as disturbance of the Angiopoietin-Tie receptor system and VEGF-VEGFR system. These profiles were related to disease activity, and largely normalized during treatment. However, a subgroup of CICTD patients showed continued elevation of CXCL10, CXCL13, galectin-9, IL-18, TNFR2, VCAM-1, and/or YKL-40 during clinically inactive disease, possibly indicating subclinical interferon-driven inflammation and/or endothelial dysfunction. CONCLUSION: CICTD-specific biomarker profiles revealed an anti-angiogenic, interferon-driven environment during active disease, with incomplete normalization under treatment. This warrants further investigation into monitoring of vascular biomarkers during clinical follow-up, or targeted interventions to minimize cardiovascular risk in the long term.

Borrelia burgdorferi sensu lato seroconversion after intravenous immunoglobulin treatment: A cohort study.

OBJECTIVE: Intravenous immunoglobulin (IVIg) consists of pooled donor immunoglobulins (IgG), possibly including anti-Borrelia burgdorferi (Bbsl) antibodies. Apparent IVIg-related Bbsl seroconversion could lead to incorrect diagnosis of Lyme borreliosis. This cohort study was designed to determine how often IVIg treatment leads to apparent Bbsl seroconversion and whether antibodies disappear post-treatment. METHODS: Sera from chronic inflammatory demyelinating polyneuropathy (CIDP) and myositis patients were analyzed, drawn pre-treatment and 6-12 weeks after the start of IVIg. In patients with apparent seroconversion, follow-up samples after treatment withdrawal were analyzed, if available. Patients treated with corticosteroids were included as controls. A two-tier protocol was used for serological testing consisting of the C6 Lyme ELISA (Oxford Immunotec) and confirmation by immunoglobulin M (IgM) and immunoglobulin G (IgG) immunoblot (Mikrogen® ). RESULTS: We included 61 patients: 51 patients were treated with IVIg and 10 with dexamethasone. Of the patients treated with IVIg, 42 had CIDP (82%) and were treated with Nanogam® (Sanquin Plasma Products). Nine patients had myositis (18%) and were treated with Privigen® (CSL Behring). Anti-Bbsl IgG seroprevalence pre-treatment was 3% (2/61). Apparent seroconversion during IVIg treatment occurred in 39% (20/51) of patients, all treated with Nanogam. Post-treatment seroreversion occurred in 92% (12/13) of patients with available follow-up samples; in 78% (7/9) seroreversion was observed within 3 months. CONCLUSIONS: Transient presence of anti-Bbsl IgG antibodies after IVIg is regularly observed. This effect appears to be dependent on the IVIg brand, probably reflecting variation in Bbsl exposure of plasma donors. Lyme borreliosis serological testing during, and weeks to months after, IVIg is therefore of limited utility.

Adaptive local false discovery rate procedures for highly spiky data and their application RNA sequencing data of yeast SET4 deletion mutants.

Chromatin dynamics are central to the regulation of gene expression and genome stability. In order to improve understanding of the factors regulating chromatin dynamics, the genes encoding these factors are deleted and the differential gene expression profiles are determined using approaches such as RNA sequencing. Here, we analyzed a gene expression dataset aimed at uncovering the function of the relatively uncharacterized chromatin regulator, Set4, in the model system Saccharomyces cerevisiae (budding yeast). The main theme of this paper focuses on identifying the highly differentially expressed genes in cells deleted for Set4 (referred to as Set4 Δ mutant dataset) compared to the wild-type yeast cells. The Set4 Δ mutant data produce a spiky distribution on the log-fold changes of their expressions, and it is reasonably assumed that genes which are not highly differentially expressed come from a mixture of two normal distributions. We propose an adaptive local false discovery rate (FDR) procedure, which estimates the null distribution of the log-fold changes empirically. We numerically show that, unlike existing approaches, our proposed method controls FDR at the aimed level (0.05) and also has competitive power in finding differentially expressed genes. Finally, we apply our procedure to analyzing the Set4 Δ mutant dataset.

Truncated rank correlation (TRC) as a robust measure of test-retest reliability in mass spectrometry data.

