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The multivariate exponential power is a useful distribution for modeling departures from normality in data by means of a tail weight scalar parameter that regulates the non-normality of the model. The incorporation of a shape asymmetry vector into the model serves to account for potential asymmetries and gives rise to the multivariate skew exponential power distribution. This work is aimed at revisiting the skew exponential power distribution taking as a starting point its formulation as a scale mixture of skew-normal distributions. The paper provides some highlights and theoretical insights on the role played by its parameters to assess two complementary aspects of the multivariate non-normality such as directional asymmetry and tail weight behavior regardless of the asymmetry. The intuition behind both issues relies on well-known mathematical ideas about skewness maximization and convex transform stochastic orderings.

Supplementary Table S5. MicroRNA TaqMan assay IDs.

Supplementary Table and Figure Legend. Legends for Supplementary Tables S1-S8 and Supplementary Figures S1-S2.

Better knowledge of the biology of breast cancer has allowed the use of new targeted therapies, leading to improved outcome. High-throughput technologies allow deepening into the molecular architecture of breast cancer, integrating different levels of information, which is important if it helps in making clinical decisions. microRNA (miRNA) and protein expression profiles were obtained from 71 estrogen receptor–positive (ER+) and 25 triple-negative breast cancer (TNBC) samples. RNA and proteins obtained from formalin-fixed, paraffin-embedded tumors were analyzed by RT-qPCR and LC/MS-MS, respectively. We applied probabilistic graphical models representing complex biologic systems as networks, confirming that ER+ and TNBC subtypes are distinct biologic entities. The integration of miRNA and protein expression data unravels molecular processes that can be related to differences in the genesis and clinical evolution of these types of breast cancer. Our results confirm that TNBC has a unique metabolic profile that may be exploited for therapeutic intervention. Cancer Res; 75(11); 2243–53. ©2015 AACR.

Supplementary Figure S2. Hypothesis about how miR449a exerts its regulatory effect over cellular metabolism.

Multivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector and a non negative mixing scalar variable, independent of the skew-normal vector, that injects tail weight behavior into the model. In this paper we look into the problem of finding the projection that maximizes skewness for vectors that follow a scale mixture of skew-normal distribution; when a simple condition on the moments of the mixing variable is fulfilled, it can be shown that the direction yielding the maximal skewness is proportional to the shape vector. This finding stresses the directional nature of the shape vector to regulate the asymmetry; it also provides the theoretical foundations motivating the skewness based projection pursuit problem in this class of distributions. Some examples that illustrate the application of our results are also given; they include a simulation experiment with artificial data, which sheds light on the usefulness and implications of our results, and the application to real data.

Breast cancer is a heterogeneous disease. In clinical practice, tumors are classified as hormonal receptor positive, Her2 positive and triple negative tumors. In previous works, our group defined a new hormonal receptor positive subgroup, the TN-like subtype, which had a prognosis and a molecular profile more similar to triple negative tumors. In this study, proteomics and Bayesian networks were used to characterize protein relationships in 96 breast tumor samples. Components obtained by these methods had a clear functional structure. The analysis of these components suggested differences in processes such as mitochondrial function or extracellular matrix between breast cancer subtypes, including our new defined subtype TN-like. In addition, one of the components, mainly related with extracellular matrix processes, had prognostic value in this cohort. Functional approaches allow to build hypotheses about regulatory mechanisms and to establish new relationships among proteins in the breast cancer context., PLoS ONE, 15 (6), ISSN:1932-6203

Breast cancer is the most frequent tumor in women and its incidence is increasing. Neoadjuvant chemotherapy has become standard of care as a complement to surgery in locally advanced or poor-prognosis early stage disease. The achievement of a complete response to neoadjuvant chemotherapy correlates with prognosis but it is not possible to predict who will obtain an excellent response. The molecular analysis of the tumor offers a unique opportunity to unveil predictive factors. In this work, gene expression profiling in 279 tumor samples from patients receiving neoadjuvant chemotherapy was performed and probabilistic graphical models were used. This approach enables addressing biological and clinical questions from a Systems Biology perspective, allowing to deal with large gene expression data and their interactions. Tumors presenting complete response to neoadjuvant chemotherapy had a higher activity of immune related functions compared to resistant tumors. Similarly, samples from complete responders presented higher expression of lymphocyte cell lineage markers, immune-activating and immune-suppressive markers, which may correlate with tumor infiltration by lymphocytes (TILs). These results suggest that the patient’s immune system plays a key role in tumor response to neoadjuvant treatment. However, future studies with larger cohorts are necessary to validate these hypotheses.

