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PubMed2006

Haplotype reconstruction and estimation of haplotype frequencies from nuclear families with only one parent available.

Recent literature has suggested that haplotype inference through close relatives, especially from nuclear families can be an alternative strategy in determining the linkage phase. In this paper, haplotype reconstruction and estimation of haplotype frequencies via expectation maximization (EM) algorithm including nuclear families with only one parent available is proposed. Parent and his (her) child are treated as parent-child pair with one shared haplotype. This reduces the number of potential haplotype pairs for both parent and child separately, resulting in a higher accuracy of the estimation. In a series of simulations, the comparisons of PHASE, GENEHUNTER, EM-based approach for complete nuclear families and our approach are carried out. In all situations, EM-based approach for trio data is comparable but slightly worse error rate than PHASE, our approach is slightly better and much faster than PHASE for incomplete trios, the performance of GENEHUNTER is very bad in simple nuclear family settings and dramatically decreased with the number of markers being increased. On the other hand, the comparison result of different sampling designs demonstrates that sampling trios is the most efficient design to estimate haplotype frequencies in populations under same genotyping cost.

Child↗
PubMed2006

A mixture model with random-effects components for clustering correlated gene-expression profiles.

MOTIVATION: The clustering of gene profiles across some experimental conditions of interest contributes significantly to the elucidation of unknown gene function, the validation of gene discoveries and the interpretation of biological processes. However, this clustering problem is not straightforward as the profiles of the genes are not all independently distributed and the expression levels may have been obtained from an experimental design involving replicated arrays. Ignoring the dependence between the gene profiles and the structure of the replicated data can result in important sources of variability in the experiments being overlooked in the analysis, with the consequent possibility of misleading inferences being made. We propose a random-effects model that provides a unified approach to the clustering of genes with correlated expression levels measured in a wide variety of experimental situations. Our model is an extension of the normal mixture model to account for the correlations between the gene profiles and to enable covariate information to be incorporated into the clustering process. Hence the model is applicable to longitudinal studies with or without replication, for example, time-course experiments by using time as a covariate, and to cross-sectional experiments by using categorical covariates to represent the different experimental classes. RESULTS: We show that our random-effects model can be fitted by maximum likelihood via the EM algorithm for which the E(expectation)and M(maximization) steps can be implemented in closed form. Hence our model can be fitted deterministically without the need for time-consuming Monte Carlo approximations. The effectiveness of our model-based procedure for the clustering of correlated gene profiles is demonstrated on three real datasets, representing typical microarray experimental designs, covering time-course, repeated-measurement and cross-sectional data. In these examples, relevant clusters of the genes are obtained, which are supported by existing gene-function annotation. A synthetic dataset is considered too. AVAILABILITY: A Fortran program blue called EMMIX-WIRE (EM-based MIXture analysis WIth Random Effects) is available on request from the corresponding author.

Algorithms↗
PubMedDate not supplied

Comparison of 180 degrees and 360 degrees acquisition for myocardial perfusion SPECT with compensation for attenuation, detector response, and scatter: Monte Carlo and mathematical observer results.

BACKGROUND: The optimal projection data acquisition strategy for myocardial perfusion (MP) single photon emission computed tomography (SPECT) remains controversial. METHODS: We compared MP SPECT using 180 degrees and 360 degrees projection data obtained with the same acquisition time, reconstructed either with filtered back projection (FBP) or the iterative ordered-subsets expectation maximization (OS-EM) algorithm with various combinations of attenuation, detector response, and scatter compensation using mathematical observers and a myocardial defect detection task. We used Monte Carlo-simulated projection data from a population of 3-dimensional nurbs-based cardiac-torso (NCAT) phantoms with ranges of variability in patient anatomy, organ uptake, defect location, defect size, and noise level based on clinical data. Projection data from 180 degrees and 360 degrees acquisitions were generated by assuming the same acquisition time. After iterative or FBP reconstruction, standard postprocessing methods were applied. For each acquisition and reconstruction method, we optimized the number of iterations and cut-off frequency of the Butterworth filter using the Channelized Hotelling Observer methodology. The optimum set of parameters was that which gave the maximum area under the curve. RESULTS: For both acquisition protocols, OS-EM with compensations provided better performance than FBP or OS-EM without compensation. For FBP, the optimized 180 degrees acquisition provided a statistically significant increase in AUC as compared with optimized 360 degrees acquisition. For OS-EM, the AUCs for 180 degrees were slightly larger than for 360 degrees acquisitions when comparing images reconstructed with the same compensations. However, the differences were smaller and not statistically significant. CONCLUSION: With optimized reconstruction and filtering parameters, 180 degrees acquisition provided a statistically significant improvement over 360 degrees acquisition for FBP reconstruction. However, for OS-EM the differences were small and not statistically significant.

