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Results for “Likelihood Functions”

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At least 145 records · Page 8Linked to original sources
PubMed2000

A transitional model of barrier methods compliance with unbalanced loss to follow-up.

Differential loss to follow-up can substantially influence the evaluation of treatment effects on a dichotomous outcome of interest in longitudinal trials. The use of transitional models incorporating loss to follow-up as an additional category of response and the nature of the correlated responses can provide a comprehensive view of a trial with unbalanced loss to follow-up. Under the Markov assumption, transitional models estimate the probability of changing from one outcome to another outcome between follow-up visits. Patterns of the response variable can be described by the estimated transition probabilities. The effects of intervention and covariates on the outcome of interest can also be estimated using a conditional likelihood function or a multinomial logit regression. Data from a randomized barrier method study designed to compare the proportion of participants using barrier methods consistently in two counselling groups are used to illustrate the proposed model.

Adolescent↗
PubMed2006

Model comparison of generalized linear mixed models.

Generalized linear mixed models (GLMMs) have been widely appreciated in biological and medical research. Maximum likelihood estimation has received a great deal of attention. Comparatively, not much has been done on model comparison or hypotheses testing. In this article, we propose a path sampling procedure to compute the observed-data log-likelihood function, so that the Bayesian information criterion (BIC) can be applied to model comparison or hypothesis testing. Advantages of the proposed path sampling procedure are discussed. Two medical data sets are analysed for providing illustrative examples of the proposed methodology.

Air Pollution↗
PubMed1989

Misclassification in more than one factor in a case-control study: a combination of Mantel-Haenszel and maximum likelihood approaches.

Misclassification can arise in the case-control setting in both the risk factor of interest, and in a potential confounder. If true status is not ascertainable, but an independent replicated sample is available, adjusted maximum likelihood estimates of the individual binomial proportions can be obtained, and hence a relative risk estimate of the Mantel-Haenszel type constructed. An interval estimate on the latter can be calculated using the asymptotic properties of the likelihood function. The method is illustrated by application to a case-control study of breast cancer risk and such lifestyle attributes as diet, smoking and alcohol consumption, in which misclassification was anticipated and consequently repeatability data were collected.

Breast Neoplasms↗
PubMed1998

The application of model-based complexity inference method to molecular evolution analysis.

In this study, a new method based on the concept of complexity in inductive inference is proposed for reconstructing molecular phylogenetic tree. This method describes the complexity of molecular phylogenetic tree by three terms, which are related to tree topology, the branch lengths and fitness between the model and data measured by likelihood function. The computer simulation is used to investigate the efficiency of this method. The results suggest that this method is superior to the traditional methods because it avoids excess-complexity in the tree model estimation available from DNA sequence.

Base Sequence↗
PubMed2000

A two-stage estimator of the dependence parameter for the Clayton-Oakes model.

This paper describes the properties of a two-stage estimator of the dependence parameter in the Clayton-Oakes multivariate failure time model. The parameter is estimated from a likelihood function in which the marginal hazard functions are replaced by estimates. The method extends the approach of Shih and Louis (1995) and Genest, Ghoudi and Rivest (1995) to allow the marginal hazard for failure times to follow a stratified Cox (1972) model. The method is computationally simple and under mild regularity conditions produces a consistent, asymptotically normal estimator.

Humans↗
PubMed2005

Phylogenetic MCMC algorithms are misleading on mixtures of trees.

Markov chain Monte Carlo (MCMC) algorithms play a critical role in the Bayesian approach to phylogenetic inference. We present a theoretical analysis of the rate of convergence of many of the widely used Markov chains. For N characters generated from a uniform mixture of two trees, we prove that the Markov chains take an exponentially long (in N) number of iterations to converge to the posterior distribution. Nevertheless, the likelihood plots for sample runs of the Markov chains deceivingly suggest that the chains converge rapidly to a unique tree. Our results rely on novel mathematical understanding of the log-likelihood function on the space of phylogenetic trees. The practical implications of our work are that Bayesian MCMC methods can be misleading when the data are generated from a mixture of trees. Thus, in cases of data containing potentially conflicting phylogenetic signals, phylogenetic reconstruction should be performed separately on each signal.

Algorithms↗
PubMed2005

Improving the efficiency of SPR moves in phylogenetic tree search methods based on maximum likelihood.

