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A Bayesian method for synthesizing evidence. The Confidence Profile Method.

This article describes a collection of meta-analysis techniques based on Bayesian statistics for interpreting, adjusting, and combining evidence to estimate parameters and outcomes important to the assessment of health technologies. The result of an analysis by the Confidence Profile Method is a joint posterior probability distribution for the parameters of interest, from which marginal distributions for any particular parameter can be calculated. The method can be used to analyze problems involving a variety of types of outcomes, a variety of measures of effect, and a variety of experimental designs. This article presents the elements necessary for analysis, including prior distributions, likelihood functions, and specific models for experimental designs that include adjustment for biases.

Bayes Theorem

AIDS in Ireland: the reporting delay distribution and the implementation of integral equation models.

This paper deals with two basic aspects concerning the modelling of AIDS incidence in the context of Irish data. We describe initially the adjustment of the number of AIDS cases (Xij) to allow for reporting delays, where a simple form of the likelihood function for the Xij is supported by GLIM. Subsequently, we consider the accessibility of numerical solution (through a NAG routine) of the integral equation models generated by the back-projection method for the adjusted AIDS cases. Results for the Irish data are summarized for various choices of the incidence distribution.

Acquired Immunodeficiency Syndrome

Sparse Logistic Regression on Genomic Data for Prediction of Tumour Pathological Subtype.

The correct prediction of tumour subtype is critical for the treatment of cancer patients to maximise the chance of survival. The patients' genomic information, such as copy number alterations (CNA) profile, has increasingly become an important factor in the prediction to supplement the traditional pathological subtyping. The incorporation of the CNA information in a prediction model, such as logistic regression, faces two major statistical challenges: first, how to estimate the model parameters in the thousands and, second, how to deal with the correlation of CNA between genomic regions. To address them, we propose a sparse logistic regression model with random effects where some of its parameters are estimated to zero while the other parameters are non-zero. In effect, a variable selection is embedded in the modelling. To deal with the correlation of CNA across genomic regions, we extend further the model to incorporate an additional penalty in the corresponding likelihood function in the logistic regression. The results show that we can identify selected genomic regions that are informative to distinguish different tumour subtypes, while giving a good prediction ability. We illustrate the methodology using CNA dataset from a lung cancer cohort.

Journal Article

Ancestral inference. I. The problem and the method.

A method for inferring the ancestral genotypes for the founders of a population is developed. This method uses the algorithms for the computation of probabilities on pedigrees of arbitrary complexity, developed by Cannings et al. (1978) and implemented by Thompson (1977b). When characteristics are simply determined by underlying genotypes the inference problem is simplified, and larger and more complex pedigrees may therefore be analysed. The problem of estimating the allele frequencies to be used in computing prior genotype probabilities for those founders on whom a likelihood function is not required is discussed. The same method allows us to compute extinction probabilities for any combination of original founder genes; these probabilities are interesting parameters of pedigree structure, which, since they relate to the actual genes present in a population, help to provide a clearer understanding of observed distributions of autosomal traits.

Gene Frequency

Likelihood estimation of quantitative genetic parameters when selection occurs: models and problems.

Conceptual aspects of estimation of genetic components of variance and covariance under selection are discussed, with special attention to likelihood methods. Certain selection processes are described and alternative likelihoods that can be used for analysis are specified. There is a mathematical relationship between the likelihoods that permits comparing the relative amount of information contained in them. Theoretical arguments and evidence indicate that point inferences made from likelihood functions are not affected by some forms of selection.

Animals

Classification of human muscle stretch receptor afferents: a Bayesian approach.

1. A sample of 124 human muscle afferents originating from the finger extensor muscles were recorded from the radial nerve in the upper arm. A method is described to formalize the classification of units in muscle spindle primary and secondary afferents and Golgi tendon organ afferents on the basis of a few, nonrigorous assumptions. The classification was based on experimental data that largely have been described in a series of previous papers, although some additional data were collected in the present study. 2. The units were subjected to five tests providing identification data: twitch contraction test, ramp-and-hold stretch, small-amplitude sinusoidal stretches superimposed on ramp stretch, stretch sensitization, and isometric contraction/relaxation. From these five tests the following eight response features were extracted: response to maximal isometric twitch contractions, type of stretch sensitization, correlation between discharge rate and contractile force, response to sudden isometric relaxation, presence or absence of an initial burst, deceleration response, prompt silencing at slow muscle shortening, and driving by small-amplitude sinusoidal stretches. 3. A Bayesian decision procedure was adopted to classify the units on the basis of the eight discriminators. As a first step, units were provisionally classified into muscle spindle primary and secondary afferents, and Golgi tendon organ afferents, by intuitively weighting their responses to the identification tests. Prior probabilities were estimated on the basis of the provisional classification. The eight response features were analyzed and tabulated for all afferents, and the likelihood functions of the tests were directly calculated on the basis of these data.(ABSTRACT TRUNCATED AT 250 WORDS)

Electrophysiology

Familial aggregation of lipids and lipoproteins in families ascertained through random and nonrandom probands in the Iowa Lipid Research Clinics family study.

