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PubMed1997

Meta-MEME: motif-based hidden Markov models of protein families.

MOTIVATION: Modeling families of related biological sequences using Hidden Markov models (HMMs), although increasingly widespread, faces at least one major problem: because of the complexity of these mathematical models, they require a relatively large training set in order to accurately recognize a given family. For families in which there are few known sequences, a standard linear HMM contains too many parameters to be trained adequately. RESULTS: This work attempts to solve that problem by generating smaller HMMs which precisely model only the conserved regions of the family. These HMMs are constructed from motif models generated by the EM algorithm using the MEME software. Because motif-based HMMs have relatively few parameters, they can be trained using smaller data sets. Studies of short chain alcohol dehydrogenases and 4Fe-4S ferredoxins support the claim that motif-based HMMs exhibit increased sensitivity and selectivity in database searches, especially when training sets contain few sequences.

Alcohol Dehydrogenase↗

PubMed2002

A dissimilarity matrix between protein atom classes based on Gaussian mixtures.

MOTIVATION: Previously, Rantanen et al. (2001; J. Mol. Biol., 313, 197-214) constructed a protein atom-ligand fragment interaction library embodying experimentally solved, high-resolution three-dimensional (3D) structural data from the Protein Data Bank (PDB). The spatial locations of protein atoms that surround ligand fragments were modeled with Gaussian mixture models, the parameters of which were estimated with the expectation-maximization (EM) algorithm. In the validation analysis of this library, there was strong indication that the protein atom classification, 24 classes, was too large and that a reduction in the classes would lead to improved predictions. RESULTS: Here, a dissimilarity (distance) matrix that is suitable for comparison and fusion of 24 pre-defined protein atom classes has been derived. Jeffreys' distances between Gaussian mixture models are used as a basis to estimate dissimilarities between protein atom classes. The dissimilarity data are analyzed both with a hierarchical clustering method and independently by using multidimensional scaling analysis. The results provide additional insight into the relationships between different protein atom classes, giving us guidance on, for example, how to readjust protein atom classification and, thus, they will help us to improve protein--ligand interaction predictions. CONTACT: vira@utu.fi

Cluster Analysis↗

PubMed2003

Clustering of time-course gene expression data using a mixed-effects model with B-splines.

MOTIVATION: Time-course gene expression data are often measured to study dynamic biological systems and gene regulatory networks. To account for time dependency of the gene expression measurements over time and the noisy nature of the microarray data, the mixed-effects model using B-splines was introduced. This paper further explores such mixed-effects model in analyzing the time-course gene expression data and in performing clustering of genes in a mixture model framework. RESULTS: After fitting the mixture model in the framework of the mixed-effects model using an EM algorithm, we obtained the smooth mean gene expression curve for each cluster. For each gene, we obtained the best linear unbiased smooth estimate of its gene expression trajectory over time, combining data from that gene and other genes in the same cluster. Simulated data indicate that the methods can effectively cluster noisy curves into clusters differing in either the shapes of the curves or the times to the peaks of the curves. We further demonstrate the proposed method by clustering the yeast genes based on their cell cycle gene expression data and the human genes based on the temporal transcriptional response of fibroblasts to serum. Clear periodic patterns and varying times to peaks are observed for different clusters of the cell-cycle regulated genes. Results of the analysis of the human fibroblasts data show seven distinct transcriptional response profiles with biological relevance. AVAILABILITY: Matlab programs are available on request from the authors.

Algorithms↗

PubMed2003

Discovering molecular pathways from protein interaction and gene expression data.

In this paper, we describe an approach for identifying 'pathways' from gene expression and protein interaction data. Our approach is based on the assumption that many pathways exhibit two properties: their genes exhibit a similar gene expression profile, and the protein products of the genes often interact. Our approach is based on a unified probabilistic model, which is learned from the data using the EM algorithm. We present results on two Saccharomyces cerevisiae gene expression data sets, combined with a binary protein interaction data set. Our results show that our approach is much more successful than other approaches at discovering both coherent functional groups and entire protein complexes.

