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PubMed2006

A statistical model for dissecting genomic imprinting through genetic mapping.

As a result of nonequivalent genetic contribution of maternal and paternal genomes to offsprings, genomic imprinting or called parent-of-origin effect, has been broadly identified in plants, animals and humans. Its role in shaping organism's development has been unanimously recognized. However, statistical methods for identifying imprinted quantitative trait loci (iQTL) and estimating the imprinted effect have not been well developed. In this article, we propose an efficient statistical procedure for genomewide estimating and testing the effects of significant iQTL underlying the quantitative variation of interested traits. The developed model can be applied to two different genetic cross designs, backcross and F(2) families derived from inbred lines. The proposed procedure is built within the maximum likelihood framework and implemented with the EM algorithm. Extensive simulation studies show that the proposed model is well performed in a variety of situations. To demonstrate the usefulness of the proposed approach, we apply the model to a published data in an F(2) family derived from LG/S and SM/S mouse stains. Two partially maternal imprinting iQTL are identified which regulate the growth of body weight. Our approach provides a testable framework for identifying and estimating iQTL involved in the genetic control of complex traits.

Algorithms↗
PubMed2005

A mixture of experts network structure for breast cancer diagnosis.

Mixture of experts (ME) is a modular neural network architecture for supervised learning. This paper illustrates the use of ME network structure to guide diagnosing of breast cancer. Expectation-maximization (EM) algorithm was used for training the ME so that the learning process is decoupled in a manner that fits well with the modular structure. Diagnosis tasks are among the most interesting activities in which to implement intelligent systems. Specifically, diagnosis is an attempt to accurately forecast the outcome of a specific situation, using as input information obtained from a concrete set of variables that potentially describe the situation. The ME network structure was implemented for breast cancer diagnosis using the attributes of each record in the Wisconsin breast cancer database. To improve diagnostic accuracy, the outputs of expert networks were combined by a gating network simultaneously trained in order to stochastically select the expert that is performing the best at solving the problem. For the Wisconsin breast cancer diagnosis problem, the obtained total classification accuracy by the ME network structure was 98.85%. The ME network structure achieved accuracy rates which were higher than that of the stand-alone neural network models.

Algorithms↗
PubMed2007

Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the MONOLIX software.

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.

Administration, Oral↗
PubMed2005

Simultaneous modelling of survival and longitudinal data with an application to repeated quality of life measures.

In biomedical studies, interest often focuses on the relationship between patient's characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches.

Algorithms↗
PubMedDate not supplied

A computer program for the statistical analysis of disease prevalence data from survival/sacrifice experiments.

This paper presents a computer program for analyzing disease prevalence data from animal survival experiments in which there may also be some serial sacrifice. The method has been described in Biometrics 35 (1979) 221-234. The user is interrogated about the details of particular models he wishes to fit. Then a generalized EM algorithm is used to compute maximum likelihood estimates of various quantities of interest concerning the effects of treatment, time and presence of other diseases on the prevalences and lethalities of specific diseases of interest.

Animals↗
PubMed1986

Estimation of growth curves from longitudinal data collected at irregular time intervals.

A general procedure for fitting growth curves is proposed that can be applied to longitudinal data even if observations are missing or irregularly spaced. Maximum likelihood estimates for mean growths are obtained from an EM algorithm. Estimates for standard errors, percentiles, and growth velocities are also produced. The techniques are demonstrated through the use of growth data from a longitudinal study of sickle cell disease.

Algorithms↗
PubMedDate not supplied

Parametric inference for epidemic models.

The likelihood function corresponding to epidemic data is often very complicated. We illustrate that the EM algorithm can sometimes help to simplify likelihood inferences. Difficulties with likelihood inferences about parameters of epidemic models have established a role for martingale methods. These are methods of statistical inference based on estimating equations derived from the rich theory of martingales, and they have produced simple methods of inference in a number of important applications to epidemic data. We contrast likelihood methods with martingale methods and determine which specific assumptions cause changes in inferences about the infection potential of a disease. It is found that the martingale-based estimate of the infection potential remains unaltered under a variety of commonly used model specifications but that the precision of this estimate changes as model assumptions are altered.

Algorithms↗
PubMed1996

MIXREG: a computer program for mixed-effects regression analysis with autocorrelated errors.