Algorithms↗
PubMed2004

Haplotype frequency estimation error analysis in the presence of missing genotype data.

BACKGROUND: Increasingly researchers are turning to the use of haplotype analysis as a tool in population studies, the investigation of linkage disequilibrium, and candidate gene analysis. When the phase of the data is unknown, computational methods, in particular those employing the Expectation-Maximisation (EM) algorithm, are frequently used for estimating the phase and frequency of the underlying haplotypes. These methods have proved very successful, predicting the phase-known frequencies from data for which the phase is unknown with a high degree of accuracy. Recently there has been much speculation as to the effect of unknown, or missing allelic data - a common phenomenon even with modern automated DNA analysis techniques - on the performance of EM-based methods. To this end an EM-based program, modified to accommodate missing data, has been developed, incorporating non-parametric bootstrapping for the calculation of accurate confidence intervals. RESULTS: Here we present the results of the analyses of various data sets in which randomly selected known alleles have been relabelled as missing. Remarkably, we find that the absence of up to 30% of the data in both biallelic and multiallelic data sets with moderate to strong levels of linkage disequilibrium can be tolerated. Additionally, the frequencies of haplotypes which predominate in the complete data analysis remain essentially the same after the addition of the random noise caused by missing data. CONCLUSIONS: These findings have important implications for the area of data gathering. It may be concluded that small levels of drop out in the data do not affect the overall accuracy of haplotype analysis perceptibly, and that, given recent findings on the effect of inaccurate data, ambiguous data points are best treated as unknown.

Alleles↗
PubMed2004

Simultaneous feature selection and clustering using mixture models.

Clustering is a common unsupervised learning technique used to discover group structure in a set of data. While there exist many algorithms for clustering, the important issue of feature selection, that is, what attributes of the data should be used by the clustering algorithms, is rarely touched upon. Feature selection for clustering is difficult because, unlike in supervised learning, there are no class labels for the data and, thus, no obvious criteria to guide the search. Another important problem in clustering is the determination of the number of clusters, which clearly impacts and is influenced by the feature selection issue. In this paper, we propose the concept of feature saliency and introduce an expectation-maximization (EM) algorithm to estimate it, in the context of mixture-based clustering. Due to the introduction of a minimum message length model selection criterion, the saliency of irrelevant features is driven toward zero, which corresponds to performing feature selection. The criterion and algorithm are then extended to simultaneously estimate the feature saliencies and the number of clusters.

Algorithms↗
PubMed2002

Adaptive quality-based clustering of gene expression profiles.

MOTIVATION: Microarray experiments generate a considerable amount of data, which analyzed properly help us gain a huge amount of biologically relevant information about the global cellular behaviour. Clustering (grouping genes with similar expression profiles) is one of the first steps in data analysis of high-throughput expression measurements. A number of clustering algorithms have proved useful to make sense of such data. These classical algorithms, though useful, suffer from several drawbacks (e.g. they require the predefinition of arbitrary parameters like the number of clusters; they force every gene into a cluster despite a low correlation with other cluster members). In the following we describe a novel adaptive quality-based clustering algorithm that tackles some of these drawbacks. RESULTS: We propose a heuristic iterative two-step algorithm: First, we find in the high-dimensional representation of the data a sphere where the "density" of expression profiles is locally maximal (based on a preliminary estimate of the radius of the cluster-quality-based approach). In a second step, we derive an optimal radius of the cluster (adaptive approach) so that only the significantly coexpressed genes are included in the cluster. This estimation is achieved by fitting a model to the data using an EM-algorithm. By inferring the radius from the data itself, the biologist is freed from finding an optimal value for this radius by trial-and-error. The computational complexity of this method is approximately linear in the number of gene expression profiles in the data set. Finally, our method is successfully validated using existing data sets. AVAILABILITY: http://www.esat.kuleuven.ac.be/~thijs/Work/Clustering.html

Algorithms↗
PubMed2006

Constrained Gaussian mixture model framework for automatic segmentation of MR brain images.