In this paper, we define a new skewness ordering that enables stochastic comparisons for vectors that follow a multivariate skew-normal distribution. The new ordering is based on the canonical transformation associated with the multivariate skew-normal distribution and on the well-known convex transform order applied to the only skewed component of such canonical transformation. We examine the connection between the proposed ordering and the multivariate convex transform order studied by Belzunce et al. (TEST 24(4):813–834, 2015). Several standard skewness measures like Mardia’s and Malkovich–Afifi’s indices are revisited and interpreted in connection with the new ordering; we also study its relationship with the J-divergence between skew-normal and normal random vectors and with the Negentropy. Some artificial data are used in simulation experiments to illustrate the theoretical discussion; a real data application is provided as well.

Background Metabolomics has a great potential in the development of new biomarkers in cancer and it has experiment recent technical advances. Methods In this study, metabolomics and gene expression data from 67 localized (stage I to IIIB) breast cancer tumor samples were analyzed, using (1) probabilistic graphical models to define associations using quantitative data without other a priori information; and (2) Flux Balance Analysis and flux activities to characterize differences in metabolic pathways. Results On the one hand, both analyses highlighted the importance of glutamine in breast cancer. Moreover, cell experiments showed that treating breast cancer cells with drugs targeting glutamine metabolism significantly affects cell viability. On the other hand, these computational methods suggested some hypotheses and have demonstrated their utility in the analysis of metabolomics data and in associating metabolomics with patient’s clinical outcome. Conclusions Computational analyses applied to metabolomics data suggested that glutamine metabolism is a relevant process in breast cancer. Cell experiments confirmed this hypothesis. In addition, these computational analyses allow associating metabolomics data with patient prognosis.

Triple-negative breast cancer is a heterogeneous disease characterized by a lack of hormonal receptors and HER2 overexpression. It is the only breast cancer subgroup that does not benefit from targeted therapies, and its prognosis is poor. Several studies have developed specific molecular classifications for triple-negative breast cancer. However, these molecular subtypes have had little impact in the clinical setting. Gene expression data and clinical information from 494 triple-negative breast tumors were obtained from public databases. First, a probabilistic graphical model approach to associate gene expression profiles was performed. Then, sparse k-means was used to establish a new molecular classification. Results were then verified in a second database including 153 triple-negative breast tumors treated with neoadjuvant chemotherapy. Clinical and gene expression data from 494 triple-negative breast tumors were analyzed. Tumors in the dataset were divided into four subgroups (luminal-androgen receptor expressing, basal, claudin-low and claudin-high), using the cancer stem cell hypothesis as reference. These four subgroups were defined and characterized through hierarchical clustering and probabilistic graphical models and compared with previously defined classifications. In addition, two subgroups related to immune activity were defined. This immune activity showed prognostic value in the whole cohort and in the luminal subgroup. The claudin-high subgroup showed poor response to neoadjuvant chemotherapy. Through a novel analytical approach we proved that there are at least two independent sources of biological information: cellular and immune. Thus, we developed two different and overlapping triple-negative breast cancer classifications and showed that the luminal immune-positive subgroup had better prognoses than the luminal immune-negative. Finally, this work paves the way for using the defined classifications as predictive features in the neoadjuvant scenario.

Metabolomics has a great potential in the development of new biomarkers in cancer. In this study, metabolomics and gene expression data from breast cancer tumor samples were analyzed, using (1) probabilistic graphical models to define associations using quantitative data without othera prioriinformation; and (2) Flux Balance Analysis and flux activities to characterize differences in metabolic pathways. On the one hand, both analyses highlighted the importance of glutamine in breast cancer. Moreover, cell experiments showed that treating breast cancer cells with drugs targeting glutamine metabolism significantly affects cell viability. On the other hand, these computational methods suggested some hypotheses and have demonstrated their utility in the analysis of metabolomics data and in associating metabolomics with patient’s clinical outcome.

