Probabilistic segmentation and intensity estimation for microarray images

We describe a probabilistic approach to simultaneous image segmentation and intensity estimation for complementary DNA microarray experiments. The approach overcomes several limitations of existing methods. In particular, it (a) uses a flexible Markov random field approach to segmentation that allows for a wider range of spot shapes than existing methods, including relatively common 'doughnut-shaped' spots; (b) models the image directly as background plus hybridization intensity, and estimates the two quantities simultaneously, avoiding the common logical error that estimates of foreground may be less than those of the corresponding background if the two are estimated separately; and (c) uses a probabilistic modeling approach to simultaneously perform segmentation and intensity estimation, and to compute spot quality measures. We describe two approaches to parameter estimation: a fast algorithm, based on the expectation-maximization and the iterated conditional modes algorithms, and a fully Bayesian framework. These approaches produce comparable results, and both appear to offer some advantages over other methods. We use an HIV experiment to compare our approach to two commercial software products: Spot and Arrayvision.     

Modeling microarray data using a threshold mixture model

An important goal of microarray studies is the detection of genes that show significant changes in expression when two classes of biological samples are being compared. We present an ANOVA-style mixed model with parameters for array normalization, overall level of gene expression, and change of expression between the classes. For the latter we assume a mixing distribution with a probability mass concentrated at zero, representing genes with no changes, and a normal distribution representing the level of change for the other genes. We estimate the parameters by optimizing the marginal likelihood. To make this practical, Laplace approximations and a backfitting algorithm are used. The performance of the model is studied by simulation and by application to publicly available data sets.     

Unsupervised assessment of microarray data quality using a Gaussian mixture model

Background  

Quality assessment of microarray data is an important and often challenging aspect of gene expression analysis. This task frequently involves the examination of a variety of summary statistics and diagnostic plots. The interpretation of these diagnostics is often subjective, and generally requires careful expert scrutiny.     

Assessment of reliability of microarray data and estimation of signal thresholds using mixture modeling

DNA microarray is an important tool for the study of gene activities but the resultant data consisting of thousands of points are error-prone. A serious limitation in microarray analysis is the unreliability of the data generated from low signal intensities. Such data may produce erroneous gene expression ratios and cause unnecessary validation or post-analysis follow-up tasks. In this study, we describe an approach based on normal mixture modeling for determining optimal signal intensity thresholds to identify reliable measurements of the microarray elements and subsequently eliminate false expression ratios. We used univariate and bivariate mixture modeling to segregate the microarray data into two classes, low signal intensity and reliable signal intensity populations, and applied Bayesian decision theory to find the optimal signal thresholds. The bivariate analysis approach was found to be more accurate than the univariate approach; both approaches were superior to a conventional method when validated against a reference set of biological data that consisted of true and false gene expression data. Elimination of unreliable signal intensities in microarray data should contribute to the quality of microarray data including reproducibility and reliability of gene expression ratios.     

Background correction for cDNA microarray images using the TV+L1 model

MOTIVATION: Background correction is an important preprocess in cDNA microarray data analysis. A variety of methods have been used for this purpose. However, many kinds of backgrounds, especially inhomogeneous ones, cannot be estimated correctly using any of the existing methods. In this paper, we propose the use of the TV+L1 model, which minimizes the total variation (TV) of the image subject to an L1-fidelity term, to correct background bias. We demonstrate its advantages over the existing methods by both analytically discussing its properties and numerically comparing it with morphological opening. RESULTS: Experimental results on both synthetic data and real microarray images demonstrate that the TV+L1 model gives the restored intensity that is closer to the true data than morphological opening. As a result, this method can serve an important role in the preprocessing of cDNA microarray data.     