An automated algorithm for tissue segmentation of noisy, low-contrast magnetic resonance (MR) images of the brain is presented. A mixture model composed of a large number of Gaussians is used to represent the brain image. Each tissue is represented by a large number of Gaussian components to capture the complex tissue spatial layout. The intensity of a tissue is considered a global feature and is incorporated into the model through tying of all the related Gaussian parameters. The expectation-maximization (EM) algorithm is utilized to learn the parameter-tied, constrained Gaussian mixture model. An elaborate initialization scheme is suggested to link the set of Gaussians per tissue type, such that each Gaussian in the set has similar intensity characteristics with minimal overlapping spatial supports. Segmentation of the brain image is achieved by the affiliation of each voxel to the component of the model that maximized the a posteriori probability. The presented algorithm is used to segment three-dimensional, T1-weighted, simulated and real MR images of the brain into three different tissues, under varying noise conditions. Results are compared with state-of-the-art algorithms in the literature. The algorithm does not use an atlas for initialization or parameter learning. Registration processes are therefore not required and the applicability of the framework can be extended to diseased brains and neonatal brains.

Algorithms↗
PubMed2003

Decomposing gene expression into cellular processes.

We propose a probabilistic model for cellular processes, and an algorithm for discovering them from gene expression data. A process is associated with a set of genes that participate in it; unlike clustering techniques, our model allows genes to participate in multiple processes. Each process may be active to a different degree in each experiment. The expression measurement for gene g in array a is a sum, over all processes in which g participates, of the activity levels of these processes in array a. We describe an iterative procedure, based on the EM algorithm, for decomposing the expression matrix into a given number of processes. We present results on Yeast gene expression data, which indicate that our approach identifies real biological processes.

Algorithms↗
PubMed2004

Performance-based classifier combination in atlas-based image segmentation using expectation-maximization parameter estimation.

It is well known in the pattern recognition community that the accuracy of classifications obtained by combining decisions made by independent classifiers can be substantially higher than the accuracy of the individual classifiers. We have previously shown this to be true for atlas-based segmentation of biomedical images. The conventional method for combining individual classifiers weights each classifier equally (vote or sum rule fusion). In this paper, we propose two methods that estimate the performances of the individual classifiers and combine the individual classifiers by weighting them according to their estimated performance. The two methods are multiclass extensions of an expectation-maximization (EM) algorithm for ground truth estimation of binary classification based on decisions of multiple experts (Warfield et al., 2004). The first method performs parameter estimation independently for each class with a subsequent integration step. The second method considers all classes simultaneously. We demonstrate the efficacy of these performance-based fusion methods by applying them to atlas-based segmentations of three-dimensional confocal microscopy images of bee brains. In atlas-based image segmentation, multiple classifiers arise naturally by applying different registration methods to the same atlas, or the same registration method to different atlases, or both. We perform a validation study designed to quantify the success of classifier combination methods in atlas-based segmentation. By applying random deformations, a given ground truth atlas is transformed into multiple segmentations that could result from imperfect registrations of an image to multiple atlas images. In a second evaluation study, multiple actual atlas-based segmentations are combined and their accuracies computed by comparing them to a manual segmentation. We demonstrate in both evaluation studies that segmentations produced by combining multiple individual registration-based segmentations are more accurate for the two classifier fusion methods we propose, which weight the individual classifiers according to their EM-based performance estimates, than for simple sum rule fusion, which weights each classifier equally.

Algorithms↗
PubMed2006

Parameter estimation in stochastic mammogram model by heuristic optimization techniques.