MOTIVATION: Maximum likelihood (ML) methods have become very popular for constructing phylogenetic trees from sequence data. However, despite noticeable recent progress, with large and difficult datasets (e.g. multiple genes with conflicting signals) current ML programs still require huge computing time and can become trapped in bad local optima of the likelihood function. When this occurs, the resulting trees may still show some of the defects (e.g. long branch attraction) of starting trees obtained using fast distance or parsimony programs. METHODS: Subtree pruning and regrafting (SPR) topological rearrangements are usually sufficient to intensively search the tree space. Here, we propose two new methods to make SPR moves more efficient. The first method uses a fast distance-based approach to detect the least promising candidate SPR moves, which are then simply discarded. The second method locally estimates the change in likelihood for any remaining potential SPRs, as opposed to globally evaluating the entire tree for each possible move. These two methods are implemented in a new algorithm with a sophisticated filtering strategy, which efficiently selects potential SPRs and concentrates most of the likelihood computation on the promising moves. RESULTS: Experiments with real datasets comprising 35-250 taxa show that, while indeed greatly reducing the amount of computation, our approach provides likelihood values at least as good as those of the best-known ML methods so far and is very robust to poor starting trees. Furthermore, combining our new SPR algorithm with local moves such as PHYML's nearest neighbor interchanges, the time needed to find good solutions can sometimes be reduced even more.

Algorithms↗
PubMed2004

Reconstructing phylogeny by quadratically approximated maximum likelihood.

Maximum likelihood (ML) for phylogenetic inference from sequence data remains a method of choice, but has computational limitations. In particular, it cannot be applied for a global search through all potential trees when the number of taxa is large, and hence a heuristic restriction in the search space is required. In this paper, we derive a quadratic approximation, QAML, to the likelihood function whose maximum is easily determined for a given tree. The derivation depends on Hadamard conjugation, and hence is limited to the simple symmetric models of Kimura and of Jukes and Cantor. Preliminary testing has demonstrated the accuracy of QAML is close to that of ML.

Algorithms↗
PubMed2003

Semiparametric estimation of tag loss and reporting rates for tag-recovery experiments using exact time-at-liberty data.

We present a semiparametric likelihood approach to estimating reporting rates and tag-loss rates from the tags returned from capture-recapture studies. Such studies are commonly used to estimate critical population parameters. Tag loss rates are estimated using double-tagged animals, while reporting rates are estimated using information from high-reward tags. A likelihood function is constructed based on the conditional distribution of the type of tag returned (low or high reward, single or double tag), given that a tag has been returned. This involves many sparse 5 x 1 tag-return contingency tables, and choosing a good functional form for the tag loss rate is difficult with such data. We model tag-loss rates using monotone-smoothing splines, and use these nonparametric estimates to diagnose the parametric form of the tag-loss rate. The nonparametric methods can also be used directly to model tag-loss rates.

Animals↗
PubMed2004

Generalized linear mixed models with varying coefficients for longitudinal data.

The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.

Biometry↗
PubMed2001

Analysis of aerosol distribution inside the object "shelter" at the Chernobyl nuclear reactor site.

Results of the aerosol sampling inside the Object Shelter at the Chornobyl nuclear reactor site are considered in the work. The results show a consistent and significant contribution of submicron fraction to the total aerosol activity. Different methods of interpretation of impactor data series are compared in order to indicate and detect in the most effective way the submicron fraction as a separate component of the distribution. The methods used are as follows-method of probabilistic-logarithmic scale, method of likelihood function, non-linear approximation by sum of several log-normal distributions, and restoration of the initial distribution using passage functions of impactor cascades. Practically all the collected data on aerosol distribution inside the Shelter show a distinct submicron component. The contribution of the submicron component into the total aerosol activity is about 35%. Influence of the actual aerosol distribution on the dose coefficients is analyzed.

Aerosols↗
PubMed2004

A maximum likelihood approach for image registration using control point and intensity.

Registration of multidate or multisensor images is an essential process in many image processing applications including remote sensing, medical image analysis, and computer vision. Control point (CP) and intensity are the two basic features used separately for image registration in the literature. In this paper, an exact maximum likelihood (EML) registration method, which combines both CP and intensity, is proposed for image alignment. The EML registration method maximizes the likelihood function based CP and intensity to estimate the registration parameters, including affine transformation and CP coordinates. The explicit formulas of the Cramer-Rao bound (CRB) are also derived for the proposed EML and conventional image registration algorithms. The performances of these image registration techniques are evaluated with the CRBs.

Algorithms↗
PubMed2006

Optimal representation of sensory information by neural populations.