BackgroundMuscle-invasive bladder tumors are associated with high risk of relapse and metastasis even after neoadjuvant chemotherapy and radical cystectomy. Therefore, further therapeutic options are needed and molecular characterization of the disease may help to identify new targets.ObjectiveThe aim of this work is to characterize muscle-invasive bladder tumors at molecular levels using computational analyses.Design, Settings and ParticipantsThe TCGA cohort of muscle-invasive bladder cancer patients was used to describe these tumors.Outcome Measurements and Statistical AnalysisProbabilistic graphical models, layer analyses based on sparse k-means coupled with Consensus Cluster, and Flux Balance Analysis were applied to characterize muscle-invasive bladder tumors at functional level.ResultsLuminal and Basal groups were identified, and an immune molecular layer with independent value was also described. Luminal tumors had decreased activity in the nodes of epidermis development and extracellular matrix, and increased activity in the node of steroid metabolism leading to a higher expression of androgen receptor.This fact points to androgen receptor as a therapeutic target in this group. Basal tumors were highly proliferative according to Flux Balance Analysis, which make these tumors good candidates for neoadjuvant chemotherapy. Immune-high group had higher expression of immune biomarkers, suggesting that this group may benefit from immune therapy.ConclusionsOur approach, based on layer analyses, established a Luminal group candidate for androgen receptor inhibitor therapy, a proliferative Basal group which seems to be a good candidate for chemotherapy, and an immune-high group candidate for immunotherapy.Patient SummaryMuscle-invasive bladder cancer has a poor prognosis in spite of appropriate therapy. Therefore, it is still necessary to characterize these tumors to propose new therapeutic targets. In this work we used computational analyses to characterize these tumors and propose treatments.

Breast cancer is a heterogeneous disease. In clinical practice, tumors are classified as hormonal receptor positive, Her2 positive and triple negative tumors. In previous works, our group defined a new hormonal receptor positive subgroup, the TN-like subtype, which has a prognosis and a molecular profile more similar to triple negative tumors. In this study, proteomics and Bayesian networks were used to characterize protein relationships in 106 breast tumor samples. Components obtained by these methods had a clear functional structure. The analysis of these components suggested differences in processes such as metastasis or proliferation between breast cancer subtypes, including our new subtype TN-like. In addition, one of the components, mainly related with metastasis, had prognostic value in this cohort. Functional approaches allow to build hypotheses about regulatory mechanisms and to establish new relationships among proteins in the breast cancer context.Author SummaryBreast cancer classification in the clinical practice is defined by three biomarkers (estrogen receptor, progesterone receptor and HER2) into hormone receptor positive, HER2+ and triple negative breast cancer (TNBC). Our group recently described a new ER+ subtype with molecular characteristics and prognosis similar to TNBC. In this study we propose a mathematical method, the Bayesian networks, as a useful tool to study protein interactions and differential biological processes in breast cancer subtypes, characterizing differences in relevant processes such as proliferation or metastasis and associated them with patient prognosis.

Traditionally, bladder cancer has been classified based on histology features. Recently, some works have proposed a molecular classification of invasive bladder tumors. To determine whether proteomics can define molecular subtypes of muscle invasive urothelial cancer (MIUC) and allow evaluating the status of biological processes and its clinical value. 58 MIUC patients who underwent curative surgical resection at our institution between 2006 and 2012 were included. Proteome was evaluated by high-throughput proteomics in routinely archive FFPE tumor tissue. New molecular subgroups were defined. Functional structure and individual proteins prognostic value were evaluated and correlated with clinicopathologic parameters. 1,453 proteins were quantified, leading to two MIUC molecular subgroups. A protein-based functional structure was defined, including several nodes with specific biological activity. The functional structure showed differences between subtypes in metabolism, focal adhesion, RNA and splicing nodes. Focal adhesion node has prognostic value in the whole population. A 6-protein prognostic signature, associated with higher risk of relapse (5 year DFS 70% versus 20%) was defined. Additionally, we identified two MIUC subtypes groups. Prognostic information provided by pathologic characteristics is not enough to understand MIUC behavior. Proteomics analysis may enhance our understanding of prognostic and classification. These findings can lead to improving diagnosis and treatment selection in these patients.