Algorithms↗

PubMed2003

Genome-wide discovery of transcriptional modules from DNA sequence and gene expression.

In this paper, we describe an approach for understanding transcriptional regulation from both gene expression and promoter sequence data. We aim to identify transcriptional modules--sets of genes that are co-regulated in a set of experiments, through a common motif profile. Using the EM algorithm, our approach refines both the module assignment and the motif profile so as to best explain the expression data as a function of transcriptional motifs. It also dynamically adds and deletes motifs, as required to provide a genome-wide explanation of the expression data. We evaluate the method on two Saccharomyces cerevisiae gene expression data sets, showing that our approach is better than a standard one at recovering known motifs and at generating biologically coherent modules. We also combine our results with binding localization data to obtain regulatory relationships with known transcription factors, and show that many of the inferred relationships have support in the literature.

Algorithms↗

PubMed2003

Gene networks inference using dynamic Bayesian networks.

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.

Algorithms↗

PubMed2004

Statistical modeling of sequencing errors in SAGE libraries.

MOTIVATION: Sequencing errors may bias the gene expression measurements made by Serial Analysis of Gene Expression (SAGE). They may introduce non-existent tags at low abundance and decrease the real abundance of other tags. These effects are increased in the longer tags generated in LongSAGE libraries. Current sequencing technology generates quite accurate estimates of sequencing error rates. Here we make use of the sequence neighborhood of SAGE tags and error estimates from the base-calling software to correct for such errors. RESULTS: We introduce a statistical model for the propagation of sequencing errors in SAGE and suggest an Expectation-Maximization (EM) algorithm to correct for them given observed sequences in a library and base-calling error estimates. We tested our method using simulated and experimental SAGE libraries. When comparing SAGE libraries, we found that sequencing errors can introduce considerable bias. High abundance tags may be falsely called as significantly differentially expressed, especially when comparing libraries with different levels of sequencing errors and/or of different size. Truly, differentially expressed tags have decreased significance as 'true'-tag counts are generally underestimated. This may alter if tags near the threshold of differential expression are called significant. Moreover, the number of different transcripts present in a library is overestimated as false tags are introduced at low abundance. Our correction method adjusts the tag counts to be closer to the true counts and is able to partly correct for biases introduced by sequencing errors. AVAILABILITY: An implementation using R is distributed as an R package. An online version is available at http://tagcalling.mbgproject.org

Algorithms↗

PubMed2005

Accounting for probe-level noise in principal component analysis of microarray data.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.

Algorithms↗

PubMed2006

Incorporating gene functions as priors in model-based clustering of microarray gene expression data.

MOTIVATION: Cluster analysis of gene expression profiles has been widely applied to clustering genes for gene function discovery. Many approaches have been proposed. The rationale is that the genes with the same biological function or involved in the same biological process are more likely to co-express, hence they are more likely to form a cluster with similar gene expression patterns. However, most existing methods, including model-based clustering, ignore known gene functions in clustering. RESULTS: To take advantage of accumulating gene functional annotations, we propose incorporating known gene functions as prior probabilities in model-based clustering. In contrast to a global mixture model applicable to all the genes in the standard model-based clustering, we use a stratified mixture model: one stratum corresponds to the genes of unknown function while each of the other ones corresponding to the genes sharing the same biological function or pathway; the genes from the same stratum are assumed to have the same prior probability of coming from a cluster while those from different strata are allowed to have different prior probabilities of coming from the same cluster. We derive a simple EM algorithm that can be used to fit the stratified model. A simulation study and an application to gene function prediction demonstrate the advantage of our proposal over the standard method. CONTACT: weip@biostat.umn.edu

Algorithms↗

PubMed2006

Segmentation and intensity estimation of microarray images using a gamma-t mixture model.

