PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Likelihood Functions”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19Linked to original sources
PubMed1977

Estimation of relative risk from matched pairs in epidemiologic research.

The matched pairs design is often used in epidemiologic research, both in prospective and retrospective studies. The Kraus estimator of relative risk (1958) has been derived in a number of ways. The development presented here employs an unconditional likelihood function. The estimator is shown to be valid only when disease incidence is low and relative risk is constant over the levels of the covariate. Asymptotic variances are derived.

Epidemiologic Methods↗
PubMed1997

[An improved ISRA algorithm for ECT].

Image space reconstruction algorithm (ISRA) is a new kind of method for ECT reconstruction. Unlike the ML-EM algorithm which maximizes likelihood function of Possion distribution, ISRA searches for the minimum non-negative mean square solution. In this paper, an improved ISRA (IISRA) algorithm is proposed. A comparison between the algorithms (ISRA and IISRA) demonstrates that the result of IISRA is closer to the test image than that of ISRA. In addition, the IIRSA inherits some properties of ISRA such as convergence.

Algorithms↗
PubMed2005

Likelihood-enhanced fast translation functions.

This paper is a companion to a recent paper on fast rotation functions [Storoni et al. (2004), Acta Cryst. D60, 432-438], which showed how a Taylor-series expansion of the maximum-likelihood rotation function leads to improved likelihood-enhanced fast rotation functions. In a similar manner, it is shown here how linear and quadratic Taylor-series expansions and least-squares approximations of the maximum-likelihood translation function lead to likelihood-enhanced translation functions, which can be calculated by FFT and which are more sensitive to the correct translation than the traditional correlation-coefficient fast translation function. These likelihood-enhanced translation targets for molecular-replacement searches have been implemented in the program Phaser using the Computational Crystallography Toolbox (cctbx).

Bacterial Proteins↗
PubMed2005

Reliability estimation of grouped functional imaging data using penalized maximum likelihood.

We analyzed grouped fMRI data and developed a reliability analysis for such data using the method of penalized maximum likelihood (ML). Specifically, this technique was applied to a somatosensory paradigm that used a mechanical probe to provide noxious stimuli to the foot, and a paradigm consisting of four levels of graded peripheral neuromuscular electrical stimulation (NMES). In each case, reliability maps of activation were generated. Receiver operating characteristic (ROC) curves were constructed in the case of the graded NMES paradigm for each level of stimulation, which revealed an increase in the specificity of activation with increasing stimulation levels. In addition, penalized ML was used to determine whether the grouped reliability maps obtained from one stimulus level were significantly different from those obtained at other levels. The results show a significant difference (P < 0.01) in the reliability of activation from one stimulation level to the next. These results are in agreement with those obtained using generalized linear modeling (GLM). While the reliability maps generated are not directly comparable, they are qualitatively similar to those obtained by controlling the expected false discovery rate (FDR). The proposed methodology can be used to objectively compare activation maps between groups, as well as to perform reliability assessments. Furthermore, this method potentially can be used to assess the longitudinal effect of treatment therapies within a group.

Analysis of Variance↗
PubMed1994

Combining two-point genetic linkage analyses using mapping functions.

A likelihood ratio statistic is proposed for combining two-point genetic linkage analyses when the two-point analyses are between a trait and a well-defined map of markers. It is assumed that the two-point analyses are independent, as in the case of choosing only the most informative marker per family. The asymptotic distribution of the likelihood ratio statistic is derived under the null hypothesis of no linkage of the trait with a map of 2 markers, with intermarker genetic distance delta. This distribution is shown to be a chi-square mixture distribution with mixing probability depending on delta and the assumed mapping function. We use this asymptotic result to approximate the distribution of the likelihood ratio statistic for the more general case of more than 2 markers. Simulation results indicate that this may be reasonable. Power is evaluated by simulations and results indicate that this approach, which constrains the intermarker distances to their known values, tends to be more powerful than other methods proposed in the literature.

Bias↗
PubMed2005

A robust bulk-solvent correction and anisotropic scaling procedure.

A reliable method for the determination of bulk-solvent model parameters and an overall anisotropic scale factor is of increasing importance as structure determination becomes more automated. Current protocols require the manual inspection of refinement results in order to detect errors in the calculation of these parameters. Here, a robust method for determining bulk-solvent and anisotropic scaling parameters in macromolecular refinement is described. The implementation of a maximum-likelihood target function for determining the same parameters is also discussed. The formulas and corresponding derivatives of the likelihood function with respect to the solvent parameters and the components of anisotropic scale matrix are presented. These algorithms are implemented in the CCTBX bulk-solvent correction and scaling module.

Algorithms↗
PubMed2005

Accelerated penalized weighted least-squares and maximum likelihood algorithms for reconstructing transmission images from PET transmission data.