In this note we address the problem of finding the direction with maximal skewness for a random vector that follows a multivariate skew-t distribution. The result relies on the well-known representation of the multivariate skew-t distribution as a scale mixture of skew-normal multivariate distributions.

Metabolic reprogramming is a hallmark of cancer. We and other authors have previously shown that breast cancer subtypes present metabolism differences. In this study, breast cancer cell lines were treated with metformin and rapamycin. The response was heterogeneous across various breast cancer cells, leading to cell cycle disruption in specific conditions. The molecular effects of these treatments were characterized using sublethal doses, SNP genotyping and mass spectrometry-based proteomics. Protein expression was analyzed using probabilistic graphical models, showing that treatments elicit various responses in some biological processes, providing insights into cell responses to metabolism drugs. Moreover, a flux balance analysis approach using protein expression values was applied, showing that predicted growth rates were comparable with cell viability measurements and suggesting an increase in reactive oxygen species response enzymes due to metformin treatment. In addition, a method to assess flux differences in whole pathways was proposed. Our results show that these various approaches provide complementary information, which can be used to suggest hypotheses about the drugs’ mechanisms of action and the response to drugs that target metabolism.

Breast cancer is a heterogeneous disease comprising a variety of entities with various genetic backgrounds. Estrogen receptor-positive, human epidermal growth factor receptor 2-negative tumors typically have a favorable outcome; however, some patients eventually relapse, which suggests some heterogeneity within this category. In the present study, we used proteomics and miRNA profiling techniques to characterize a set of 102 either estrogen receptor-positive (ER+)/progesterone receptor-positive (PR+) or triple-negative formalin-fixed, paraffin-embedded breast tumors. Protein expression-based probabilistic graphical models and flux balance analyses revealed that some ER+/PR+ samples had a protein expression profile similar to that of triple-negative samples and had a clinical outcome similar to those with triple-negative disease. This probabilistic graphical model-based classification had prognostic value in patients with luminal A breast cancer. This prognostic information was independent of that provided by standard genomic tests for breast cancer, such as MammaPrint, OncoType Dx and the 8-gene Score, The authors would like to acknowledge funding from grants PI12/00444, PI12/01016 and PI15/01310 from the Instituto de Salud Carlos III, Spanish Economy and Competitiveness Ministry, Spain, and co-funded by the FEDER program, “Una forma de hacer Europa”. This study has also been supported by the PRIME-XS project, grant agreement number 262067, funded by the EU’s Seventh Framework Program for Research. AG-P and RL-V are supported by Instituto de Salud Carlos III, and the Spanish Economy and Competitiveness Ministry grants, CA12/00258 and CA12/00264, respectively. . We want to particularly acknowledge the patients in this study for their participation and to the IdiPAZ, I+12 and O+EHUN Biobanks for the generous gifts of clinical samples used in this study. LT-F is supported by the Spanish Economy and Competitiveness Ministry (DI-15-07614). IdiPAZ, I+12 and O+EHUN Biobanks are supported by Instituto de Salud Carlos III, Spanish Economy and Competitiveness Ministry (RD09/0076/00073, RD09/0076/00118 and RD09/0076/00140, respectively) and FarmaIndustria, through the Cooperation Program in Clinical and Translational Research of the Community of Madrid and Basque Autonomous Community