MOTIVATION: We present a new approach to the analysis of images for complementary DNA microarray experiments. The image segmentation and intensity estimation are performed simultaneously by adopting a two-component mixture model. One component of this mixture corresponds to the distribution of the background intensity, while the other corresponds to the distribution of the foreground intensity. The intensity measurement is a bivariate vector consisting of red and green intensities. The background intensity component is modeled by the bivariate gamma distribution, whose marginal densities for the red and green intensities are independent three-parameter gamma distributions with different parameters. The foreground intensity component is taken to be the bivariate t distribution, with the constraint that the mean of the foreground is greater than that of the background for each of the two colors. The degrees of freedom of this t distribution are inferred from the data but they could be specified in advance to reduce the computation time. Also, the covariance matrix is not restricted to being diagonal and so it allows for nonzero correlation between R and G foreground intensities. This gamma-t mixture model is fitted by maximum likelihood via the EM algorithm. A final step is executed whereby nonparametric (kernel) smoothing is undertaken of the posterior probabilities of component membership. The main advantages of this approach are: (1) it enjoys the well-known strengths of a mixture model, namely flexibility and adaptability to the data; (2) it considers the segmentation and intensity simultaneously and not separately as in commonly used existing software, and it also works with the red and green intensities in a bivariate framework as opposed to their separate estimation via univariate methods; (3) the use of the three-parameter gamma distribution for the background red and green intensities provides a much better fit than the normal (log normal) or t distributions; (4) the use of the bivariate t distribution for the foreground intensity provides a model that is less sensitive to extreme observations; (5) as a consequence of the aforementioned properties, it allows segmentation to be undertaken for a wide range of spot shapes, including doughnut, sickle shape and artifacts. RESULTS: We apply our method for gridding, segmentation and estimation to cDNA microarray real images and artificial data. Our method provides better segmentation results in spot shapes as well as intensity estimation than Spot and spotSegmentation R language softwares. It detected blank spots as well as bright artifact for the real data, and estimated spot intensities with high-accuracy for the synthetic data. AVAILABILITY: The algorithms were implemented in Matlab. The Matlab codes implementing both the gridding and segmentation/estimation are available upon request. SUPPLEMENTARY INFORMATION: Supplementary material is available at Bioinformatics online.

Algorithms↗

PubMed2000

A meta-analysis of case-control and cohort studies with interval-censored exposure data: application to chorionic villus sampling.

Chorionic villus sampling (CVS) is a valued method of prenatal diagnosis that is often preferred over amniocentesis because it can be performed earlier, but which has also raised concern over a possible association with increased risk of terminal transverse limb deficiency (TTLD). We present and apply a meta-analytic method for estimating a combined dose-response effect from a series of case-control and cohort studies in which the exposure variable is interval-censored. Assuming coarsening at random for the interval-censoring, and calling upon the familiar result of Cornfield to pool case-control and cohort information on the association between a rare binary outcome and a multilevel exposure variable, we form a likelihood-based model to assess the effect of gestational age at the time of CVS on the presence or absence of a rare birth defect. Effect estimates are computed with a variant of the EM algorithm termed the method of weights, which enables the use of standard weighted regression software. Our findings suggest that CVS exposure at early gestational age leads to an increased risk of TTLD.

Journal Article↗

PubMed2002

Maximum likelihood estimation in random effects cure rate models with nonignorable missing covariates.

We introduce a method of parameter estimation for a random effects cure rate model. We also propose a methodology that allows us to account for nonignorable missing covariates in this class of models. The proposed method corrects for possible bias introduced by complete case analysis when missing data are not missing completely at random and is motivated by data from a pair of melanoma studies conducted by the Eastern Cooperative Oncology Group in which clustering by cohort or time of study entry was suspected. In addition, these models allow estimation of cure rates, which is desirable when we do not wish to assume that all subjects remain at risk of death or relapse from disease after sufficient follow-up. We develop an EM algorithm for the model and provide an efficient Gibbs sampling scheme for carrying out the E-step of the algorithm.

Journal Article↗

PubMed2002

The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure.

In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring.

Journal Article↗

PubMed2004

Generalized additive models for cancer mapping with incomplete covariates.

