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At least 163 records · Page 9Linked to original sources
PubMed2005

Stochastic vs. deterministic uptake of dodecanedioic acid by isolated rat livers.

Deterministic and stochastic differential equations models of the uptake of dodecanedioic acid (C12) are fitted to experimental data obtained on nine isolated, perfused rat livers. 11500 mug of C12 were injected as a bolus into the perfusing liver solution. The concentrations of C12 in perfusate samples taken over 2 h from the beginning of the experiments were analyzed by High Performance Liquid Chromatography (HPLC). A two-compartment deterministic model is studied. To include spontaneous erratic variations in the metabolic processes the parameter for the uptake rate is randomized to obtain a stochastic differential equations model. Parameters are estimated in a two-step procedure: first, parameters in the drift part are estimated by least squares; then, the diffusion parameter is estimated using Monte-Carlo simulations to approximate the unknown likelihood function. Parameter estimation is carried out over a wide range of reasonable measurement error variances to check robustness of estimates. It is concluded that the kinetics of dodecanedioic acid, in the experimental conditions discussed, is well approximated by a model including spontaneous erratic variations in the liver uptake rate.

Algorithms↗
PubMed2002

[Estimation of the recombination fraction by the maximum likelihood method in mapping interacting genes relative to marker loci].

For mapping nonlinked interacting genes relative to marker loci, the recombination fractions can be calculated by using the log-likelihood functions were derived that permit estimation of recombinant fractions by solving the ML equations on the basis of F2 data at various types of interaction. In some cases, the recombinant fraction estimates are obtained in the analytical form while in others they are numerically calculated from concrete experimental data. With the same type of epistasis the log-functions were shown to differ depending on the functional role (suppression or epistasis) of the mapped gene. Methods for testing the correspondence of the model and the recombination fraction estimates to the experimental data are discussed. In ambiguous cases, analysis of the linked marker behavior makes it possible to differentiate gene interaction from distorted single-locus segregation, which at some forms of interaction imitate phenotypic ratios.

Chromosome Mapping↗
PubMed1997

Generalized likelihood ratios for quantitative diagnostic test scores.

The reduction of quantitative diagnostic test scores to the dichotomous case is a wasteful and unnecessary simplification in the era of high-speed computing. Physicians could make better use of the information embedded in quantitative test results if modern generalized curve estimation techniques were applied to the likelihood functions of Bayes' theorem. Hand calculations could be completely avoided and computed graphical summaries provided instead. Graphs showing posttest probability of disease as a function of pretest probability with confidence intervals (POD plots) would enhance acceptance of these techniques if they were immediately available at the computer terminal when test results were retrieved. Such constructs would also provide immediate feedback to physicians when a valueless test had been ordered.

Algorithms↗
PubMed1998

Some aspects of measurement error in explanatory variables for continuous and binary regression models.

A simple form of measurement error model for explanatory variables is studied incorporating classical and Berkson cases as particular forms, and allowing for either additive or multiplicative errors. The work is motivated by epidemiological problems, and therefore consideration is given not only to continuous response variables but also to logistic regression models. The possibility that different individuals in a study have errors of different types is also considered. The relatively simple estimation procedures proposed for use with cohort data and case-control data are checked by simulation, under the assumption of various error structures. The results show that even in situations where conventional analysis yields slope estimates that are on average attenuated by a factor of approximately 50 per cent, estimates obtained using the proposed amended likelihood functions are within 5 per cent of their true values. The work was carried out to provide a method for the analysis of lung cancer risk following residential radon exposure, but it should be applicable to a wide variety of situations.

Adolescent↗
PubMed2005

Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm.

Pharmacokinetic/pharmacodynamic modelling is most often performed using non-linear mixed-effects models based on ordinary differential equations with uncorrelated intra-individual residuals. More sophisticated residual error models as e.g. stochastic differential equations (SDEs) with measurement noise can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. This general approach enables a decomposition of the intra-individual residual variation epsilon into system noise w and measurement noise e. The present work describes implementation of SDEs in a non-linear mixed-effects model, where parameter estimation was performed by a novel approximation of the likelihood function. This approximation is constructed by combining the First-Order Conditional Estimation (FOCE) method used in non-linear mixed-effects modelling with the Extended Kalman Filter used in models with SDEs. Fundamental issues concerning the proposed model and estimation algorithm are addressed by simulation studies, concluding that system noise can successfully be separated from measurement noise and inter-individual variability.

Algorithms↗
PubMed2006

An empirical examination of the standard errors of maximum likelihood phylogenetic parameters under the molecular clock via bootstrapping.

