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PubMed2004

Characterisation of SNP haplotype structure in chemokine and chemokine receptor genes using CEPH pedigrees and statistical estimation.

Chemokine signals and their cell-surface receptors are important modulators of HIV-1 disease and cancer. To aid future case/control association studies, aim to further characterise the haplotype structure of variation in chemokine and chemokine receptor genes. To perform haplotype analysis in a population-based association study, haplotypes must be determined by estimation, in the absence of family information or laboratory methods to establish phase. Here, test the accuracy of estimates of haplotype frequency and linkage disequilibrium by comparing estimated haplotypes generated with the expectation maximisation (EM) algorithm to haplotypes determined from Centre d'Etude Polymorphisme Humain (CEPH) pedigree data. To do this, they have characterised haplotypes comprising alleles at 11 biallelic loci in four chemokine receptor genes (CCR3, CCR2, CCR5 and CCRL2), which span 150 kb on chromosome 3p21, and haplotyes of nine biallelic loci in six chemokine genes [MCP-1(CCL2), Eotaxin(CCL11), RANTES(CCL5), MPIF-1(CCL23), PARC(CCL18) and MIP-1alpha(CCL3)] on chromosome 17q11-12. Forty multi-generation CEPH families, totalling 489 individuals, were genotyped by the TaqMan 5'-nuclease assay. Phased haplotypes and haplotypes estimated from unphased genotypes were compared in 103 grandparents who were assumed to have mated at random. For the 3p21 single nucleotide polymorphism (SNP) data, haplotypes determined by pedigree analysis and haplotypes generated by the EM algorithm were nearly identical. Linkage disequilibrium, measured by the D' statistic, was nearly maximal across the 150 kb region, with complete disequilibrium maintained at the extremes between CCR3-Y17Y and CCRL2-I243V. D'-values calculated from estimated haplotypes on 3p21 had high concordance with pairwise comparisons between pedigree-phased chromosomes. Conversely, there was less agreement between analyses of haplotype frequencies and linkage disequilibrium using estimated haplotypes when compared with pedigree-phased haplotypes of SNPs on chromosome 17q11-12. These results suggest that, while estimations of haplotype frequency and linkage disequilibrium may be relatively simple in the 3p21 chemokine receptor cluster in population samples, the more complex environment on chromosome 17q11-12 will require a higher resolution haplotype analysis.

Algorithms↗
PubMedDate not supplied

Back-projection of German AIDS data using information on dates of tests.

The paper presents an application of back-projection methods to the reported AIDS data which are collected by the AIDS Center in the Federal Office of Health, Berlin. The analysis is based on all data reported up to 31 December 1992. The data are broken down by major risk groups. Correction for reporting delays takes into account temporal changes in their distribution. The paper applies the EMS algorithm for the estimation of HIV incidence. The incubation period is modelled according to a convolution of several exponential distributions which describe time dependent phenomena like change of case definition and therapy effects. For each case it is reported whether an antibody test has been performed before diagnosis, and if yes, at what time this test was performed. The modelling of the incubation distribution takes into account the transition from a state 'not yet tested' into a state 'tested'. Only tested individuals in three pre-AIDS states are eligible for treatment. The model allows us to estimate not only the current total HIV prevalence but also a breakdown into those that are not yet tested, those that are tested but not yet treated and those that are under treatment. The results depend on the assumptions about the effect of treatment and on the degree of smoothing applied in the EMS algorithm.

Acquired Immunodeficiency Syndrome↗
PubMed1998

The frequency distribution of the number of ion pairs in irradiated tissue.