Bayesian networks (BNs) have become an essential tool for reasoning under uncertainty in complex models. In particular, the subclass of Gaussian Bayesian networks (GBNs) can be used to model continuous variables with Gaussian distributions. Here we focus on the task of learning GBNs from data. Factorization of the multivariate Gaussian joint density according to a directed acyclic graph (DAG) provides an alternative and interchangeable representation of a GBN by using the Gaussian conditional univariate densities of each variable given its parents in the DAG. With this latter conditional specification of a GBN, the learning process involves determination of the mean vector, regression coefficients and conditional variances parameters. Some approaches have been proposed to learn these parameters from a Bayesian perspective using different priors, and therefore some hyperparameter values are tuned. Our goal is to deal with the usual prior distributions given by the normal/inverse gamma form and to evaluate the effect of prior hyperparameter choice on the posterior distribution. As usual in Bayesian robustness, a large class of priors expressed by many hyperparameter values should lead to a small collection of posteriors. From this perspective and using Kullback-Leibler divergence to measure prior and posterior deviations, a local sensitivity measure is proposed to make comparisons. If a robust Bayesian analysis is developed by studying the sensitivity of Bayesian answers to uncertain inputs, this method will also be useful for selecting robust hyperparameter values.

Introduction Muscle-invasive bladder cancer (MIBC) is associated with a high risk of relapse and metastasis. The standard treatment consists of radical cystectomy followed by cisplatin-based chemotherapy. Therefore, the molecular characterisation of MIBC in order to find new therapeutic targets is still necessary. Material and methods In this study, using The Cancer Genome Atlas (TCGA) cohort, functional structure and layer analyses were done to characterise MIBC tumours at functional level. Functional structure was developed using probabilistic graphical models and gene ontology analyses. Layer analyses were based on sparse k-means and Consensus Cluster Algorithm (CCA). Sparse k-means assigns a weight to each variable, based on its relevance in the sample classification. Then, a CCA using variables that were selected by the sparse K-means method was applied to define the optimum number of groups for each case. This sparse k-means-CCA workflow was performed successive times to explore the existence of independent informative molecular layers. Once relevant genes for one molecular layer are identified, these genes were removed from the dataset and the sparse k-means-CCA workflow was performed again, allowing the identification of different layers of molecular information and establishing different classifications based on various molecular features. Gene ontology analyses were done for each layer. Results and discussions A probabilistic graphical model with a functional structure was obtained. Sixteen layers were functionally characterised and the first three layers were analysed in depth. The first layer defined luminal and basal groups. Luminal tumours had a better prognosis than basal ones. Strikingly, luminal tumours showed higher expression of the androgen receptor, suggesting that this group is a good candidate for receiving treatment with androgen receptor inhibitors. The second layer established two groups based on genes related to extracellular matrix function. Lastly, the third layer defined two groups on the basis of immune information. The immune high group had a better prognosis and was characterised by higher expression of CTLA4 and PDL1, so this group may be a candidate for receiving immunotherapy. Conclusion Using probabilistic graphical models and layer analyses it is possible to establish independently a molecular and an immune classification. Using these approaches, we also proposed a specific treatment for luminal tumours (androgen receptor inhibitors) and for immune high tumours (immunotherapy).

Background The molecular analysis of melanoma has improved our understanding of the disease. The Cancer Genome Atlas (TCGA) Network proposed the molecular classification of melanoma in three subtypes: keratin-high, immune-high and membrane-low. However, this classification has not translated into therapeutic advances so far. Immunotherapy has contributed to improve survival, yet the mechanisms explaining differences in efficacy have not been elucidated. The aim of this study is to characterize the immune status of melanoma tumors through gene expression, and to analyze if these differences have an impact in the response to immunotherapy. Methods A probabilistic graphical model, followed by successive sparse k-means and consensus cluster analyses, was used to classify melanoma tumor samples from the TCGA cohort. Findings were translated into a cohort of patients treated with anti-PD1 antibodies (GSE78220, Hugo W et al) as a validation dataset. Results A probabilistic graphical model, including the 2,971 more variable genes from 472 melanoma samples from the TCGA dataset was built, and the resulting graph was processed to seek functional structures. Sparse k-means selected 119 genes. Gene ontology analysis showed that these genes were mainly related with immune processes. Immune genes split the population into two groups with different immune status. The so-called immune-high group included 232 patients (49%) and the immune-low group groups 238 patients (51%). The validation dataset GSE78220 provided mRNA expression in melanomas being treated with anti-PD-1 antibodies (28 biopsies belonging to 27 patients). The immune layer was translated to the new cohort by centroid method: 9 patients had immune-low tumors, whereas the remaining 18 had immune-high tumors. Kaplan Meier analysis using the clinical data from the GSE78220 cohort found a favorable response in patients with immune-low tumors (90% long-term survival). Conclusions We found a gene signature related to the tumor immune status that split the TCGA cohort in two groups. When applied to a cohort of patients treated with anti-PD1 antibodies, the group with immune-low tumors had 90% of long-term survival. Legal entity responsible for the study The authors. Funding Has not received any funding. Disclosure All authors have declared no conflicts of interest.