MIXREG is a program that provides estimates for a mixed-effects regression model (MRM) for normally-distributed response data including autocorrelated errors. This model can be used for analysis of unbalanced longitudinal data, where individuals may be measured at a different number of timepoints, or even at different timepoints. Autocorrelated errors of a general form or following an AR(1), MA(1), or ARMA(1,1) form are allowable. This model can also be used for analysis of clustered data, where the mixed-effects model assumes data within clusters are dependent. The degree of dependency is estimated jointly with estimates of the usual model parameters, thus adjusting for clustering. MIXREG uses maximum marginal likelihood estimation, utilizing both the EM algorithm and a Fisher-scoring solution. For the scoring solution, the covariance matrix of the random effects is expressed in its Gaussian decomposition, and the diagonal matrix reparameterized using the exponential transformation. Estimation of the individual random effects is accomplished using an empirical Bayes approach. Examples illustrating usage and features of MIXREG are provided.

Adolescent↗
PubMed1994

Sensitivity and specificity of diagnostic tests in acute maxillary sinusitis determined by maximum likelihood in the absence of an external standard.

This study shows how to obtain maximum likelihood estimates of test sensitivities and specificities in case of lack of an external standard, using the Expectation Maximisation (EM) algorithm. This method is used to compare four diagnostic tests in patients suspected of acute maxillary sinusitis. Data were analyzed from published studies. Antral aspiration is the test with the highest diagnostic value. The diagnostic value of a positive clinical examination (according to explicit criteria) and of a positive radiograph or ultrasound are comparable. A negative radiograph is of more diagnostic value than a negative clinical examination or ultrasound. The width of the confidence intervals may be too small, due to model deviations which may give incorrect standard errors. However, the estimated likelihood ratios adequately reflect the relative value of the diagnostic tests considered, even when the assumption of independence is dropped.

Acute Disease↗
PubMed2006

Effect of the density of the C(18) surface coverage on the adsorption mechanism of a cationic compound and on the silanol activity of the stationary phase in reversed phase liquid chromatography.

RPLC columns with different surface coverages (a C(1) endcapped column with a bonding density of 3.92 micromol/m(2) and four C(18)-bonded, endcapped columns, with octadecyl chain densities of 0.42, 1.01, 2.03, and 3.15 micromol/m(2)) were used to investigate the effects of the density of the surface coverage of RPLC columns on the adsorption mechanism of a cationic compound, amitriptyline chloride, and on the silanol activity of these columns. The mobile phases used were acetonitrile-water (30/70, v/v) solutions, buffered at either pH 2.7 or pH 6.9. At pH 2.7, the residual silanol groups are not ionized. At pH 6.9, some of these groups are ionized and these surface anions can strongly interact with the cationic compound. The adsorption isotherms were measured by frontal analysis (FA) at pH 2.7 and by frontal analysis by characteristic points (FACP) at pH 6.9, because the very high retention observed at neutral pH made FA measurements excessively long and poorly accurate. The adsorption energy distributions (AEDs) were calculated when possible, according to the expectation-maximization (EM) algorithm. A bimodal and a trimodal energy distribution were found for all the columns at pH 2.7 and 6.9, respectively. The third site measured at pH 6.9 was attributed to the strong ion-exchange interactions between the ionized silanol groups and the amitriptylinium cation. The contribution of the ionized silanol groups to the overall retention is maximum for the phases with intermediary bonding densities (1.01 and 2.03 micromol/m(2)). The peak tailing is most pronounced for the lowest (C(1) column) and the highest (3.15 micromol/m(2)) surface coverages.

Adsorption↗
PubMed2006

A SAS macro for parametric and semiparametric mixture cure models.

Cure models have been developed to analyze failure time data with a cured fraction. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. Mixture cure models assume that the studied population is a mixture of susceptible individuals, who may experience the event of interest, and non-susceptible individuals that will never experience it. The aim of this paper is to propose a SAS macro to estimate parametric and semiparametric mixture cure models with covariates. The cure fraction can be modelled by various binary regression models. Parametric and semiparametric models can be used to model the survival of uncured individuals. The maximization of the likelihood function is performed using SAS PROC NLMIXED for parametric models and through an EM algorithm for the Cox's proportional hazards mixture cure model. Indications and limitations of the proposed macro are discussed and an example in the field of cancer clinical trials is shown.

Algorithms↗
PubMed2005

A mixture of experts network structure for modelling Doppler ultrasound blood flow signals.