The statistical distribution of the number of ion pairs per ionizing event in a small volume simulating a tissue sphere was obtained by applying the Expectation-Maximization (EM) algorithm to experimental spectra measured by exposing a Rossi-type spherical proportional counter to gamma radiation. The normalized experimental spectrum, r(x), which is the distribution of the number of ion pairs per event from both the primary track and the subsequent electron multiplication, can be represented as Sum(n) p(n) x f(n,x), where the f(n,x)'s for n = 1, 2, 3, ..., n are the normalized spectra for exactly 1, 2, 3, ..., n primary ion pairs and are calculated by convoluting the single-electron spectrum. The coefficients pn represent the mixing proportions of the spectra corresponding to 1, 2, 3, ..., n ion pairs in forming the experimental spectrum. The single-electron spectrum used in our calculations is the distribution of the number of ion pairs due to the multiplication process, and it is represented in analytical form by the Gamma distribution f(1,x) = a x x(b) x e(-cx), where x is energy, usually in eV, and a, b and c are constants. The EM algorithm is an iterative procedure for computing the maximum likelihood or maximum a posteriori estimates of the mixing proportions p(n), which we also refer to as the primary distribution of ion pairs in a microscopic spherical tissue-equivalent volume. The experimental and primary spectra are presented for simulated tissue spheres ranging from 0.25 to 8 microm in diameter exposed to 60Co gamma radiation.

Cobalt Radioisotopes↗
PubMed2001

Population pharmacokinetic modelling of carbamazepine by using the iterative Bayesian (IT2B) and the nonparametric EM (NPEM) algorithms: implications for dosage.

OBJECTIVE: To estimate individual and population postinduction pharmacokinetics of carbamazepine (CBZ) in epileptic adult and paediatric patients who received chronic CBZ monotherapy. METHODS: We have used the USC*PACK collection of PC programs for the estimations. The preinduction CBZ metabolism was also estimated in 16 volunteers after a single dose of CBZ (200 mg). We used a linear one-compartmental model with oral absorption and found the pharmacokinetic parameter values of CBZ behaviour to be in good agreement with those reported earlier. RESULTS: Serum CBZ concentrations correlated poorly with daily doses in both the adult and child populations. Because of the diversity within the population, use of the mean population model without knowledge of an individual patient's pharmacokinetic characteristics gives poor prediction. In contrast, the individual Bayesian posterior models gave good prediction for all subjects in the population, due to the removal of the interindividual variability. CONCLUSION: This approach permits one to individualize drug therapy for patients even when only sparse therapeutic drug monitoring (TDM) data are available. Future individual CBZ serum level predictions were acceptable from a clinical point of view (mean absolute error = 13.2 +/- 9.7%). The optimal sampling strategy approach helped to design an optimal cost-effective TDM protocol for CBZ therapy management.

Adult↗
PubMed1995

Transmission maximum-likelihood reconstruction with ordered subsets for cone beam CT.

An iterative algorithm is presented for accelerated reconstruction of cone beam transmission CT data (CBCT). CBCT supplies an attenuation map for SPECT attenuation compensation and anatomical correlation. Iterative algorithms are necessary to reduce truncation artifacts and 3D reconstruction artifacts. An existing transmission maximum-likelihood algorithm (TRML) is accurate but the reconstruction time is too long. The new algorithm is a modified EM algorithm, based on ordered subsets (OSEM). OSEM was evaluated in comparison to TRML using a thorax phantom and a 3D Defrise phantom. A wide range of image measures were evaluated, including spatial resolution, noise, log likelihood, region quantification, truncation artifact removal, and 3D artifact removal. For appropriate subset size, OSEM produced essentially the same image as TRML, but required only one-tenth as many iterations. Thus, adequate images were available in two to four iterations (20-30 min on a SPARC 2 workstation). Further, OSEM still approximately maximizes likelihood: divergence occurs only for very high (and clinically irrelevant) iterations. Ordered subsets are likely to be useful in other geometries (fan and parallel) and for emission CT as well. Therefore, with ordered subsets, high-quality iterative reconstruction is now available in clinically practical reconstructions times.

Algorithms↗
PubMed2005

A semiparametric method for estimating population size for capture-recapture experiments with random covariates in continuous time.