The molecular clock theory has greatly enlightened our understanding of macroevolutionary events. Maximum likelihood (ML) estimation of divergence times involves the adoption of fixed calibration points, and the confidence intervals associated with the estimates are generally very narrow. The credibility intervals are inferred assuming that the estimates are normally distributed, which may not be the case. Moreover, calculation of standard errors is usually carried out by the curvature method and is complicated by the difficulty in approximating second derivatives of the likelihood function. In this study, a standard primate phylogeny was used to examine the standard errors of ML estimates via the bootstrap method. Confidence intervals were also assessed from the posterior distribution of divergence times inferred via Bayesian Markov Chain Monte Carlo. For the primate topology under evaluation, no significant differences were found between the bootstrap and the curvature methods. Also, Bayesian confidence intervals were always wider than those obtained by ML.

Animals↗
PubMed2003

Local influence analysis of structural equation models with continuous and ordinal categorical variables.

This paper proposes a method to assess the local influence of minor perturbations for a structural equation model with continuous and ordinal categorical variables. The key idea is to treat the latent variables as hypothetical missing data and then apply Cook's approach to the conditional expectation of the complete-data log-likelihood function in the corresponding EM algorithm for deriving the normal curvature and the conformal normal curvature. Building blocks for achieving the diagnostic measures are computed via observations generated by the Gibbs sampler. It is shown that the proposed methodology is relatively simple to implement, computationally efficient, and feasible for a wide variety of perturbation schemes. Two illustrative real examples are presented.

Acquired Immunodeficiency Syndrome↗
PubMed2005

Improvement of mapping accuracy by unifying linkage and association analysis.

It is well known that pedigree/family data record information on the coexistence in founder haplotypes of alleles at nearby loci and the cotransmission from parent to offspring that reveal different, but complementary, profiles of the genetic architecture. Either conventional linkage analysis that assumes linkage equilibrium or family-based association tests (FBATs) capture only partial information, leading to inefficiency. For example, FBATs will fail to detect even very tight linkage in the case where no allelic association exists, while a violation of the assumption of linkage equilibrium will result in biased estimation and reduced efficiency in linkage mapping. In this article, by using a data augmentation technique and the EM algorithm, we propose a likelihood-based approach that embeds both linkage and association analyses into a unified framework for general pedigree data. Relative to either linkage or association analysis, the proposed approach is expected to have greater estimation accuracy and power. Monte Carlo simulations support our theoretical expectations and demonstrate that our new methodology: (1) is more powerful than either FBATs or classic linkage analysis; (2) can unbiasedly estimate genetic parameters regardless of whether association exists, thus remedying the bias and less precision of traditional linkage analysis in the presence of association; and (3) is capable of identifying tight linkage alone. The new approach also holds the theoretical advantage that it can extract statistical information to the maximum extent and thereby improve mapping accuracy and power because it integrates multilocus population-based association study and pedigree-based linkage analysis into a coherent framework. Furthermore, our method is numerically stable and computationally efficient, as compared to existing parametric methods that use the simplex algorithm or Newton-type methods to maximize high-order multidimensional likelihood functions, and also offers the computation of Fisher's information matrix. Finally, we apply our methodology to a genetic study on bone mineral density (BMD) for the vitamin D receptor (VDR) gene and find that VDR is significantly linked to BMD at the one-third region of the wrist.

Algorithms↗
PubMedDate not supplied

Down and out: estimating the relationship between mental health and unemployment.

We utilized a unique dataset of Montreal residents to estimate the relationship between employment and mental health, controlling for endogeneity. We applied a maximum likelihood, simultaneous equation generalized probit model to estimate jointly the determinants of an individual's latent index of employability and their mental health as measured by the Psychiatric Symptom Index (PSI). The likelihood function was adjusted to account for the fact that individuals were sampled based on their employment status, and also for the fact that repeated observations of individuals in different periods were used in the analysis. We found tangible beneficial effects of mental health on employability. In addition, employment appears to improve mental health. The ML estimates of the endogenous relationship between employment and mental health indicate that OLS estimates are biased upwards, but the effects of unemployment on deteriorating mental health are not spurious.

Adult↗
PubMed2006

Maximum likelihood estimation of molecular motor kinetics from staircase dwell-time sequences.

Molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. High resolution single molecule recordings of motor steps appear as a stochastic sequence of dwells, resembling a staircase. Staircase data can also be obtained from other molecular machines such as F1 -ATPase, RNA polymerase, or topoisomerase. We developed a maximum likelihood algorithm that estimates the rate constants between different conformational states of the protein, including motor steps. We model the motor with a periodic Markov model that reflects the repetitive chemistry of the motor step. We estimated the kinetics from the idealized dwell-sequence by numerical maximization of the likelihood function for discrete-time Markov models. This approach eliminates the need for missed event correction. The algorithm can fit kinetic models of arbitrary complexity, such as uniform or alternating step chemistry, reversible or irreversible kinetics, ATP concentration and mechanical force-dependent rates, etc. The method allows global fitting across stationary and nonstationary experimental conditions, and user-defined a priori constraints on rate constants. The algorithm was tested with simulated data, and implemented in the free QuB software.