A Bayesian mixture model for metaanalysis of microarray studies

The increased availability of microarray data has been calling for statistical methods to integrate findings across studies. A common goal of microarray analysis is to determine differentially expressed genes between two conditions, such as treatment vs control. A recent Bayesian metaanalysis model used a prior distribution for the mean log-expression ratios that was a mixture of two normal distributions. This model centered the prior distribution of differential expression at zero, and separated genes into two groups only: expressed and nonexpressed. Here, we introduce a Bayesian three-component truncated normal mixture prior model that more flexibly assigns prior distributions to the differentially expressed genes and produces three groups of genes: up and downregulated, and nonexpressed. We found in simulations of two and five studies that the three-component model outperformed the two-component model using three comparison measures. When analyzing biological data of Bacillus subtilis, we found that the three-component model discovered more genes and omitted fewer genes for the same levels of posterior probability of differential expression than the two-component model, and discovered more genes for fixed thresholds of Bayesian false discovery. We assumed that the data sets were produced from the same microarray platform and were prescaled.     

Bayesian mixture model based clustering of replicated microarray data

MOTIVATION: Identifying patterns of co-expression in microarray data by cluster analysis has been a productive approach to uncovering molecular mechanisms underlying biological processes under investigation. Using experimental replicates can generally improve the precision of the cluster analysis by reducing the experimental variability of measurements. In such situations, Bayesian mixtures allow for an efficient use of information by precisely modeling between-replicates variability. RESULTS: We developed different variants of Bayesian mixture based clustering procedures for clustering gene expression data with experimental replicates. In this approach, the statistical distribution of microarray data is described by a Bayesian mixture model. Clusters of co-expressed genes are created from the posterior distribution of clusterings, which is estimated by a Gibbs sampler. We define infinite and finite Bayesian mixture models with different between-replicates variance structures and investigate their utility by analyzing synthetic and the real-world datasets. Results of our analyses demonstrate that (1) improvements in precision achieved by performing only two experimental replicates can be dramatic when the between-replicates variability is high, (2) precise modeling of intra-gene variability is important for accurate identification of co-expressed genes and (3) the infinite mixture model with the 'elliptical' between-replicates variance structure performed overall better than any other method tested. We also introduce a heuristic modification to the Gibbs sampler based on the 'reverse annealing' principle. This modification effectively overcomes the tendency of the Gibbs sampler to converge to different modes of the posterior distribution when started from different initial positions. Finally, we demonstrate that the Bayesian infinite mixture model with 'elliptical' variance structure is capable of identifying the underlying structure of the data without knowing the 'correct' number of clusters. AVAILABILITY: The MS Windows based program named Gaussian Infinite Mixture Modeling (GIMM) implementing the Gibbs sampler and corresponding C++ code are available at http://homepages.uc.edu/~medvedm/GIMM.htm SUPPLEMENTAL INFORMATION: http://expression.microslu.washington.edu/expression/kayee/medvedovic2003/medvedovic_bioinf2003.html     

Implications of a statistical occurrence model for mixture toxicity estimation

This study provides a method for characterizing the effects of concentration variability and correlation among co-acting compounds on mixture toxicity, considering the implications of missing chemical data. The method is explored by developing a set of multiple occurrence scenarios for mixtures of related chemicals. The calculations are performed for hypothetical mixtures of a group of ten synthetic antibiotics that have been tested on marine bacterium to fit dose-response relationships for long-term bioluminescence inhibition of Vibrio fischeri. Mixture toxicities are computed and compared for the assumptions of independent joint action theory and concentration/dose addition theory. The study results show that higher variability in concentrations is associated with higher effective (average) mixture toxicity, in this application by as much as a factor of ten for mixtures with highly variable component concentrations. Moreover, omitting the most toxic compounds caused mixture toxicities to be underestimated by a factor of approximately two. We recommend a pre-assessment of the effect of different chemical occurrence patterns and variability on mixture toxicity to help prioritize needs for further co-occurrence data and toxicity studies.     