We present penalized weighted least-squares (PWLS) and penalized maximum-likelihood (PML) methods for reconstructing transmission images from positron emission tomography transmission data. First, we view the problem of minimizing the weighted least-squares (WLS) and maximum likelihood objective functions as a sequence of nonnegative least-squares minimization problems. This viewpoint follows from using certain quadratic functions as surrogate functions for the WLS and maximum likelihood objective functions. Second, we construct surrogate functions for a class of penalty functions that yield closed form expressions for the iterates of the PWLS and PML algorithms. Due to the slow convergence of the PWLS and PML algorithms, accelerated versions of them are developed that are theoretically guaranteed to monotonically decrease their respective objective functions. In experiments using real phantom data, the PML images produced the most accurate attenuation correction factors. On the other hand, the PWLS images produced images with the highest levels of contrast for low-count data.

Algorithms↗
PubMed2002

Hidden Markov models for the onset and progression of bronchiolitis obliterans syndrome in lung transplant recipients.

Chronic rejection in lung transplant recipients is monitored by repeated measurement of forced expiratory volume in one second (FEV1). This marker is measured at irregular intervals and is also affected by covariates and short-term fluctuation. This paper describes the use of hidden Markov models for the underlying staged functional decline. Maximum likelihood methods are used to simultaneously estimate disease progression rates and the effects of mismeasurement and covariates.

Bronchiolitis Obliterans↗
PubMed1999

A survey of output intensity and potential for depth of cure among light-curing units in clinical use.

OBJECTIVES: The light intensity of curing lights used in private dental offices was measured using commercial curing and heat radiometers and related to uniformity of cure depth of standardized composite specimens. METHODS: The intensity of 130 curing light from 107 dental offices was measured with curing and heat radiometers. Due to analogue readings, results were recorded in steps of 25 mW cm-2 and assigned a category number. A total of 50 lights were randomly selected to polymerize standardized 3 mm thick composite cylinders. The composite was irradiated for 50 s according to the manufacturer's instructions. The Knoop hardness value was measured at the top and bottom surfaces and the uniformity of cure depth was calculated from the ratio of these two values. RESULTS: Light intensity measured by the curing and heat radiometers was in the range of 25-825 and 0-325 mW cm-2, respectively. Functions of maximum likelihood estimation of the top and bottom surface hardness were 57 N/N + 1.3 and 80 N/N + 17.7, respectively (N = light intensity category number). The relationship between the logarithmic transformation of the hardness ratio and light intensity was linear (R2 = 0.84 p < 0.001). CONCLUSION: According to the manufacturer, a curing light is considered as unsuitable for use with a reading of < 200 mW cm-2 by the curing radiometer and > 50 mW cm-2 by the heat radiometer. Applying these criteria to the present study, 46% of the lights (without repetitions) required repair or replacement. The strong correlation found between the hardness ratio and light intensity verifies the usefulness of the curing radiometer in predicting the polymerization ability of the light activation units.

Composite Resins↗
PubMedDate not supplied

Joint classification and pairing of human chromosomes.

We reexamine the problems of computer-aided classification and pairing of human chromosomes, and propose to jointly optimize the solutions of these two related problems. The combined problem is formulated into one of optimal three-dimensional assignment with an objective function of maximum likelihood. This formulation poses two technical challenges: 1) estimation of the posterior probability that two chromosomes form a pair and the pair belongs to a class and 2) good heuristic algorithms to solve the three-dimensional assignment problem which is NP-hard. We present various techniques to solve these problems. We also generalize our algorithms to cases where the cell data are incomplete as often encountered in practice.

Algorithms↗
PubMed2006

A mixed-effects regression model for longitudinal multivariate ordinal data.

A mixed-effects item response theory model that allows for three-level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies. This model allows for the estimation of different item factor loadings (item discrimination parameters) for the multiple outcomes. The covariates in the model do not have to follow the proportional odds assumption and can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is proposed utilizing multidimensional Gauss-Hermite quadrature for integration of the random effects. An iterative Fisher scoring solution, which provides standard errors for all model parameters, is used. An analysis of a longitudinal substance use data set, where four items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk or high) are repeatedly measured over time, is used to illustrate application of the proposed model.

Data Interpretation, Statistical↗
PubMed2003

Functional mapping for quantitative trait loci governing growth rates: a parametric model.