The appearance of disproportionately large amounts of high-density breast parenchyma in mammograms has been found to be a strong indicator of the risk of developing breast cancer. Hence, the breast density model is popular for risk estimation or for monitoring breast density change in prevention or intervention programs. However, the efficiency of such a stochastic model depends on the accuracy of estimation of the model's parameter set. We propose a new approach-heuristic optimization-to estimate more accurately the model parameter set as compared to the conventional and popular expectation-maximization (EM) algorithm. After initial segmentation of a given mammogram, the finite generalized Gaussian mixture (FGGM) model is constructed by computing the statistics associated with different image regions. The model parameter set thus obtained is estimated by particle swarm optimization (PSO) and evolutionary programming (EP) techniques, where the objective function to be minimized is the relative entropy between the image histogram and the estimated density distributions. When our heuristic approach was applied to different categories of mammograms from the Mini-MIAS database, it yielded lower floor of estimation error in 109 out of 112 cases (97.3 %), and 101 out of 102 cases (99.0%), for the number of image regions being five and eight, respectively, with the added advantage of faster convergence rate, when compared to the EM approach. Besides, the estimated density model preserves the number of regions specified by the information-theoretic criteria in all the test cases, and the assessment of the segmentation results by radiologists is promising.

Algorithms↗
PubMed1995

Simultaneous emission and transmission measurements for attenuation correction in whole-body PET.

UNLABELLED: We describe a methodology for measuring and correcting for attenuation in whole-body PET using simultaneous emission and transmission (SET) measurements. METHODS: The main components of the methodology are: (a) sinogram windowing of low activity (< or = 50 MBq) rotating 68Ge/Ga rod sources, (b) segmented attenuation correction (SAC) and (c) maximum likelihood reconstruction using the ordered subsets EM (OS-EM) algorithm. The methods were implemented on a whole-body positron emission tomograph. Quantitative accuracy and the signal-to-noise ratio (SNR) were measured for a thorax-tumor phantom as functions of acquisition time (range: 2-20 min per position). RESULTS: When a typical rod source activity (200 MBq 68Ge/Ga) was used, emission SNR was 60% lower in simultaneous than in separate measurements. The difference was only 14% when the rods contained 45 MBq 68Ge/Ga. The SNR was further improved by SAC in conjunction with OS-EM reconstruction and the relative gain increased with increasing acquisition time. Quantitative estimates of tumor, liver and lung radioactivity agreed with values obtained from a separate high count measurement to within 8%, independent of acquisition time. CONCLUSION: Attenuation correction of whole-body PET images is feasible using SET measurements. There is good quantitative agreement with conventional methods and increased noise is offset by the use of SAC and OS-EM reconstruction.

Adult↗
PubMed2003

A haplotype-based algorithm for multilocus linkage disequilibrium mapping of quantitative trait loci with epistasis.

For tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.

Algorithms↗
PubMed2003

Finding the "genuine" schizotype: a model and method for resolving heterogeneity in performance on laboratory measures in experimental psychopathology research.

Heterogeneity in the performance of persons affected with schizophrenia or schizotypic psychopathology on various laboratory tasks has long been recognized, both for its consistency across tasks and studies and for the massive methodological and substantive challenges it poses for experimental psychopathology, genetic, and other investigations. Traditional multivariate techniques, such as factor analysis, discriminant function analysis, and cluster analysis, have all been deemed inadequate for resolving heterogeneity, because of one or another statistical limitation. Here, an objective statistical approach based on a formal statistical model that uses the ubiquitous and well-developed expectation-maximization (EM) algorithm (A. P. Dempster, N. M. Laird, & D. B. Rubin, 1977) is presented, which enables one effectively to partition a group of experimental subjects, in this case identified initially using the well-known Perceptual Aberration Scale (L. J. Chapman, J. P. Chapman, & M. L. Raulin, 1978), in a manner that reduces heterogeneity and allows for the separation of what are termed genuine and false-positive schizotypes. The validity of the parsing strategy was supported by reference to other laboratory indexes of relevance to schizophrenia and schizotypy that were not included in the initial EM-based analyses. The potential utility of this approach is discussed with reference to future schizophrenia and schizotypy research.

Adolescent↗
PubMed2003

Inference on haplotype effects in case-control studies using unphased genotype data.