A semiparametric estimation procedure is proposed to model capture-recapture data with the aim of estimating the population size for a closed population. Individuals' covariates are possibly time dependent and missing at noncaptured times and may be measured with error. A set of estimating equations (EEs) based on covariate process and capture-recapture data is constructed to estimate the relevant parameters and the population size. These EEs can be solved by an algorithm similar to an EM algorithm. Simulation results show that the proposed procedures work better than the naive estimate. In some cases they are even better than "ideal" estimates, for which the true values of covariates are available for all captured subjects over the entire experimental period. We apply the method to a capture-recapture experiment on the bird species Prinia flaviventris in Hong Kong.

Algorithms↗
PubMed2006

An integrated-likelihood method for estimating genetic differentiation between populations.

The aim of this article is to develop an integrated-likelihood (IL) approach to estimate the genetic differentiation between populations. The conventional maximum-likelihood (ML) and pseudolikelihood (PL) methods that use sample counts of alleles may cause severe underestimations of FST, which means overestimations of theta=4Nm, when the number of sampling localities is small. To reduce such bias in the estimation of genetic differentiation, we propose an IL method in which the mean allele frequencies over populations are regarded as nuisance parameters and are eliminated by integration. To maximize the IL function, we have developed two algorithms, a Monte Carlo EM algorithm and a Laplace approximation. Our simulation studies show that the method proposed here outperforms the conventional ML and PL methods in terms of unbiasedness and precision. The IL method was applied to real data for Pacific herring and African elephants.

Algorithms↗
PubMedDate not supplied

Population kinetics and conditional assessment of the optimal dosage regimen using the P-PHARM software package.

The adjustment of individual dosage regimen is an adaptive control process based upon an individual response to a pharmacokinetic model. To attain this objective, it is very helpful to know the characteristics of the population to which the subject belongs, in terms of mean parameters and interindividual variability. Usually the available information consists of incomplete and sparse data. For this reason it is essential to employ a computational methodology based on non-linear mixed-effect procedures in order to obtain a population parameter estimate. A Bayesian methodology can then be applied from the population parameters to the specific data for the individual requiring a dosage adjustment (such data includes drug concentration(s) of the active drug, demographic data, etc). The result of the Bayesian calculation supplies the required individual pharmacokinetic parameters. An optimal dosage regimen can be defined on the basis of therapeutical criteria (concentration ranges) as well as practical constraints such as: the size of available unitary drug dosages, feasible drug intake times, penalties associated with expected concentrations falling outside the therapeutic concentration ranges. In this paper we present the methodology and results obtained using the P-Pharm software tool. P-Pharm implements a non-linear mixed-effect population parameter estimation algorithm based on the EM algorithm. This method allows the inclusion of explicit variables into the calculations, it implements an individual Bayesian parameter estimation procedure and also an algorithm for the conditional assessment of the optimal dosage regimen given a list of practical constraints.

Algorithms↗
PubMed2003

A new EM-based training algorithm for RBF networks.

In this paper, we propose a new Expectation-Maximization (EM) algorithm which speeds up the training of feedforward networks with local activation functions such as the Radial Basis Function (RBF) network. In previously proposed approaches, at each E-step the residual is decomposed equally among the units or proportionally to the weights of the output layer. However, these approaches tend to slow down the training of networks with local activation units. To overcome this drawback in this paper we use a new E-step which applies a soft decomposition of the residual among the units. In particular, the decoupling variables are estimated as the posterior probability of a component given an input-output pattern. This adaptive decomposition takes into account the local nature of the activation function and, by allowing the RBF units to focus on different subregions of the input space, the convergence is improved. The proposed EM training algorithm has been applied to the nonlinear modeling of a MESFET transistor.

Algorithms↗
PubMed1990

Counting algorithms for linkage.