Introduction / Objectives MicroRNAs (miRNAs) constitute a new class of small noncoding RNAs that control post-transcriptionally the expression of gene products, either modulating directly protein translation, or regulating the stability of messenger RNA. There is increasing evidence of the role that miRNAs play in regulating breast cancer gene expression. However, there is little knowledge about the function and targets of miRNAs, and how they regulate complete processes or pathways. The main objective of this study was to unravel biological processes and signaling pathways regulated by miRNAs in breast cancer comparing their expression with the expression of the proteins they regulate. New statistical approaches were conducted in order to associate miRNA and protein quantification results with breast cancer subtype and to evaluate the association of miRNAs and protein expression patterns. Materials and Methods MicroRNA and protein expression were obtained from 79 breast cancer FFPE samples (16 TNBCs and 63 Luminal tumors). RNA was extracted from FFPE samples using RecoverAll (Ambion). MicroRNA expression was analyzed by RT-qPCR using TaqMan Arrays (Applied Biosystems). We selected for subsequent analysis those miRNAs with significant correlation between FF and FFPE samples. Protein extracts from FFPE samples were prepared in 2% SDS buffer using a protocol based on heat-induced antigen retrieval (Gámez-Pozo A et al. Mol Biosyst. 2011; 7: 2368-74). Protein abundance was calculated on the basis of normalized spectral protein intensity (LFQ intensity) using MaxQuant. Probabilistic graphical models are being applied successfully to represent complex biological systems as networks. In this phase of the study, we have chosen an appropriate methodology in the analysis of high dimensional data selecting a forest which minimizes the BIC criterion. This procedure extends the Chow and Liu's approach to the Gaussian case. The software used for implementation is based on the R library gRapHD. Results We measured the expression of 90 miRNAs in 79 breast cancer samples using RT-qPCR. We identified and quantified more than 3000 protein groups. We selected for subsequent analyses more than 1000 quantifiable proteins, defined as those identified at least in 75% of the samples in at least one type of sample with more than two unique peptides. Then, we analyzed the relations between miRNA and protein expressions. We identified miRNAs strongly related with processes considered as hallmarks of cancer, such as cellular adhesion, using probabilistic graphical models. Conclusions The integration of miRNA and protein expression patterns may be useful to describe how miRNAs regulate biological processes and signaling pathways in breast cancer. There is a need of new statistical approaches to evaluate these relations and to obtain meaningful information from such complex and massive data. Citation Information: Cancer Res 2013;73(24 Suppl): Abstract nr P4-07-07.

The multivariate exponential power family is considered for n-dimensional random variables, Z, with a known partition Z=(Y,X) of dimensions p and n-p, respectively, with interest focusing on the conditional distribution Y|X. An infinitesimal variation of any parameter of the joint distribution produces perturbations in both the conditional and marginal distributions. The aim of the study was to determine the local effect of kurtosis deviations using the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, Y|X and X, is used to define a relative sensitivity measure of the conditional distribution family {Y|X=x}. Finally, simulated results suggest that for large dimensions, the measure is approximately equal to the ratio p/n, and then the effect of non-normality with respect to kurtosis depends only on the relative size of the variables considered in the partition of the random vector.

