Listen to genes : dealing with microarray data in the frequency domain

Background: We present a novel and systematic approach to analyze temporal microarray data. The approach includes normalization, clustering and network analysis of genes. Methodology: Genes are normalized using an error model based uniform normalization method aimed at identifying and estimating the sources of variations. The model minimizes the correlation among error terms across replicates. The normalized gene expressions are then clustered in terms of their power spectrum density. The method of complex Granger causality is introduced to reveal interactions between sets of genes. Complex Granger causality along with partial Granger causality is applied in both time and frequency domains to selected as well as all the genes to reveal the interesting networks of interactions. The approach is successfully applied to Arabidopsis leaf microarray data generated from 31,000 genes observed over 22 time points over 22 days. Three circuits: a circadian gene circuit, an ethylene circuit and a new global circuit showing a hierarchical structure to determine the initiators of leaf senescence are analyzed in detail. Conclusions: We use a totally data-driven approach to form biological hypothesis. Clustering using the power-spectrum analysis helps us identify genes of potential interest. Their dynamics can be captured accurately in the time and frequency domain using the methods of complex and partial Granger causality. With the rise in availability of temporal microarray data, such methods can be useful tools in uncovering the hidden biological interactions. We show our method in a step by step manner with help of toy models as well as a real biological dataset. We also analyse three distinct gene circuits of potential interest to Arabidopsis researchers

Vertical wind profile characterization and identification of patterns based on a shape clustering algorithm

Wind power plants are becoming a generally accepted resource in the generation mix of many utilities. At the same time, the size and the power rating of individual wind turbines have increased considerably. Under these circumstances, the sector is increasingly demanding an accurate characterization of vertical wind speed profiles to estimate properly the incoming wind speed at the rotor swept area and, consequently, assess the potential for a wind power plant site. The present paper describes a shape-based clustering characterization and visualization of real vertical wind speed data. The proposed solution allows us to identify the most likely vertical wind speed patterns for a specific location based on real wind speed measurements. Moreover, this clustering approach also provides characterization and classification of such vertical wind profiles. This solution is highly suitable for a large amount of data collected by remote sensing equipment, where wind speed values at different heights within the rotor swept area are available for subsequent analysis. The methodology is based on z-normalization, shape-based distance metric solution and the Ward-hierarchical clustering method. Real vertical wind speed profile data corresponding to a Spanish wind power plant and collected by using a commercialWindcube equipment during several months are used to assess the proposed characterization and clustering process, involving more than 100000 wind speed data values. All analyses have been implemented using open-source R-software. From the results, at least four different vertical wind speed patterns are identified to characterize properly over 90% of the collected wind speed data along the day. Therefore, alternative analytical function criteria should be subsequently proposed for vertical wind speed characterization purposes.The authors are grateful for the financial support from the Spanish Ministry of the Economy and Competitiveness and the European Union —ENE2016-78214-C2-2-R—and the Spanish Education, Culture and Sport Ministry —FPU16/042

Modelling Survival Data to Account for Model Uncertainty: A Single Model or Model Averaging?

This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a\ud mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single ???best??? model, where\ud ???best??? is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to\ud account for model uncertainty. This was illustrated using a case study in which the aim was the description of\ud lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate\ud that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the\ud data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample\ud size was reduced, no single model was revealed as ???best???, suggesting that a BMA approach would be appropriate.\ud Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can\ud provide robust predictions and facilitate more detailed investigation of the relationships between gene expression\ud and patient survival

Bayesian hierarchical clustering for studying cancer gene expression data with unknown statistics

Clustering analysis is an important tool in studying gene expression data. The Bayesian hierarchical clustering (BHC) algorithm can automatically infer the number of clusters and uses Bayesian model selection to improve clustering quality. In this paper, we present an extension of the BHC algorithm. Our Gaussian BHC (GBHC) algorithm represents data as a mixture of Gaussian distributions. It uses normal-gamma distribution as a conjugate prior on the mean and precision of each of the Gaussian components. We tested GBHC over 11 cancer and 3 synthetic datasets. The results on cancer datasets show that in sample clustering, GBHC on average produces a clustering partition that is more concordant with the ground truth than those obtained from other commonly used algorithms. Furthermore, GBHC frequently infers the number of clusters that is often close to the ground truth. In gene clustering, GBHC also produces a clustering partition that is more biologically plausible than several other state-of-the-art methods. This suggests GBHC as an alternative tool for studying gene expression data. The implementation of GBHC is available at https://sites. google.com/site/gaussianbhc

A Copula Model Approach to Identify the Differential Gene Expression

Deoxyribonucleic acid, more commonly known as DNA, is a complex double helix-shaped molecule present in all living organisms and hosts thousands of genes. However, only a few genes exhibit differential expression and play a vital role in a particular disease such as breast cancer. Microarray technology is one of the modern technologies developed to study these gene expressions. There are two major microarray technologies available for expression analysis: Spotted cDNA array and oligonucleotide array. The focus of our research is the statistical analysis of data that arises from the spotted cDNA microarray. Numerous models have been proposed in the literature to identify differentially expressed genes from the red and green intensities measured by the cDNA microarrays. Motivated by the Bayesian models described in Newton et al. (2001) and Mav and Chaganty (2004), we propose two models for the joint distribution of the red and green intensities using a Gaussian copula, which accounts for the dependence. In both models, we assume the marginals are distributed as gamma. The differentially expressed genes were identified by calculating the Bayes estimates of the differential expression under the first proposed copula model. The second copula model incorporates a latent Bernoulli variable, which indicates differential expression. The EM algorithm is applied to calculate the posterior probabilities of differential expression for the second model. The posterior probabilities rank the genes. We conducted two simulation studies to check the parameter estimation for the Gaussian copula-based models. We show that our models improve the models given in Newton et al. (2001) and Mav and Chaganty (2004). We have also studied the use of Weibull distribution instead of gamma distribution for the marginals. Our analysis shows that the copula models with Weibull marginals provide a better fit and improve the identification of genes. Finally, we illustrate the application of our models on samples of Escherichia coli microarrays data

Dirichlet process mixtures under affine transformations of the data

Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation and clustering. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformations of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.Comment: 36 pages, 7 Figure

A comparative study of machine learning methods for time-to-event survival data for radiomics risk modelling

Radiomics applies machine learning algorithms to quantitative imaging data to characterise the tumour phenotype and predict clinical outcome. For the development of radiomics risk models, a variety of different algorithms is available and it is not clear which one gives optimal results. Therefore, we assessed the performance of 11 machine learning algorithms combined with 12 feature selection methods by the concordance index (C-Index), to predict loco- regional tumour control (LRC) and overall survival for patients with head and neck squamous cell carcinoma. The considered algorithms are able to deal with continuous time-to-event survival data. Feature selection and model building were performed on a multicentre cohort (213 patients) and validated using an independent cohort (80 patients). We found several combinations of machine learning algorithms and feature selection methods which achieve similar results, e.g., MSR-RF: C-Index = 0.71 and BT-COX: C-Index = 0.70 in combination with Spearman feature selection. Using the best performing models, patients were stratified into groups of low and high risk of recurrence. Significant differences in LRC were obtained between both groups on the validation cohort. Based on the presented analysis, we identified a subset of algorithms which should be considered in future radiomics studies to develop stable and clinically relevant predictive models for time-to-event endpoints