Automatic analysis of DNA microarray images using mathematical morphology

MOTIVATION: DNA microarrays are an experimental technology which consists in arrays of thousands of discrete DNA sequences that are printed on glass microscope slides. Image analysis is an important aspect of microarray experiments. The aim of this step is to reduce an image of spots into a table with a measure of the intensity for each spot. Efficient, accurate and automatic analysis of DNA spot images is essential in order to use this technology in laboratory routines. RESULTS: We present an automatic non-supervised set of algorithms for a fast and accurate spot data extraction from DNA microarrays using morphological operators which are robust to both intensity variation and artefacts. The approach can be summarised as follows. Initially, a gridding algorithm yields the automatic segmentation of the microarray image into spot quadrants which are later individually analysed. Then the analysis of the spot quadrant images is achieved in five steps. First, a pre-quantification, the spot size distribution law is calculated. Second, the background noise extraction is performed using a morphological filtering by area. Third, an orthogonal grid provides the first approach to the spot locus. Fourth, the spot segmentation or spot boundaries definition is carried out using the watershed transformation. And fifth, the outline of detected spots allows the signal quantification or spot intensities extraction; in this respect, a noise model has been investigated. The performance of the algorithm has been compared with two packages: ScanAlyze and Genepix, showing its robustness and precision.     

Segmentation of cDNA microarray spots using markov random field modeling

Motivation: Spot segmentation is a critical step in microarraygene expression data analysis. Therefore, the performance ofsegmentation may substantially affect the results of subsequentstages of the analysis, such as the detection of differentiallyexpressed genes. Several methods have been developed to segmentmicroarray spots from the surrounding background. In this study,we have proposed a new approach based on Markov random field(MRF) modeling and tested its performance on simulated and realmicroarray images against a widely used segmentation methodbased on Mann–Whitney test adopted by QuantArray software(Boston, MA). Spot addressing was performed using QuantArray.We have also devised a simulation method to generate microarrayimages with realistic features. Such images can be used as goldstandards for the purposes of testing and comparing differentsegmentation methods, and optimizing segmentation parameters. Results: Experiments on simulated and 14 actual microarray imagesets show that the proposed MRF-based segmentation method candetect spot areas and estimate spot intensities with higheraccuracy. Availability: The algorithms were implemented in Matlab^TM (TheMathworks, Inc., Natick, MA) environment. The codes for MRF-basedsegmentation and image simulation methods are available uponrequest. Contact: demirkaya{at}ieee.org     

Habitat-Net: Segmentation of habitat images using deep learning

Understanding environmental factors that influence forest health, as well as the occurrence and abundance of wildlife, is a central topic in forestry and ecology. However, the manual processing of field habitat data is time-consuming and months are often needed to progress from data collection to data interpretation. To shorten the time to process the data we propose here Habitat-Net: a novel deep learning application based on Convolutional Neural Networks (CNN) to segment habitat images of tropical rainforests. Habitat-Net takes color images as input and after multiple layers of convolution and deconvolution, produces a binary segmentation of the input image. We worked on two different types of habitat datasets that are widely used in ecological studies to characterize the forest conditions: canopy closure and understory vegetation. We trained the model with 800 canopy images and 700 understory images separately and then used 149 canopy and 172 understory images to test the performance of Habitat-Net. We compared the performance of Habitat-Net to the performance of a simple threshold based method, manual processing by a second researcher and a CNN approach called U-Net, upon which Habitat-Net is based. Habitat-Net, U-Net and simple thresholding reduced total processing time to milliseconds per image, compared to 45 s per image for manual processing. However, the higher mean Dice coefficient of Habitat-Net (0.94 for canopy and 0.95 for understory) indicates that accuracy of Habitat-Net is higher than that of both the simple thresholding (0.64, 0.83) and U-Net (0.89, 0.94). Habitat-Net will be of great relevance for ecologists and foresters, who need to monitor changes in their forest structures. The automated workflow not only reduces the time, it also standardizes the analytical pipeline and, thus, reduces the degree of uncertainty that would be introduced by manual processing of images by different people (either over time or between study sites).     