Adenosine Triphosphate↗
PubMedDate not supplied

A framework establishing clear decision criteria for the assessment of drug efficacy.

Much has been published on various aspects of data analysis and reporting from clinical trials within the biopharmaceutical environment. This ranges from regulatory guidelines on the format and content of registration dossiers to recommendations on data presentation and the statistical methodologies that are appropriate for the diverse types of data one observes in clinical trials. Little has been written about designing a clinical trial analysis and reporting package that focuses on the decisions that must be made throughout the drug development process. Pharmaceutical companies today are under enormous pressure to develop drugs quickly and (cost-) efficiently. Because of this, drugs often move into the later phases of drug development before evidence from prior phases is completely understood. This provides a challenge to clinical trialists to design and execute a clinical trial programme which can expedite drug development. The statistician, as a clinical trialist, must strive to determine the optimum analytical methodology that facilitates decision making for this clinical trial programme. This paper proposes a new framework for the assessment of efficacy in drug development called the 'one programme, one p-value' framework. This framework will accelerate drug development by providing clear criteria for the decisions which must be made along the way. The 'one programme, one p-value' framework is based on the notion that the clinical trial programme comprises exploratory and confirmatory phases. The use of the likelihood function in the exploratory phase facilitates the decision whether (or when) to move into the confirmatory phase. The confirmatory phase consists of one confirmatory trial with a single hypothesis test of the drug's efficacy; hence 'one p-value'. Sponsor interaction with regulatory agencies is necessary at each decision point. Finally, the paper considers how analysis and reporting of efficacy data can be accomplished from a clinical trial programme as described.

Clinical Trials as Topic↗
PubMed1996

A computer program for regression analysis of ordered categorical repeated measurements.

RMORD is an easy-to-use FORTRAN program for the analysis of clustered ordinal data using the method of Stram, Wei, and Ware. This method constitutes an extension of the proportional-odds model to the situation in which groups of responses are correlated. At each measurement occasion, a proportional-odds regression model is fit to the data by maximizing the occasion-specific likelihood function. The joint asymptotic distribution of the occasion-specific regression parameter estimators is obtained along with a consistent estimator of their asymptotic covariance matrix. RMORD may be used when ordinal measurements are obtained at a common set of observation times for multiple subjects or clusters. Both missing data and covariates which vary within clusters can be accommodated. The program can be run on microcomputers, workstations, and mainframe computers. Two examples illustrating the usage and features of RMORD are provided.

Age Distribution↗
PubMed2005

Coarse master equation from Bayesian analysis of replica molecular dynamics simulations.

We use Bayesian inference to derive the rate coefficients of a coarse master equation from molecular dynamics simulations. Results from multiple short simulation trajectories are used to estimate propagators. A likelihood function constructed as a product of the propagators provides a posterior distribution of the free coefficients in the rate matrix determining the Markovian master equation. Extensions to non-Markovian dynamics are discussed, using the trajectory "paths" as observations. The Markovian approach is illustrated for the filling and emptying transitions of short carbon nanotubes dissolved in water. We show that accurate thermodynamic and kinetic properties, such as free energy surfaces and kinetic rate coefficients, can be computed from coarse master equations obtained through Bayesian inference.

Bayes Theorem↗
PubMed2006

Mutation parameters from DNA sequence data using graph theoretic measures on lineage trees.

MOTIVATION: B cells responding to antigenic stimulation can fine-tune their binding properties through a process of affinity maturation composed of somatic hypermutation, affinity-selection and clonal expansion. The mutation rate of the B cell receptor DNA sequence, and the effect of these mutations on affinity and specificity, are of critical importance for understanding immune and autoimmune processes. Unbiased estimates of these properties are currently lacking due to the short time-scales involved and the small numbers of sequences available. RESULTS: We have developed a bioinformatic method based on a maximum likelihood analysis of phylogenetic lineage trees to estimate the parameters of a B cell clonal expansion model, which includes somatic hypermutation with the possibility of lethal mutations. Lineage trees are created from clonally related B cell receptor DNA sequences. Important links between tree shapes and underlying model parameters are identified using mutual information. Parameters are estimated using a likelihood function based on the joint distribution of several tree shapes, without requiring a priori knowledge of the number of generations in the clone (which is not available for rapidly dividing populations in vivo). A systematic validation on synthetic trees produced by a mutating birth-death process simulation shows that our estimates are precise and robust to several underlying assumptions. These methods are applied to experimental data from autoimmune mice to demonstrate the existence of hypermutating B cells in an unexpected location in the spleen.