In this paper local sensitivity measures are proposed to evaluate deviations from multivariate normality caused by asymmetry; the model we use to regulate asymmetry is the multivariate skew-normal distribution because it reflects the deviation in a very tractable way. The paper also examines the connection between local sensitivity and Mardia’s and Malkovich-Afifi’s skewness indices. Once the local sensitivity measures have been introduced, we study the effect of local perturbations in asymmetry on the conditional distributions; this issue has important implications because there are many procedures in statistics and other fields where the output depends on the distribution of some variables for known values of the others. The proposed measures use the Kullback-Leibler divergence to evaluate dissimilarities between probability distributions in order to assess deviation from normality on the joint distribution and on the marginal and conditional distributions as well. The results are illustrated with some examples

In this work, we evaluate the sensitivity of Gaussian Bayesian networks to perturbations or uncertainties in the regression coefficients of the network arcs and the conditional distributions of the variables. The Kullback-Leibler divergence measure is used to compare the original network to its perturbation. By setting the regression coefficients to zero or non-zero values, the proposed method can remove or add arcs, making it possible to compare different network structures. The methodology is implemented with some case studies.

Introduction Melanoma is the most lethal malignancy of the skin. The Cancer Genome Atlas (TCGA) Network proposed a molecular classification of melanoma, consisting in three subtypes: keratin-high, immune-high and membrane-low. However, this classification has not been translated into therapeutic advances yet. The aim of this study is to characterise molecular differences of melanoma at biological and molecular levels and propose a novel molecular classification with clinical impact. Material and methods A novel approach based on the existence of different molecular informative layers was used in this study to establish independent sets of information. A probabilistic graphical model, followed by successive sparse k-means and consensus cluster analyses were used to classify melanoma tumour samples from the TCGA cohort. Then, molecular classification was validated in another public cohort: GSE65904. Results and discussions We established that there were at least two different kinds of molecular information: an immune layer and a histological layer. Immune high and immune low groups were established based on immune layer information. Keratin low-proliferation low, melanogenesis high-membrane low, melanogenesis low-membrane high and keratin high groups were established based on molecular layer information. This suggests that the information related to the immune system is independent from other molecular features and is distributed among the groups established by the TCGA classification. Besides, the immune and histological assignments showed different clinical outcomes in another dataset, identifying two immune groups with prognostic value. Conclusion In this work we proposed a novel analytical approach based on informative molecular layers. In this way, two independent classifications, an immune-based and a histological-based classification, were established. Immune classification showed prognostic value in an independent cohort. Besides, the histological and the immune layers may deserve additional research for define new potential targeted therapies.

The problem of modeling Bayesian networks with continuous nodes deals with discrete approximations and conditional linear Gaussian models. In this article we have considered the possibility of using the exponential power family as conditional probability densities. It will be shown that for some platikurtic conditional distributions\ in this family, conditional regression functions are constant. These results give conditions to avoid compatibility problems when distributions with lighter tails than the normal are used in the description of conditional densities to specify joint densities, like in Bayesian networks.

Better knowledge of the biology of breast cancer has allowed the use of new targeted therapies, leading to improved outcome. High-throughput technologies allow deepening into the molecular architecture of breast cancer, integrating different levels of information, which is important if it helps in making clinical decisions. microRNA (miRNA) and protein expression profiles were obtained from 71 estrogen receptor–positive (ER+) and 25 triple-negative breast cancer (TNBC) samples. RNA and proteins obtained from formalin-fixed, paraffin-embedded tumors were analyzed by RT-qPCR and LC/MS-MS, respectively. We applied probabilistic graphical models representing complex biologic systems as networks, confirming that ER+ and TNBC subtypes are distinct biologic entities. The integration of miRNA and protein expression data unravels molecular processes that can be related to differences in the genesis and clinical evolution of these types of breast cancer. Our results confirm that TNBC has a unique metabolic profile that may be exploited for therapeutic intervention. Cancer Res; 75(11); 2243–53. ©2015 AACR.

An ordinal scale based on the concentration of the spectral distribution at low frequencies is proposed to compare the smoothness of weakly stationary processes. Some characterizations, basic properties and applications of this partial ordering are discussed. It is proved that both smoothing operations and usual smoothness measures agree with the new order.

An important issue in the analysis of gene expression microarray data is concerned with the extraction of valuable genetic interactions from high dimensional data sets containing gene expression levels collected for a small sample of assays. Past and ongoing research efforts have been focused on biomarker selection for phenotype classification. Usually, many genes convey useless information for classifying the outcome and should be removed from the analysis; on the other hand, some of them may be highly correlated, which reveals the presence of redundant expressed information. In this paper we propose a method for the selection of highly predictive genes having a low redundancy in their expression levels. The predictive accuracy of the selection is assessed by means of Classification and Regression Trees (CART) models which enable assessment of the performance of the selected genes for classifying the outcome variable and will also uncover complex genetic interactions. The method is illustrated throughout the paper using a public domain colon cancer gene expression data set.