Mixture of experts (ME) is a modular neural network architecture for supervised learning. This paper illustrates the use of ME network structure to guide modelling Doppler ultrasound blood flow signals. Expectation-Maximization (EM) algorithm was used for training the ME so that the learning process is decoupled in a manner that fits well with the modular structure. The ophthalmic and internal carotid arterial Doppler signals were decomposed into time-frequency representations using discrete wavelet transform and statistical features were calculated to depict their distribution. The ME network structures were implemented for diagnosis of ophthalmic and internal carotid arterial disorders using the statistical features as inputs. To improve diagnostic accuracy, the outputs of expert networks were combined by a gating network simultaneously trained in order to stochastically select the expert that is performing the best at solving the problem. The ME network structure achieved accuracy rates which were higher than that of the stand-alone neural network models.

Adult↗
PubMed2006

Association of HLA-DR, -DQ, and vitamin D receptor alleles and haplotypes with tuberculosis in the Venda of South Africa.

The vitamin D receptor (VDR) and the human leukocyte antigen (HLA) class II complex affect innate and/or adaptive immunity against Mycobacterium tuberculosis. HLA-DRB1, HLA-DQB1, and VDR gene (VDR) polymorphisms were previously associated with tuberculosis (TB) and are here investigated as candidates for TB susceptibility in the Venda population of South Africa. Genomic DNA from 95 patients with pulmonary tuberculosis (PTB) and 117 ethnically matched, healthy controls were typed for HLA-DRB1, DRB3, DRB4, DRB5, DQB1, and VDR polymorphisms FokI, BsmI, ApaI, and TaqI using polymerase chain reaction-sequence specific primers (PCR-SSP). Allele and haplotype frequencies were calculated by the estimator maximum (EM) algorithm. DRB1*1302 phenotype was significantly associated with TB occurring at a significantly higher allele frequency in cases than controls and found in haplotype with DQB1*0602/3. DQB1*0301-0304 phenotype was significantly associated with TB and found in haplotype with DRB1*1101-1121, showing significant linkage disequilibrium (LD) in both cases and controls. Only DRB1*1101-1121-DQB1*05 was significantly associated with TB based on the sequential Bonferroni p value. VDR SNP phenotypes were not associated with TB, but the haplotype F-b-A-T significantly protected from TB. In conclusion, common African HLA-DRB1 and -DQB1 variants, previously associated with protection from malaria and hepatitis B/C virus persistence, predispose the Venda to TB, whereas the proposedly active VDR haplotype F-b-A-T showed significant protection.

Alleles↗
PubMed2005

A nonparametric approach to extract information from interspike interval data.

In this work we develop an approach to extracting information from neural spike trains. Using the expectation-maximization (EM) algorithm, interspike interval data from experiments and simulations are fitted by mixtures of distributions, including Gamma, inverse Gaussian, log-normal, and the distribution of the interspike intervals of the leaky integrate-and-fire model. In terms of the Kolmogorov-Smirnov test for goodness-of-fit, our approach is proved successful (P>0.05) in fitting benchmark data for which a classical parametric approach has been shown to fail before. In addition, we present a novel method to fit mixture models to censored data, and discuss two examples of the application of such a method, which correspond to the case of multiple-trial and multielectrode array data. A MATLAB implementation of the algorithm is available for download from .

Action Potentials↗
PubMed2006

A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci.

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.

Algorithms↗
PubMed2005

Modelling bivariate count series with excess zeros.

Bivariate time series of counts with excess zeros relative to the Poisson process are common in many bioscience applications. Failure to account for the extra zeros in the analysis may result in biased parameter estimates and misleading inferences. A class of bivariate zero-inflated Poisson autoregression models is presented to accommodate the zero-inflation and the inherent serial dependency between successive observations. An autoregressive correlation structure is assumed in the random component of the compound regression model. Parameter estimation is achieved via an EM algorithm, by maximizing an appropriate log-likelihood function to obtain residual maximum likelihood estimates. The proposed method is applied to analyze a bivariate series from an occupational health study, in which the zero-inflated injury count events are classified as either musculoskeletal or non-musculoskeletal in nature. The approach enables the evaluation of the effectiveness of a participatory ergonomics intervention at the population level, in terms of reducing the overall incidence of lost-time injury and a simultaneous decline in the two mean injury rates.

Accidents, Occupational↗
PubMed2006

Longitudinal analysis of haplotypes and polymorphisms of the APOA5 and APOC3 genes associated with variation in serum triglyceride levels: the Bogalusa Heart Study.