The Lander-Green algorithm is algebraically different from the EM algorithm that maximizes likelihood. In our experience the numerical difference is very small. Since computations are no easier or convergence faster for the Lander-Green algorithm, there is no reason to prefer it to EM. As suggested by Green (personal communication), layering is advantageous. Occasional updating of the information weights might also be considered to accelerate mapping.

Algorithms↗
PubMed2002

Generalized character process models: estimating the genetic basis of traits that cannot be observed and that change with age or environmental conditions.

The genetic analysis of characters that change as a function of some independent and continuous variable has received increasing attention in the biological and statistical literature. Previous work in this area has focused on the analysis of normally distributed characters that are directly observed. We propose a framework for the development and specification of models for a quantitative genetic analysis of function-valued characters that are not directly observed, such as genetic variation in age-specific mortality rates or complex threshold characters. We employ a hybrid Markov chain Monte Carlo algorithm involving a Monte Carlo EM algorithm coupled with a Markov chain approximation to the likelihood, which is quite robust and provides accurate estimates of the parameters in our models. The methods are investigated using simulated data and are applied to a large data set measuring mortality rates in the fruit fly, Drosophila melanogaster.

Age Factors↗
PubMed1989

Efficient computation of lod scores: genotype elimination, genotype redefinition, and hybrid maximum likelihood algorithms.

Calculation of multilocus lod scores presents challenging problems in numerical analysis, combinatories, programming, and genetics. It is possible to accelerate these computations by exploiting the simple pedigree structure of a CEPH-type pedigree consisting of a nuclear family plus all four grandparents. Lathrop et al. (1986) have done this by introducing likelihood factorization and transformation rules and Lander & Green (1987) by the method of 'hidden Markov chains'. The present paper explores an alternative approach based on genotype redefinition in the grandparents and systematic phase elimination in all pedigree members. All three approaches accelerate the computation of a single likelihood. Equally relevant to multilocus mapping are search strategies for finding the maximum likelihood estimates of recombination fractions. Hybrid algorithms that start with the EM algorithm and switch midway to quasi-Newton algorithms show promise. These issues are investigated in the context of a simulated 10 locus example. This same example allows us to illustrate a simple strategy for determining locus order.

Algorithms↗
PubMed2001

Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, three-layer nets and ME-RBF-SVM models.

After introducing the fundamentals of BYY system and harmony learning, which has been developed in past several years as a unified statistical framework for parameter learning, regularization and model selection, we systematically discuss this BYY harmony learning on systems with discrete inner-representations. First, we shown that one special case leads to unsupervised learning on Gaussian mixture. We show how harmony learning not only leads us to the EM algorithm for maximum likelihood (ML) learning and the corresponding extended KMEAN algorithms for Mahalanobis clustering with criteria for selecting the number of Gaussians or clusters, but also provides us two new regularization techniques and a unified scheme that includes the previous rival penalized competitive learning (RPCL) as well as its various variants and extensions that performs model selection automatically during parameter learning. Moreover, as a by-product, we also get a new approach for determining a set of 'supporting vectors' for Parzen window density estimation. Second, we shown that other special cases lead to three typical supervised learning models with several new results. On three layer net, we get (i) a new regularized ML learning, (ii) a new criterion for selecting the number of hidden units, and (iii) a family of EM-like algorithms that combines harmony learning with new techniques of regularization. On the original and alternative models of mixture-of-expert (ME) as well as radial basis function (RBF) nets, we get not only a new type of criteria for selecting the number of experts or basis functions but also a new type of the EM-like algorithms that combines regularization techniques and RPCL learning for parameter learning with either least complexity nature on the original ME model or automated model selection on the alternative ME model and RBF nets. Moreover, all the results for the alternative ME model are also applied to other two popular nonparametric statistical approaches, namely kernel regression and supporting vector machine. Particularly, not only we get an easily implemented approach for determining the smoothing parameter in kernel regression, but also we get an alternative approach for deciding the set of supporting vectors in supporting vector machine.