A nonparametric mixture model for cure rate estimation

Nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis. In this paper, we study a general nonparametric mixture model. The proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured. The EM algorithm, the marginal likelihood approach, and multiple imputations are employed to estimate parameters of interest in the model. This model extends models and improves estimation methods proposed by other researchers. It also extends Cox's proportional hazards regression model by allowing a proportion of event-free patients and investigating covariate effects on that proportion. The model and its estimation method are investigated by simulations. An application to breast cancer data, including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers, confirms the conclusions from the parametric model but not those from the existing nonparametric model.     

A Laplace mixture model for identification of differential expression in microarray experiments

Microarrays have become an important tool for studying the molecular basis of complex disease traits and fundamental biological processes. A common purpose of microarray experiments is the detection of genes that are differentially expressed under two conditions, such as treatment versus control or wild type versus knockout. We introduce a Laplace mixture model as a long-tailed alternative to the normal distribution when identifying differentially expressed genes in microarray experiments, and provide an extension to asymmetric over- or underexpression. This model permits greater flexibility than models in current use as it has the potential, at least with sufficient data, to accommodate both whole genome and restricted coverage arrays. We also propose likelihood approaches to hyperparameter estimation which are equally applicable in the Normal mixture case. The Laplace model appears to give some improvement in fit to data, though simulation studies show that our method performs similarly to several other statistical approaches to the problem of identification of differential expression.     

Characterization and simulation of cDNA microarray spots using a novel mathematical model

Background  

The quality of cDNA microarray data is crucial for expanding its application to other research areas, such as the study of gene regulatory networks. Despite the fact that a number of algorithms have been suggested to increase the accuracy of microarray gene expression data, it is necessary to obtain reliable microarray images by improving wet-lab experiments. As the first step of a cDNA microarray experiment, spotting cDNA probes is critical to determining the quality of spot images.     

Risk assessment for quantitative responses using a mixture model

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.     

A mixture model approach to detecting differentially expressed genes with microarray data

An exciting biological advancement over the past few years is the use of microarray technologies to measure simultaneously the expression levels of thousands of genes. The bottleneck now is how to extract useful information from the resulting large amounts of data. An important and common task in analyzing microarray data is to identify genes with altered expression under two experimental conditions. We propose a nonparametric statistical approach, called the mixture model method (MMM), to handle the problem when there are a small number of replicates under each experimental condition. Specifically, we propose estimating the distributions of a t -type test statistic and its null statistic using finite normal mixture models. A comparison of these two distributions by means of a likelihood ratio test, or simply using the tail distribution of the null statistic, can identify genes with significantly changed expression. Several methods are proposed to effectively control the false positives. The methodology is applied to a data set containing expression levels of 1,176 genes of rats with and without pneumococcal middle ear infection.     

Semi-supervised learning via penalized mixture model with application to microarray sample classification

MOTIVATION: It is biologically interesting to address whether human blood outgrowth endothelial cells (BOECs) belong to or are closer to large vessel endothelial cells (LVECs) or microvascular endothelial cells (MVECs) based on global expression profiling. An earlier analysis using a hierarchical clustering and a small set of genes suggested that BOECs seemed to be closer to MVECs. By taking advantage of the two known classes, LVEC and MVEC, while allowing BOEC samples to belong to either of the two classes or to form their own new class, we take a semi-supervised learning approach; for high-dimensional data as encountered here, we propose a penalized mixture model with a weighted L1 penalty to realize automatic feature selection while fitting the model. RESULTS: We applied our penalized mixture model to a combined dataset containing 27 BOEC, 28 LVEC and 25 MVEC samples. Analysis results indicated that the BOEC samples appeared to form their own new class. A simulation study confirmed that, compared with the standard mixture model with or without initial variable selection, the penalized mixture model performed much better in identifying relevant genes and forming corresponding clusters. The penalized mixture model seems to be promising for high-dimensional data with the capability of novel class discovery and automatic feature selection.