Maps depicting cancer incidence rates have become useful tools in public health research, giving valuable information about the spatial variation in rates of disease. Typically, these maps are generated using count data aggregated over areas such as counties or census blocks. However, with the proliferation of geographic information systems and related databases, it is becoming easier to obtain exact spatial locations for the cancer cases and suitable control subjects. The use of such point data allows us to adjust for individual-level covariates, such as age and smoking status, when estimating the spatial variation in disease risk. Unfortunately, such covariate information is often subject to missingness. We propose a method for mapping cancer risk when covariates are not completely observed. We model these data using a logistic generalized additive model. Estimates of the linear and non-linear effects are obtained using a mixed effects model representation. We develop an EM algorithm to account for missing data and the random effects. Since the expectation step involves an intractable integral, we estimate the E-step with a Laplace approximation. This framework provides a general method for handling missing covariate values when fitting generalized additive models. We illustrate our method through an analysis of cancer incidence data from Cape Cod, Massachusetts. These analyses demonstrate that standard complete-case methods can yield biased estimates of the spatial variation of cancer risk.

Algorithms↗

PubMed1994

High resolution of quantitative traits into multiple loci via interval mapping.

A very general method is described for multiple linear regression of a quantitative phenotype on genotype [putative quantitative trait loci (QTLs) and markers] in segregating generations obtained from line crosses. The method exploits two features, (a) the use of additional parental and F1 data, which fixes the joint QTL effects and the environmental error, and (b) the use of markers as cofactors, which reduces the genetic background noise. As a result, a significant increase of QTL detection power is achieved in comparison with conventional QTL mapping. The core of the method is the completion of any missing genotypic (QTL and marker) observations, which is embedded in a general and simple expectation maximization (EM) algorithm to obtain maximum likelihood estimates of the model parameters. The method is described in detail for the analysis of an F2 generation. Because of the generality of the approach, it is easily applicable to other generations, such as backcross progenies and recombinant inbred lines. An example is presented in which multiple QTLs for plant height in tomato are mapped in an F2 progeny, using additional data from the parents and their F1 progeny.

Chromosome Mapping↗

PubMed1996

A general Monte Carlo method for mapping multiple quantitative trait loci.

In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm for fitting multiple-QTL models to such data. Implementation of this algorithm is straightforward in standard statistical software, but computation may take much time. The method may be generalized to cope with more complex models for animal and human pedigrees. A practical example is presented, where a three-QTL model is adopted in an outbreeding situation with dominant markers. The example is concerned with the linkage between randomly amplified polymorphic DNA (RAPD) markers and QTLs for partial resistance to Fusarium oxysporum in lily.

Algorithms↗

PubMed1999

A random model approach to mapping quantitative trait loci for complex binary traits in outbred populations.

Mapping quantitative trait loci (QTL) for complex binary traits is more challenging than for normally distributed traits due to the nonlinear relationship between the observed phenotype and unobservable genetic effects, especially when the mapping population contains multiple outbred families. Because the number of alleles of a QTL depends on the number of founders in an outbred population, it is more appropriate to treat the effect of each allele as a random variable so that a single variance rather than individual allelic effects is estimated and tested. Such a method is called the random model approach. In this study, we develop the random model approach of QTL mapping for binary traits in outbred populations. An EM-algorithm with a Fisher-scoring algorithm embedded in each E-step is adopted here to estimate the genetic variances. A simple Monte Carlo integration technique is used here to calculate the likelihood-ratio test statistic. For the first time we show that QTL of complex binary traits in an outbred population can be scanned along a chromosome for their positions, estimated for their explained variances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.

Breeding↗

PubMed2000

Multipoint mapping of viability and segregation distorting loci using molecular markers.

In line-crossing experiments, deviations from Mendelian segregation ratios are usually observed for some markers. We hypothesize that these deviations are caused by one or more segregation-distorting loci (SDL) linked to the markers. We develop both a maximum-likelihood (ML) method and a Bayesian method to map SDL using molecular markers. The ML mapping is implemented via an EM algorithm and the Bayesian method is performed via the Markov chain Monte Carlo (MCMC). The Bayesian mapping is computationally more intensive than the ML mapping but can handle more complicated models such as multiple SDL and variable number of SDL. Both methods are applied to a set of simulated data and real data from a cross of two Scots pine trees.

Alleles↗