Algorithms↗
PubMed2006

Cerebrovascular segmentation from TOF using stochastic models.

In this paper, we present an automatic statistical approach for extracting 3D blood vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) data. The voxels of the dataset are classified as either blood vessels or background noise. The observed volume data is modeled by two stochastic processes. The low level process characterizes the intensity distribution of the data, while the high level process characterizes their statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The parameters of the low level process are estimated using the expectation maximization (EM) algorithm. Since the convergence of the EM is sensitive to the initial estimate of the model parameters, an automatic method for parameter initialization, based on histogram analysis, is provided. To improve the quality of segmentation achieved by the proposed low level model especially in the regions of significantly vascular signal loss, the high level process is modeled as a Markov random field (MRF). Since MRF is sensitive to edges and the intracranial vessels represent roughly 5% of the intracranial volume, 2D MRF will destroy most of the small and medium sized vessels. Therefore, to reduce this limitation, we employed 3D MRF, whose parameters are estimated using the maximum pseudo likelihood estimator (MPLE), which converges to the true likelihood under large lattice. Our proposed model exhibits a good fit to the clinical data and is extensively tested on different synthetic vessel phantoms and several 2D/3D TOF datasets acquired from two different MRI scanners. Experimental results showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

Algorithms↗
PubMed1998

An iterative algorithm for X-ray CT fluoroscopy.

X-ray computed tomography fluoroscopy (CTF) enables image guidance of interventions, synchronization of scanning with contrast bolus arrival, and motion analysis. However, filtered backprojection (FB), the current method for CTF image reconstruction, is subject to motion and metal artifacts from implants, needles, or other surgical instruments. Reduced target lesion conspicuity may result from increased image noise associated with reduced tube current. In this report, we adapt the row-action expectation-maximization (EM) algorithm for CTF. Because time-dependent variation in images is localized during CTF, the row-action EM-like algorithm allows rapid convergence. More importantly, this iterative CTF algorithm has fewer metal artifacts and better low-contrast performance than FB.

Algorithms↗
PubMed2003

Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms.

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).

Algorithms↗
PubMed2001

The design and implementation of COSEM, an iterative algorithm for fully 3-D listmode data.

In this paper,we present coincidence-list-ordered sets expectation-maximization (COSEM), an algorithm for iterative image reconstruction directly from list-mode coincidence acquisition data. The COSEM algorithm is based on the ordered sets EM algorithm for binned data but has several extensions that makes it suitable for rotating two planar detector tomographs. We develop the COSEM algorithm and extend it to include analytic calculation of detection probability, noise reducing iterative filtering schemes, and on-the-fly attenuation correction methods. We present an adaptation of COSEM to the Varicam\VG camera and show results from clinical and phantom studies.

Algorithms↗
PubMedDate not supplied

Essential latent knowledge for protein-protein interactions: analysis by an unsupervised learning approach.

Protein-protein interactions play a number of central roles in many cellular functions, including DNA replication, transcription and translation, signal transduction, and metabolic pathways. A recent increase in the number of protein-protein interactions has made predicting unknown protein-protein interactions important for the understanding of living cells. However, the protein-protein interactions experimentally obtained so far are often incomplete and contradictory and, consequently, existing computational prediction methods have integrated evidence (latent knowledge of proteins) from different and more reliable sources. Analyzing the relationships between proteins and the latent knowledge is important to understanding the cellular processes. For this analysis, we propose a new probabilistic model for protein-protein interactions by considering the latent knowledge of proteins. We further present an efficient learning algorithm for this model, based on an EM algorithm. Experimental results have shown that in a supervised test setting, the proposed method outperformed five other competing methods by a statistically significant factor in all cases. Using the probability parameters of a trained model, we have further shown the latent knowledge that is essential to predicting protein-protein interactions. Overall, our experimental results confirm that our proposed model is especially effective for analyzing protein-protein interactions from a viewpoint of the latent knowledge of proteins.

Algorithms↗