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PubMedDate not supplied

Likelihood of pregnancy in individuals with idiopathic/cryptogenic epilepsy: social and biologic influences.

We interviewed 1,558 adults with idiopathic/cryptogenic epilepsy ascertained from voluntary organizations and 316 of their siblings without epilepsy to determine their personal history of marriage and pregnancy. We examined the effects of seizure type, age at onset, and family history of epilepsy on the sex-specific likelihood of pregnancy in individuals with idiopathic/cryptogenic epilepsy as compared with their same-sex siblings. Overall, men with idiopathic/cryptogenic epilepsy were only 36% as likely as male unaffected siblings ever to have fathered a pregnancy. In men, the reduced likelihood of fathering a pregnancy was associated with partial-onset seizures, early age at onset (< 20 years), and a negative family history of epilepsy, and the effects of these epilepsy characteristics appeared to be mediated through reduced marriage rates. Among men with epilepsy who had ever been married, reproductive disadvantage was confined to those with early-onset (< 10 years) partial epilepsy. Overall, women with idiopathic/cryptogenic epilepsy were only 37% as likely ever to have had a pregnancy as female unaffected siblings; this effect was not strongly influenced by seizure type, age at onset, or family history of epilepsy. In women who had ever been married, unlike in men, reduced likelihood of pregnancy persisted, regardless of seizure type, age at onset, or family history of epilepsy.

Adult↗

PubMed2006

A likelihood ratio approach to family-based association studies with covariates.

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

Epidemiologic Methods↗

PubMed2006

Joint modeling of survival and longitudinal data: likelihood approach revisited.

The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguing issues are examined here, including the robustness of the MLEs against departure from the normal random effects assumption, and difficulties with the profile likelihood approach to provide reliable estimates for the standard error of the MLEs. We provide insights into the robustness property and suggest to overcome the difficulty of reliable estimates for the standard errors by using bootstrap procedures. Numerical studies and data analysis illustrate our points.

Algorithms↗

PubMed1997

Maximum likelihood estimation in covariance structure analysis with truncated data.

We study an estimation procedure for maximum likelihood estimation in covariance structure analysis with truncated data, and obtain the statistical properties of the estimator as well as a test of the model structure. Truncated data with and without knowledge about the number of unmeasured observations are both considered. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which requires only first derivatives, is proposed to obtain the maximum likelihood estimates. We illustrate the statistics and parameter estimates by a fictitious example. The maximum likelihood method is compared to an alternative two-stage method.

Algorithms↗

PubMed2004

Ancestral maximum likelihood of evolutionary trees is hard.

Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task--in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years, no such hardness result has been obtained so far for ML. In this work we make a first step in this direction by proving that ancestral maximum likelihood (AML) is NP-complete. The input to this problem is a set of aligned sequences of equal length and the goal is to find a tree and an assignment of ancestral sequences for all of that tree's internal vertices such that the likelihood of generating both the ancestral and contemporary sequences is maximized. Our NP-hardness proof follows that for MP given in (Day, Johnson and Sankoff, 1986) in that we use the same reduction from Vertex Cover; however, the proof of correctness for this reduction relative to AML is different and substantially more involved.

Algorithms↗

PubMed1992

Fast computation of genetic likelihoods on human pedigree data.

Gene mapping and genetic epidemiology require large-scale computation of likelihoods based on human pedigree data. Although computation of such likelihoods has become increasingly sophisticated, fast calculations are still impeded by complex pedigree structures, by models with many underlying loci and by missing observations on key family members. The current paper 'introduces' a new method of array factorization that substantially accelerates linkage calculations with large numbers of markers. This method is not limited to nuclear families or to families with complete phenotyping. Vectorization and parallelization are two general-purpose hardware techniques for accelerating computations. These techniques can assist in the rapid calculation of genetic likelihoods. We describe our experience using both of these methods with the existing program MENDEL. A vectorized version of MENDEL was run on an IBM 3090 supercomputer. A parallelized version of MENDEL was run on parallel machines of different architectures and on a network of workstations. Applying these revised versions of MENDEL to two challenging linkage problems yields substantial improvements in computational speed.

Algorithms↗

PubMedDate not supplied

Likelihood-based models for genetic linkage analysis using affected sib pairs.