A variety of statistical methods exist for detecting haplotype-disease association through use of genetic data from a case-control study. Since such data often consist of unphased genotypes (resulting in haplotype ambiguity), such statistical methods typically apply the expectation-maximization (EM) algorithm for inference. However, the majority of these methods fail to perform inference on the effect of particular haplotypes or haplotype features on disease risk. Since such inference is valuable, we develop a retrospective likelihood for estimating and testing the effects of specific features of single-nucleotide polymorphism (SNP)-based haplotypes on disease risk using unphased genotype data from a case-control study. Our proposed method has a flexible structure that allows, among other choices, modeling of multiplicative, dominant, and recessive effects of specific haplotype features on disease risk. In addition, our method relaxes the requirement of Hardy-Weinberg equilibrium of haplotype frequencies in case subjects, which is typically required of EM-based haplotype methods. Also, our method easily accommodates missing SNP information. Finally, our method allows for asymptotic, permutation-based, or bootstrap inference. We apply our method to case-control SNP genotype data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus (FUSION) Genetics study and identify two haplotypes that appear to be significantly associated with type 2 diabetes. Using the FUSION data, we assess the accuracy of asymptotic P values by comparing them with P values obtained from a permutation procedure. We also assess the accuracy of asymptotic confidence intervals for relative-risk parameters for haplotype effects, by a simulation study based on the FUSION data.

Algorithms↗
PubMed1996

Mixture models for eye-tracking data: a case study.

Heterogeneity in biomedical data is often a source of great scientific interest and mixture models provide a general framework for modelling the various types that arise in practice. Finite mixture models model discrete subgroups within populations while continuous mixture models inflate the variance to account for over-dispersed data. A potential problem with the application of finite mixture models in practice is that these models may drastically overestimate the number of component densities when there is a lack of model fit. This can have severe consequences, leading the data analyst to attach substantive interpretations to spurious subgroups. For this reason, we propose using the continuous mixture model as an alternative when fitting finite mixture models with an arbitrary number of components. In the context of an example examining a specific oculomotor component of eye-tracking dysfunction in schizophrenia, we demonstrate why the continuous mixture model provides a viable alternative to the finite mixture model for small sample sizes. We present methods for fitting and comparing both models using the parametric bootstrap and EM algorithm, and show that the distinction between the models decreases as the number of component densities in the finite mixture model increases.

Algorithms↗
PubMed1996

A generalized Michaelis-Menten response surface.

We describe an application of recently developed generalized Michaelis-Menten response surface and non-linear mixed model methodologies to model glucose utilization in foetal sheep. More specifically, we model the response surface of glucose utilization rate in the foetal sheep as a function of glucose and insulin concentrations using a three-dimensional analogue of the Michaelis-Menten pharmacokinetic model. To account for multiple measurements per sheep, we apply the non-linear mixed effects model proposed by Lindstrom and Bates using the EM algorithm computational scheme presented by Hirst et al.

Animals↗
PubMedDate not supplied

Logistic analysis of studies with two-stage sampling: a comparison of four approaches.

This paper discusses the analysis of two-stage studies where covariates are missing or measured with error at the first stage of sampling and are validated at the second stage in a subsample. Four recently developed approaches, the weighted pseudo-likelihood method of Flanders and Greenland (1991), the pseudo-conditional likelihood methods of Breslow and Cain (1988) and Schill et al. (1993) and the maximum likelihood estimate obtained via the EM-algorithm (Wacholder and Weinberg, 1994) are reviewed, and some connections between them are established. It is shown that, with respect to odds ratio estimation, case-control designs can be analysed as if first-stage sampling had been prospective. The procedures are numerically compared with respect to asymptotic relative efficiency in a missing value setting.

Algorithms↗
PubMed1997

Estimating asymptomatic duration in cancer: the AIDS connection.

Many chronic diseases, including AIDS and cancer, do not manifest themselves clinically until some time after their inception. In studies of disease natural history, the duration of the asymptomatic period is of interest-in AIDS, to predict the epidemic's course, and in cancer, to develop efficient screening strategies. This article provides a bridge between the two fields with respect to estimation of the asymptomatic period. By adapting AIDS methodology to cancer, the article identifies a non-parametric method for estimating the duration of the asymptomatic period in cancer. The method is similar to one developed by Louis et al. (Mathematical Biosciences, 40, 111-144 (1978)), and is designed to apply to data from a cohort of individuals, screened periodically. After reviewing the similarities and differences between the AIDS and cancer contexts, we develop an EM algorithm that, at convergence, yields a maximum or saddle point of the likelihood. We investigate the performance of the algorithm by means of a simulation study, explore the effect of adding a smoothing step to the estimation procedure, and adapt the method for use with a data set in which disease prevalence is low. We apply the method to data from the HIP breast cancer screening trial.

Acquired Immunodeficiency Syndrome↗