Background One of the drawbacks we face up when analyzing gene to phenotype associations in genomic data is the ugly performance of the designed classifier due to the small sample-high dimensional data structures (n ≪ p) at hand. This is known as the peaking phenomenon, a common situation in the analysis of gene expression data. Highly predictive bivariate gene interactions whose marginals are useless for discrimination are also affected by such phenomenon, so they are commonly discarded by state of the art sequential search algorithms. Such patterns are known as weak/marginal strong bivariate interactions. This paper addresses the problem of uncovering them in high dimensional settings. Results We propose a new approach which uses the quadratic discriminant analysis (QDA) as a search engine in order to detect such signals. The choice of QDA is justified by a simulation study for a benchmark of classifiers which reveals its appealing properties. The procedure rests on an exhaustive search which explores the feature space in a blockwise manner by dividing it in blocks and by assessing the accuracy of the QDA for the predictors within each pair of blocks; the block size is determined by the resistance of the QDA to peaking. This search highlights chunks of features which are expected to contain the type of subtle interactions we are concerned with; a closer look at this smaller subset of features by means of an exhaustive search guided by the QDA error rate for all the pairwise input combinations within this subset will enable their final detection. The proposed method is applied both to synthetic data and to a public domain microarray data. When applied to gene expression data, it leads to pairs of genes which are not univariate differentially expressed but exhibit subtle patterns of bivariate differential expression. Conclusions We have proposed a novel approach for identifying weak marginal/strong bivariate interactions. Unlike standard approaches as the top scoring pair (TSP) and the CorScor, our procedure does not assume a specified shape of phenotype separation and may enrich the type of bivariate differential expression patterns that can be uncovered in high dimensional data.

As an alternative to the multivariate normal distribution we have dealt with a wider class of distributions, including the normal, that considers slightly different tail behavior than the normal tail. This is the multivariate exponential power family of distributions with a kurtosis parameter to give the possible forms of the distributions. To measure distribution deviations the Kullback-Leibler divergence will be used as an asymmetric dissimilarity measure from an information-theoretic basis. Thus, a local quantitative description of the non-normality could be established for joint distributions in this family as well as the impact this perturbation causes in the marginal and conditional distributions.

Random Forests (RF) is an ensemble method which has become widely accepted within the machine learning and bioinformatics communities in the last few years. Its predictive strength, along with some of the ingredients --- rich in information --- provided by the output, has made RF an efficient Data Mining tool for discovering patterns in data.In this paper we review the learning mechanism of RF within the classification setting and apply it to uncover bivariate interactions, carrying on useful information about an outcome, in high dimensional low sample data.We propose a divide and conquer search strategy in the variable space that benefits from the ranking of variable importances of RF at a first stage, along with the out of bag error rate (oob) of the ensemble at a second stage. The procedure combines both elements in order to capture difficult to uncover patterns in these type of data.We will show the performance of our procedure in some synthetic scenarios and will give a real application to a microarray data set in order to illustrate how it works.

In this paper the asymptotic relationship between the classical p-value and the infimum (over all unimodal and symmetric distributions) of the posterior probability in the point null hypothesis testing problem is analyzed. It is shown that the ratio between the infimum and the classical p-value has an equivalent asymptotic behavior to the hazard rate of the sample model.

The Multivariate Exponential Power family is considered for n-dimensional random variables, Z, with a known partition Z (Y,X) of dimensions p and n-p, respectively. An infinitesimal variation of any parameter produces both conditional and marginal distributions perturbations. The aim of our study is to determine the local effect of kurtosis deviations by means of the Kullback-Leibler divergence measure between probability distributions. The additive decomposition of this measure in terms of the conditional and marginal distributions, YǀX and X, has been used to define the relative sensitivity of the conditional distributions family {YǀX = x}. The obtained results show that, for large dimensions, it is nearly p/n.