Algorithms↗
PubMed2004

Quantitative genetic models for describing simultaneous and recursive relationships between phenotypes.

Multivariate models are of great importance in theoretical and applied quantitative genetics. We extend quantitative genetic theory to accommodate situations in which there is linear feedback or recursiveness between the phenotypes involved in a multivariate system, assuming an infinitesimal, additive, model of inheritance. It is shown that structural parameters defining a simultaneous or recursive system have a bearing on the interpretation of quantitative genetic parameter estimates (e.g., heritability, offspring-parent regression, genetic correlation) when such features are ignored. Matrix representations are given for treating a plethora of feedback-recursive situations. The likelihood function is derived, assuming multivariate normality, and results from econometric theory for parameter identification are adapted to a quantitative genetic setting. A Bayesian treatment with a Markov chain Monte Carlo implementation is suggested for inference and developed. When the system is fully recursive, all conditional posterior distributions are in closed form, so Gibbs sampling is straightforward. If there is feedback, a Metropolis step may be embedded for sampling the structural parameters, since their conditional distributions are unknown. Extensions of the model to discrete random variables and to nonlinear relationships between phenotypes are discussed.

Bayes Theorem↗
PubMed2005

The analysis of soil cores polluted with certain metals using the Box-Cox transformation.

To define the soil properties for a given area or country including the level of pollution, soil survey and inventory programs are essential tools. Soil data transformations enable the expression of the original data on a new scale, more suitable for data analysis. In the computer-aided interactive analysis of large data files of soil characteristics containing outliers, the diagnostic plots of the exploratory data analysis (EDA) often find that the sample distribution is systematically skewed or reject sample homogeneity. Under such circumstances the original data should be transformed. The Box-Cox transformation improves sample symmetry and stabilizes spread. The logarithmic plot of a profile likelihood function enables the optimum transformation parameter to be found. Here, a proposed procedure for data transformation in univariate data analysis is illustrated on a determination of cadmium content in the plough zone of agricultural soils. A typical soil pollution survey concerns the determination of the elements Be (16 544 values available), Cd (40 317 values), Co (22 176 values), Cr (40 318 values), Hg (32 344 values), Ni (34 989 values), Pb (40 344 values), V (20 373 values) and Zn (36 123 values) in large samples.

Agriculture↗
PubMedDate not supplied

Bayesian segmental models with multiple sequence alignment profiles for protein secondary structure and contact map prediction.

In this paper, we develop a segmental semi-Markov model (SSMM) for protein secondary structure prediction which incorporates multiple sequence alignment profiles with the purpose of improving the predictive performance. The segmental model is a generalization of the hidden Markov model where a hidden state generates segments of various length and secondary structure type. A novel parameterized model is proposed for the likelihood function that explicitly represents multiple sequence alignment profiles to capture the segmental conformation. Numerical results on benchmark data sets show that incorporating the profiles results in substantial improvements and the generalization performance is promising. By incorporating the information from long range interactions in beta-sheets, this model is also capable of carrying out inference on contact maps. This is an important advantage of probabilistic generative models over the traditional discriminative approach to protein secondary structure prediction. The Web server of our algorithm and supplementary materials are available at http://public.kgi.edu/-wild/bsm.html.

Algorithms↗
PubMed2006

Precise physical models of protein-DNA interaction from high-throughput data.

A cell's ability to regulate gene transcription depends in large part on the energy with which transcription factors (TFs) bind their DNA regulatory sites. Obtaining accurate models of this binding energy is therefore an important goal for quantitative biology. In this article, we present a principled likelihood-based approach for inferring physical models of TF-DNA binding energy from the data produced by modern high-throughput binding assays. Central to our analysis is the ability to assess the relative likelihood of different model parameters given experimental observations. We take a unique approach to this problem and show how to compute likelihood without any explicit assumptions about the noise that inevitably corrupts such measurements. Sampling possible choices for model parameters according to this likelihood function, we can then make probabilistic predictions for the identities of binding sites and their physical binding energies. Applying this procedure to previously published data on the Saccharomyces cerevisiae TF Abf1p, we find models of TF binding whose parameters are determined with remarkable precision. Evidence for the accuracy of these models is provided by an astonishing level of phylogenetic conservation in the predicted energies of putative binding sites. Results from in vivo and in vitro experiments also provide highly consistent characterizations of Abf1p, a result that contrasts with a previous analysis of the same data.

Binding Sites↗