Are there-specific quantitative trait loci (QTL) governing growth rates in biology? This is emerging as an exciting but challenging question for contemporary developmental biology, evolutionary biology, and plant and animal breeding. In this article, we present a new statistical model for mapping QTL underlying age-specific growth rates. This model is based on the mechanistic relationship between growth rates and ages established by a variety of mathematical functions. A maximum likelihood approach, implemented with the EM algorithm, is developed to provide the estimates of QTL position, growth parameters characterized by QTL effects, and residual variances and covariances. Based on our model, a number of biologically important hypotheses can be formulated concerning the genetic basis of growth. We use forest trees as an example to demonstrate the power of our model, in which a QTL for stem growth diameter growth rates is successfully mapped to a linkage group constructed from polymorphic markers. The implications of the new model are discussed.

Age Factors↗
PubMed1998

A proportional hazards model taking account of long-term survivors.

A proportional hazards (PH) model is modified to take account of long-term survivors by assuming the cumulative hazard to be bounded but otherwise unspecified to yield an improper survival function. A marginal likelihood is derived under the restriction for type I censoring patterns. For a PH model with cure, the marginal and the partial likelihood are not the same. In the absence of covariate information, the estimate of the cure rate based on the marginal likelihood reduces to the value of the Kaplan-Meier estimate at the end of the study. An example of low asymptotic efficiency of the partial likelihood as compared to the marginal, profile, and parametric likelihoods is given. An algorithm is suggested to fit the full PH model with cure.

Algorithms↗
PubMed2004

Likelihood-enhanced fast rotation functions.

Experiences with the molecular-replacement program Beast have shown that maximum-likelihood rotation targets are more sensitive to the correct orientation than traditional targets. However, this comes at a high computational cost: brute-force rotation searches can take hours or even days of computation time on current desktop computers. Series approximations to the full likelihood target have been developed that can be computed by fast Fourier transforms in minutes. These likelihood-enhanced targets are more sensitive to the correct orientation than the Crowther fast rotation function and they take advantage of information from partial solutions. The likelihood-enhanced rotation targets have been implemented in the program Phaser.

Algorithms↗
PubMed2000

Maximum-likelihood approach to strain imaging using ultrasound

A maximum-likelihood (ML) strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems. Concepts from continuum mechanics, signal analysis, and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images. The model includes three-dimensional (3-D) object motion described by affine transformations, Rayleigh scattering from random media, and 3-D system response functions. The likelihood function for these waveforms is derived to express the Fisher information matrix and variance bounds for displacement and strain estimation. The ML estimator is a generalized cross correlator for pre- and post-compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection. Experiments involving soft tissuelike media show the ML estimator approaches the Cramer-Rao error bound for small scaling deformations: at 5 MHz and 1.2% compression, the predicted lower bound for displacement errors is 4.4 microns and the measured standard deviation is 5.7 microns.

Journal Article↗
PubMed2003

Nomogram for predicting the likelihood of delayed graft function in adult cadaveric renal transplant recipients.

Delayed graft function (DGF) is the need for dialysis in the first week after transplantation. Studied were risk factors for DGF in adult (age >/=16 yr) cadaveric renal transplant recipients by means of a multivariable modeling procedure. Only donor and recipient factors known before transplantation were chosen so that the probabilities of DGF could be calculated before transplantation and appropriate preventative measures taken. Data on 19,706 recipients of cadaveric allografts were obtained from the United States Renal Data System registry (1995 to 1998). Graft losses within the first 24 h after surgery were excluded from the analysis (n = 89). Patients whose DGF information was missing or unknown (n = 2820) and patients missing one or more candidate predictors (n = 2951) were also excluded. By means of a multivariable logistic regression analysis, factors contributing to DGF in the remaining 13,846 patients were identified. After validating the logistic regression model, a nomogram was developed as a tool for identifying patients at risk for DGF. The incidence of DGF was 23.7%. Sixteen independent donor or recipient risk factors were found to predict DGF. A nomogram quantifying the relative contribution of each risk factor was created. This index can be used to calculate the risk of DGF for an individual by adding the points associated with each risk factor. The nomogram provides a useful tool for developing a pretransplantation index of the likelihood of DGF occurrence. With this index in hand, better informed treatment and allocation decisions can be made.

Adolescent↗
PubMed1990

A computer program for estimating imprecision characteristics of immunoassays.

A reliable numerical algorithm is described, together with a computer program written in FORTRAN IV and FORTRAN 77, for estimating a three-parameter variance function by approximate conditional likelihood. The function is sufficiently flexible to provide for a several thousand-fold relative change in variance and appears to be a good model for the severely heteroscedastic results obtained from immunoassays. The computer program is primarily intended for summarizing imprecision characteristics of immunoassays in the form of imprecision profiles, but the estimated variance functions have additional application whenever further parametric analysis of immunoassay results is undertaken (e.g., as a weighting function when immunoassay results are used in a least-squares regression analysis). The flexibility of the function implies useful application in any area where heteroscedasticity is particularly severe.

Algorithms↗