Risch [Am J Hum Genet 1990; 46:229-253] recently developed a likelihood method for testing genetic linkage using affected sib pairs. This paper proposes a reparameterization of the Risch likelihood in terms of genetic variance components divided by the affected-sib-pair ascertainment probability. The new parameters allow for ease of interpretation, particularly for multilocus models. A single-degree-of-freedom test of the total disease genetic effect at a marker locus can be constructed that has power comparable to the likelihood ratio 'triangle' test. Extension of the models to other types of relative pairs is also discussed. The models may be used in genome scanning and in studying single or multilocus models of inheritance.

Genetic Linkage↗

PubMed2004

Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model.

We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.

Algorithms↗

PubMed2005

Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity.

Analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals. Usually this is done for pairs of neurons at a time using correlation-based techniques. Chornoboy, Schramm, and Karr (1988) proposed maximum likelihood methods for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons. One of these methods is an iterative, continuous-time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions. We devised a discrete-time version of this algorithm that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion. In an analysis of simulated neural spike trains from ensembles of interacting neurons, the algorithm recovered the correct connectivity matrices and interaction parameters. In the analysis of spike trains from an ensemble of rat hippocampal place cells, the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons' spatial receptive fields. These results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity.

Action Potentials↗

PubMed2003

Comparison of two weighted integration models for the cueing task: linear and likelihood.

In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR's. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.

Adult↗

PubMed1996

Maximum likelihood estimates for the lifetime of bonded dental prostheses.

Clinical studies measuring the lifetime of dental prostheses produce censored data when not all specimens have failed during the course of the study. Such clinical data can be analyzed by the Weibull probability distribution function. Algorithms are presented that provide the maximum likelihood estimates of the distribution's parameters. These parameters are the characteristic lifetime (time to failure for 63% of the specimens of the total sample) and the Weibull or shape parameter. Two iterative methods for solving the maximum likelihood equations are given. These mathematical methods have been applied to the results from a retrospective clinical investigation into the lifetime assessment of resin-bonded prostheses. This study evaluated 164 resin-bonded prostheses (for 146 patients) placed between January, 1980, and May, 1985. To date (April, 1995), 47 prostheses (29%) have failed with a median time in service of 74 months (6.2 yr). For the surviving prostheses, the median time in service is 123 months (10.3 yr) and still increasing. The maximum likelihood estimate of the characteristic lifetime for these restorations is 255 months (21.3 yr). Differences in the characteristic lifetime were observed between prostheses placed anteriorly, 338 months (28 yr), and posteriorly, 207 months (17 yr). Since there are no rigorous confidence intervals for deeply censored samples, only provisional confidence bounds could be determined, which substantiated the observed differences. The Weibull modulus value of 1.5 indicates that the probability of failure for resin-bonded prostheses begins to decrease after 10 years in service.

Algorithms↗

PubMedDate not supplied

Inferences for likelihood ratios in the absence of a "gold standard".

Likelihood ratios are extensively used to evaluate the performances of diagnostic tests and to update prior odds of disease to posttest odds. Since few tests are truly 100% accurate, including many used as "gold standards," it is important to be able to estimate likelihood ratios in cases where no such standard is available. In this paper, methods to calculate point and interval estimates for likelihood ratios are described. The results numerically coincide with those reviewed by Centor when a "gold standard" is assumed available, but typically provide wider interval estimates when such a standard is not available, reflecting the increased uncertainty inherent in such situations. Unlike previous techniques, the methods do not require normal approximations or logarithmic transformations, and hence provide accurate estimates even when parameter distributions are highly skewed. The methods are illustrated using the results of two different diagnostic tests for the presence of an intestinal parasitic infection.

Algorithms↗

PubMed2005

Calculation of multipoint likelihoods using flanking marker data: a simulation study.

The calculation of multipoint likelihoods is computationally challenging, with the exact calculation of multipoint probabilities only possible on small pedigrees with many markers or large pedigrees with few markers. This paper explores the utility of calculating multipoint likelihoods using data on markers flanking a hypothesized position of the trait locus. The calculation of such likelihoods is often feasible, even on large pedigrees with missing data and complex structures. Performance characteristics of the flanking marker procedure are assessed through the calculation of multipoint heterogeneity LOD scores on data simulated for Genetic Analysis Workshop 14 (GAW14). Analysis is restricted to data on the Aipotu population on chromosomes 1, 3, and 4, where chromosomes 1 and 3 are known to contain disease loci. The flanking marker procedure performs well, even when missing data and genotyping errors are introduced.

Chromosome Mapping↗

PubMed2006

Spatio-temporal point processes, partial likelihood, foot and mouth disease.