In mass spectrometry (MS) experiments, more than thousands of peaks are detected in the space of mass-to-charge ratio and chromatographic retention time, each associated with an abundance measurement. However, a large proportion of the peaks consists of experimental noise and low abundance compounds are typically masked by noise peaks, compromising the quality of the data. In this paper, we propose a new measure of similarity between a pair of MS experiments, called truncated rank correlation (TRC). To provide a robust metric of similarity in noisy high-dimensional data, TRC uses truncated top ranks (or top m-ranks) for calculating correlation. A comprehensive numerical study suggests that TRC outperforms traditional sample correlation and Kendall's τ. We apply TRC to measuring test-retest reliability of two MS experiments, including biological replicate analysis of the metabolome in HEK293 cells and metabolomic profiling of benign prostate hyperplasia (BPH) patients. An R package trc of the proposed TRC and related functions is available at https://sites.google.com/site/dhyeonyu/software.

Online estimation of the case fatality rate using a run-off triangle data approach: An application to the Korean MERS outbreak in 2015.

This work is motivated by the recent Korean Middle East respiratory syndrome outbreak. We propose an easy online estimation procedure for the case fatality rate, ie, the proportion of deaths among the total cases during the course of an epidemic disease, which is an important indicator of the severity of a disease. The key step in our procedure is representing the data with the run-off triangle, which simultaneously takes into account two time axes, namely, the calendar and disease-duration times. We restructure the original data into run-off triangle data, where the cells contain the numbers of cured patients, deceased patients, and patients still having the disease at a given combination of calendar and disease-duration times. Based on the restructured run-off triangle data, we propose an online estimator of the case fatality rate. We numerically show the advantages of the proposed estimator compared to the existing estimators in the literature. Finally, we apply our procedure to the 2015 Korean Middle East respiratory syndrome outbreak data.

High-Throughput Omics and Statistical Learning Integration for the Discovery and Validation of Novel Diagnostic Signatures in Colorectal Cancer.

The advancement of bioinformatics and machine learning has facilitated the discovery and validation of omics-based biomarkers. This study employed a novel approach combining multi-platform transcriptomics and cutting-edge algorithms to introduce novel signatures for accurate diagnosis of colorectal cancer (CRC). Different random forests (RF)-based feature selection methods including the area under the curve (AUC)-RF, Boruta, and Vita were used and the diagnostic performance of the proposed biosignatures was benchmarked using RF, logistic regression, naïve Bayes, and k-nearest neighbors models. All models showed satisfactory performance in which RF appeared to be the best. For instance, regarding the RF model, the following were observed: mean accuracy 0.998 (standard deviation (SD) < 0.003), mean specificity 0.999 (SD < 0.003), and mean sensitivity 0.998 (SD < 0.004). Moreover, proposed biomarker signatures were highly associated with multifaceted hallmarks in cancer. Some biomarkers were found to be enriched in epithelial cell signaling in Helicobacter pylori infection and inflammatory processes. The overexpression of TGFBI and S100A2 was associated with poor disease-free survival while the down-regulation of NR5A2, SLC4A4, and CD177 was linked to worse overall survival of the patients. In conclusion, novel transcriptome signatures to improve the diagnostic accuracy in CRC are introduced for further validations in various clinical settings.

Autoantibody testing in idiopathic inflammatory myopathies.

The diagnosis and classification of idiopathic inflammatory myopathies are based mainly on clinical and histological features. The discovery of myositis-specific and myositis-associated antibodies has simplified the (sub)classification of inflammatory myopathies. Patients suspected of having an idiopathic inflammatory myopathy should undergo routine antibody testing to gain more insight into distinct phenotypes, comorbidities, treatment response and prognosis. Furthermore, autoantibody testing can help in patients with atypical patterns of weakness or with an unresolved limb-girdle myopathic phenotype, or interstitial lung disease. However, some important technical and methodological issues can hamper the interpretation of antibody testing; for example, some antibodies are not included in the widely available line blots. We aim to provide a practical review of the use of autoantibody testing in idiopathic inflammatory myopathies in clinical practice.