Sensory information is encoded by populations of neurons. The responses of individual neurons are inherently noisy, so the brain must interpret this information as reliably as possible. In most situations, the optimal strategy for decoding the population signal is to compute the likelihoods of the stimuli that are consistent with an observed neural response. But it has not been clear how the brain can directly compute likelihoods. Here we present a simple and biologically plausible model that can realize the likelihood function by computing a weighted sum of sensory neuron responses. The model provides the basis for an optimal decoding of sensory information. It explains a variety of psychophysical observations on detection, discrimination and identification, and it also directly predicts the relative contributions that different sensory neurons make to perceptual judgments.

Animals↗
PubMed2005

Bayesian cure rate frailty models with application to a root canal therapy study.

Due to natural or artificial clustering, multivariate survival data often arise in biomedical studies, for example, a dental study involving multiple teeth from each subject. A certain proportion of subjects in the population who are not expected to experience the event of interest are considered to be "cured" or insusceptible. To model correlated or clustered failure time data incorporating a surviving fraction, we propose two forms of cure rate frailty models. One model naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model. We formulate the likelihood functions based on piecewise constant hazards and derive the full conditional distributions for Gibbs sampling in the Bayesian paradigm. As opposed to the Cox frailty model, the proposed methods demonstrate great potential in modeling multivariate survival data with a cure fraction. We illustrate the cure rate frailty models with a root canal therapy data set.

Bayes Theorem↗
PubMed1993

Small-sample confidence sets for the MTD in a phase I clinical trial.

Properties of procedures for interval estimation of the maximum tolerable dose (MTD) in a Phase I clinical trial are examined, using a two-stage stochastic sampling scheme (Storer, 1989) as a paradigm for development. Although the likelihood function for the data arising from such a scheme is identical to one arising under a conditional binomial sampling assumption, intervals based on the exact distribution of the usual large-sample statistics under this assumption do not offer improvement over unadjusted intervals. However, consideration of the distribution of these statistics based on the true stochastic sampling scheme can lead to the construction of intervals with correct coverage probabilities that do not depend on the true values of the model parameters. Membership in the confidence set can be evaluated by Monte Carlo simulation at a restricted maximum likelihood estimate of the nuisance slope parameter, despite upward bias in its estimation from the up-and-down sampling scheme. The lack of information in the small-sample setting is reflected in a large proportion of confidence intervals that include infinite values for the MTD, especially when the dose-response curve is shallow. Intervals based on a likelihood ratio criterion perform best in this regard.

Algorithms↗
PubMed2006

Local solutions in the estimation of growth mixture models.

Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however, local solutions may still be problematic. Results from an empirical case study and a small Monte Carlo simulation show that failure to thoroughly consider the possible presence of local optima in the estimation of a growth mixture model can sometimes have serious consequences, possibly leading to adoption of an inferior solution that differs in substantively important ways from the actual maximum likelihood solution. Often, the defaults of current software need to be overridden to thoroughly evaluate the parameter space and obtain confidence that the maximum likelihood solution has in fact been obtained.

Adolescent↗
PubMed2000

The Bayesian evidence scheme for regularizing probability-density estimating neural networks.

Training probability-density estimating neural networks with the expectation-maximization (EM) algorithm aims to maximize the likelihood of the training set and therefore leads to overfitting for sparse data. In this article, a regularization method for mixture models with generalized linear kernel centers is proposed, which adopts the Bayesian evidence approach and optimizes the hyperparameters of the prior by type II maximum likelihood. This includes a marginalization over the parameters, which is done by Laplace approximation and requires the derivation of the Hessian of the log-likelihood function. The incorporation of this approach into the standard training scheme leads to a modified form of the EM algorithm, which includes a regularization term and adapts the hyperparameters on-line after each EM cycle. The article presents applications of this scheme to classification problems, the prediction of stochastic time series, and latent space models.

Acquired Immunodeficiency Syndrome↗
PubMed1997

Testing for treatment differences with dropouts present in clinical trials--a composite approach.

A major problem in the analysis of clinical trials is missing data from patients who drop out of the study before the predetermined schedule. In this paper we consider the situation where the outcome measure is a continuous variable and the final outcome at the end of the study is the main interest. We argue that the hypothetical complete-data marginal mean averaged over the dropout patterns is not as relevant clinically as the conditional mean of the completers together with the probability of completion or dropping out of the trial. We first take the pattern-mixture modelling approach to factoring the likelihood function, then direct the analysis to the multiple testings of a composite of hypotheses that involves the probability of dropouts and the conditional mean of the completers. We review three types of closed step-down multiple-testing procedures for this application. Data from several clinical trials are used to illustrate the proposed approach.

Bias↗