Spatio-temporal point process data arise in many fields of application. An intuitively natural way to specify a model for a spatio-temporal point process is through its conditional intensity at location x and time t, given the history of the process up to time t. Often, this results in an analytically intractable likelihood. Likelihood-based inference then relies on Monte Carlo methods which are computationally intensive and require careful tuning to each application. A partial likelihood alternative is proposed, which is computationally straightforward and can be applied routinely. The method is applied to data from the 2001 foot and mouth epidemic in the UK, using a previously published model for the spatio-temporal spread of the disease.

Animals↗

PubMed2005

Direct likelihood analysis versus simple forms of imputation for missing data in randomized clinical trials.

BACKGROUND: In many clinical trials, data are collected longitudinally over time. In such studies, missingness, in particular dropout, is an often encountered phenomenon. METHODS: We discuss commonly used but often problematic methods such as complete case analysis and last observation carried forward and contrast them with broadly valid and easy to implement direct-likelihood methods. We comment on alternatives such as multiple imputation and the expectation-maximization algorithm. RESULTS: We apply these methods in particular to data from a study with continuous outcomes. The outcomes are modelled using a general linear mixed-effects model. The bias with CC and LOCF is established in the case study and the advantages of the direct-likelihood approach shown. CONCLUSIONS: We have established formal but easy to understand arguments for a shift towards a direct-likelihood paradigm when analysing incomplete data from longitudinal clinical trials, necessitating neither imputation nor deletion.

Data Collection↗

PubMed2000

A computer program for pharmacokinetics based on maximum likelihood estimation using the gamma distribution with a probability density function: comparison with the normal distribution.

A computer program is described for maximum likelihood estimation within the gamma or normal distribution which can be used to estimate pharmacokinetic parameters. Pharmacokinetic analysis using this proposed program was investigated by the Monte Carlo method. The assumed pharmacokinetic models were a one-compartment intravenous model and an oral model. The simulated drug concentrations were generated using a 10% S.D. based on the gamma or normal distribution. The gamma or normal distribution was adopted as the probability density function (p.d.f.) to estimate model parameters. The Powell method was used to maximize the logarithmic likelihood. There were no differences in the estimated parameters in terms of statistical and frequency distributions between the gamma and normal distributions using the generated data and the p.d.f. distributions. However, the number of failures to calculate the parameters using the p.d.f. with the normal distribution was more than five times that using the gamma distribution. This result suggests that it may be necessary to evaluate the validity of results computed using the maximum likelihood estimation based on a normal distribution as a data error distribution and p.d.f.

Algorithms↗

PubMed1997

List-mode likelihood.

As photon-counting imaging systems become more complex, there is a trend toward measuring more attributes of each individual event. In various imaging systems the attributes can include several position variables, time variables, and energies. If more than about four attributes are measured for each event, it is not practical to record the data in an image matrix. Instead it is more efficient to use a simple list where every attribute is stored for every event. It is the purpose of this paper to discuss the concept of likelihood for such list-mode data. We present expressions for list-mode likelihood with an arbitrary number of attributes per photon and for both preset counts and preset time. Maximization of this likelihood can lead to a practical reconstruction algorithm with list-mode data, but that aspect is covered in a separate paper [IEEE Trans. Med. Imaging (to be published)]. An expression for lesion detectability for list-mode data is also derived and compared with the corresponding expression for conventional binned data.

Image Processing, Computer-Assisted↗

PubMed2001

Fast maximum-likelihood image-restoration algorithms for three-dimensional fluorescence microscopy.

We have evaluated three constrained, iterative restoration algorithms to find a fast, reliable algorithm for maximum-likelihood estimation of fluorescence microscopic images. Two algorithms used a Gaussian approximation to Poisson statistics, with variances computed assuming Poisson noise for the images. The third method used Csiszar's information-divergence (I-divergence) discrepancy measure. Each method included a nonnegativity constraint and a penalty term for regularization; optimization was performed with a conjugate gradient method. Performance of the methods was analyzed with simulated as well as biological images and the results compared with those obtained with the expectation-maximization-maximum-likelihood (EM-ML) algorithm. The I-divergence-based algorithm converged fastest and produced images similar to those restored by EM-ML as measured by several metrics. For a noiseless simulated specimen, the number of iterations required for the EM-ML method to reach a given log-likelihood value was approximately the square of the number required for the I-divergence-based method to reach the same value.

Algorithms↗