Permutation based testing on covariance separability.

Separability is an attractive feature of covariance matrices or matrix variate data, which can improve and simplify many multivariate procedures. Due to its importance, testing separability has attracted much attention in the past. The procedures in the literature are of two types, likelihood ratio test (LRT) and Rao's score test (RST). Both are based on the normality assumption or the large-sample asymptotic properties of the test statistics. In this paper, we develop a new approach that is very different from existing ones. We propose to reformulate the null hypothesis (the separability of a covariance matrix of interest) into many sub-hypotheses (the separability of the sub-matrices of the covariance matrix), which are testable using a permutation based procedure.We then combine the testing results of sub-hypotheses using the Bonferroni and two-stage additive procedures. Our permutation based procedures are inherently distribution free; thus it is robust to non-normality of the data. In addition, unlike the LRT, they are applicable to situations when the sample size is smaller than the number of unknown parameters in the covariance matrix. Our numerical study and data examples show the advantages of our procedures over the existing LRT and RST.

Empirical null estimation using zero-inflated discrete mixture distributions and its application to protein domain data.

In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. This article aims to select significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that the mutation counts follow a zero-inflated model in order to account for the true zeros in the count model and the excess zeros. The class of models considered is the Zero-inflated Generalized Poisson (ZIGP) distribution. Furthermore, we assumed that there exists a cut-off value such that smaller counts than this value are generated from the null distribution. We present several data-dependent methods to determine the cut-off value. We also consider a two-stage procedure based on screening process so that the number of mutations exceeding a certain value should be considered as significant mutations. Simulated and protein domain data sets are used to illustrate this procedure in estimation of the empirical null using a mixture of discrete distributions. Overall, while maintaining control of the FDR, the proposed two-stage testing procedure has superior empirical power.

Cox model with interval-censored covariate in cohort studies.

In cohort studies the outcome is often time to a particular event, and subjects are followed at regular intervals. Periodic visits may also monitor a secondary irreversible event influencing the event of primary interest, and a significant proportion of subjects develop the secondary event over the period of follow-up. The status of the secondary event serves as a time-varying covariate, but is recorded only at the times of the scheduled visits, generating incomplete time-varying covariates. While information on a typical time-varying covariate is missing for entire follow-up period except the visiting times, the status of the secondary event are unavailable only between visits where the status has changed, thus interval-censored. One may view interval-censored covariate of the secondary event status as missing time-varying covariates, yet missingness is partial since partial information is provided throughout the follow-up period. Current practice of using the latest observed status produces biased estimators, and the existing missing covariate techniques cannot accommodate the special feature of missingness due to interval censoring. To handle interval-censored covariates in the Cox proportional hazards model, we propose an available-data estimator, a doubly robust-type estimator as well as the maximum likelihood estimator via EM algorithm and present their asymptotic properties. We also present practical approaches that are valid. We demonstrate the proposed methods using our motivating example from the Northern Manhattan Study.

Enhanced construction of gene regulatory networks using hub gene information.

BACKGROUND: Gene regulatory networks reveal how genes work together to carry out their biological functions. Reconstructions of gene networks from gene expression data greatly facilitate our understanding of underlying biological mechanisms and provide new opportunities for biomarker and drug discoveries. In gene networks, a gene that has many interactions with other genes is called a hub gene, which usually plays an essential role in gene regulation and biological processes. In this study, we developed a method for reconstructing gene networks using a partial correlation-based approach that incorporates prior information about hub genes. Through simulation studies and two real-data examples, we compare the performance in estimating the network structures between the existing methods and the proposed method. RESULTS: In simulation studies, we show that the proposed strategy reduces errors in estimating network structures compared to the existing methods. When applied to Escherichia coli, the regulation network constructed by our proposed ESPACE method is more consistent with current biological knowledge than the SPACE method. Furthermore, application of the proposed method in lung cancer has identified hub genes whose mRNA expression predicts cancer progress and patient response to treatment. CONCLUSIONS: We have demonstrated that incorporating hub gene information in estimating network structures can improve the performance of the existing methods.