Polymorphisms in the APOC3 and APOA5 genes, from the APOA1/APOC3/APOA4/APOA5 gene cluster on chromosome 11q23, have been associated with interindividual variation in plasma triglycerides. APOA5 polymorphisms implicated include 2 in the promoter region (-1131 T/C and -3 A/G) and 1 in exon 2 (+56 C/G). APOC3 polymorphisms implicated include 1 (SstI) in the 3' untranslated region and 1 (-2854 G/T) in the APOC3-APOA4 intergenic region. We analyzed the associations of haplotypes and multilocus genotypes of these polymorphisms on longitudinal serum triglyceride profiles in 360 African American and 823 white subjects from the Bogalusa Heart Study. Subjects were examined from 2 to 8 times (mean +/- SD, 5.4 +/- 1.3) between 1973 and 1996, at ages ranging from 4 to 38 years, with 1978 observations in African Americans and 4465 in whites. Serum triglycerides were significantly higher among whites across all ages. Allele frequencies differed significantly between African Americans and whites at all but the APOA5 +56 C/G locus. Linkage disequilibrium among the loci was higher in whites and haplotype diversity lower: 6 haplotypes had estimated frequencies of more than 1% in African Americans, 5 in whites. Individually, all polymorphisms except APOC3 -2854 G/T showed significant associations with triglyceride levels in the full sample. However, genotype models including all 5 loci showed significant triglyceride associations for only 3 (APOC3 SstI, APOA5 -1131 T/C, and APOA5 +56 C/G); significant interactions among them indicated their effects were not independent. Neither APOC3 -2854 G/T nor APOA5 -3 A/G had significant effects when the other 3 loci were in the models. The EM algorithm was used to estimate haplotype frequencies and assign haplotype probabilities to individuals, which is conditional on their genotypes; individuals' haplotype probability vectors were then used as predictors in multilevel mixed models of longitudinal triglyceride profiles. Of haplotypes comprising, in order, APOC3 SstI and -2854 G/T and APOA5 -1131 T/C, -3 A/G, and +56 C/G, 3 were significantly associated with higher triglycerides, even after adjusting for multiple tests: GGTAG (P = .002), GTTAG (P < .0001), and CGCGC (P = .0002). Each GGTAG haplotype carried would be expected to raise triglyceride levels (relative to those of GTTAC homozygotes) by approximately 19 mg/dL, each GTTAG haplotype by approximately 15 mg/dL, and each CGCGC haplotype by approximately 7 mg/dL. Haplotypes comprising the 3 loci implicated by genotype analyses (SstI, -1131 T/C, and +56 C/G) were also tested: haplotypes C_C_C and G_T_G significantly raised triglycerides, even after adjustment for multiple comparisons (P < .002 for both), with each copy of C_C_C expected to raise triglycerides by approximately 7 mg/dL and each copy of G_T_G by approximately 15 mg/dL. Overall, our findings support those of others in associating specific polymorphisms and haplotypes in the APOA1/C3/A4/A5 gene cluster with higher serum triglyceride levels. However, the degree to which polymorphisms in the APOC3 and APOA5 genes may be independently associated with triglyceride levels remains to be determined.

Adolescent↗
PubMed2005

An empirical Bayesian solution to the source reconstruction problem in EEG.

Distributed linear solutions of the EEG source localisation problem are used routinely. In contrast to discrete dipole equivalent models, distributed linear solutions do not assume a fixed number of active sources and rest on a discretised fully 3D representation of the electrical activity of the brain. The ensuing inverse problem is underdetermined and constraints or priors are required to ensure the uniqueness of the solution. In a Bayesian framework, the conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimisation of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to various constraints. Here we formulate the conventional "Weighted Minimum Norm" (WMN) solution in terms of hierarchical linear models. An "Expectation-Maximisation" (EM) algorithm is used to obtain a "Restricted Maximum Likelihood" (ReML) estimate of the hyperparameters, before estimating the "Maximum a Posteriori" solution itself. This procedure can be considered a generalisation of previous work that encompasses multiple constraints. Our approach was compared with the "classic" WMN and Maximum Smoothness solutions, using a simplified 2D source model with synthetic noisy data. The ReML solution was assessed with four types of source location priors: no priors, accurate priors, inaccurate priors, and both accurate and inaccurate priors. The ReML approach proved useful as: (1) The regularisation (or influence of the a priori source covariance) increased as the noise level increased. (2) The localisation error (LE) was negligible when accurate location priors were used. (3) When accurate and inaccurate location priors were used simultaneously, the solution was not influenced by the inaccurate priors. The ReML solution was then applied to real somatosensory-evoked responses to illustrate the application in an empirical setting.

Algorithms↗