The aggregation of lipids [total cholesterol (CH) and triglyceride (TG)] and lipoproteins [high-density lipoprotein cholesterol (HDL) and low-density lipoprotein cholesterol (LDL)] in families ascertained through random and nonrandom probands in the Iowa Lipid Research Clinics family study was examined. Nonrandom probands were selected because their lipid levels (at a prior screening visit) exceeded a certain pre-specified threshold. The statistical method conditions the likelihood function on the actual event that the proband's value is beyond the threshold. This method allows for estimation of the path model parameters in randomly and nonrandomly ascertained families jointly and separately, thus enabling tests of heterogeneity between the two types of samples. Marked heterogeneity between the random and the hyperlipidemic samples is detected in the multifactorial transmission for TG and HDL, and moderate heterogeneity is detected for CH and LDL, with a pattern of higher genetic heritability estimates in the random than nonrandom samples. The observed pattern of heterogeneity is compatible with a higher prevalence in the random sample of certain dyslipoproteinemias that are associated with nonelevated lipids. For the random samples, genetic heritabilities are higher for CH and HDL (about 60%) than for TG and LDL (about 50%). For the nonrandom samples those estimates are about 45, 40, 35 and 30% for HDL, CH, LDL and TG, respectively. Little to no cultural (familial environmental) heritability is evident for CH and LDL, although 10-20% of the phenotypic variance is due to cultural factors for TG and HDL. These results suggest that the etiologies for lipids and lipoproteins may be quite different in random versus hyperlipidemic samples.

Adult

Temporal coupling among luteinizing hormone, follicle stimulating hormone, beta-endorphin and cortisol pulse episodes in vivo.

We have applied explicit probability equations to assess possible non-random associations among four distinct hormone series consisting of episodic luteinizing hormone, follicle stimulating hormone, beta-endorphin, and/or cortisol pulses observed under physiological conditions in normal men. Closed-form likelihood functions permitted us to demonstrate significantly coordinated patterns of multiple hormone release. A specific quadruple co-pulsatility pattern was observed, in which the two gonadotropic hormones (luteinizing hormone and follicle stimulating hormone) were co-secreted and coupled by a 10-20 min lag to the later release of beta-endorphin. In turn, beta-endorphin release episodes were followed within 0-30 min by cortisol bursts. Conditional probability analysis allowed us to reject with high statistical confidence the null hypothesis that this unique temporally specified pattern of quadruple hormone release was due to purely random associations among the four pulsatile series. We conclude that discrete hormone release episodes associated with four hormones within the gonadotropic and corticotropic axes in man exhibit significantly lagged non-random temporal coupling in vivo.

Adult

[Risk assessment of factors related to lactation of breast-feeding women by multichotomous logistic regression with stepwise procedure].

Based on Dubin and Pasternack's solution of parsimonious parameters, the authors proposed a procedure of stepwise selection of factors for establishing the Multichotomous logistic regression "best" model. Score statistic was used to select factors into model. Ratio of likelihood function was used to eliminate factors from model. The data of lactation from 129 breast-feeding women living in rural area have been analysed by the procedure. It showed that the first breast-feeding to the newborn of over 48 hours from her childbirth has negative effect while good appetite has positive effect on milk secretion. The epidemiological meaning of parameters estimated from the data was illustrated in detail.

Breast Feeding

[Control of the efficacy of anti-arrhythmia drug therapy with the ambulatory electrocardiogram. Proposal for a new analytical statistical model].

Ambulatory electrocardiography is used for evaluating antiarrhythmic drug effectiveness. Statistical methods based on the analysis of the number of ventricular ectopic beats are currently employed. These techniques are not useful to compare groups of patients with different therapies, due to the wide spontaneous variability of the ectopic beats. We propose a new statistical method, based on the likelihood function. The new method has been tested both retrospectively on 102 patients treated with different antiarrhythmic drugs and prospectively on 12 patients subjected to three consecutive control ambulatory electrocardiograms and to a fourth one after treatment with propafenone. This new statistical method was found to be useful for comparing therapeutic effectiveness between groups of patients, whereas the traditional quantitative methods are to be preferred when drug effectiveness is evaluated in the single patient.

Adrenergic beta-Antagonists

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

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

Febrile convulsions followed by nonfebrile convulsions: analysis based on a maximum likelihood method and discriminant function.

Two hundred sixty-two nontreated patients with febrile convulsions only and 107 with later nonfebrile convulsions were analyzed based on a maximum likelihood method and discriminant function. The formula for discrimination is as follows: y = 2.9193 x (basic EEG abnormality at the first examination) + 2.2134 x (more than 20 minutes in duration of convulsion) + 1.7358 (fever under 38.4 degrees C before convulsion) + 1.7005 x (specific EEG abnormality at the first examination) + 1.6703 x (more than 5 recurrences) + 1.5610 x (over 4 years of age at the last convulsion) + 1.4921 x (exogenous causes) + 0.3741 x (family histroy of febrile convulsions among second or third relatives)--3.0397. If an item is positive, coefficient x 1 is to be used, and if it is negative, coefficient x 0 is to be applied. When one classifies patients with y greater than 0 as the FCC group, and those with y less than 0 as the FC group, misclassification may be theoretically expected in 18.9% of cases (accuracy in 81.1%).

Age Factors

Features of "near-death experience" in relation to whether or not patients were near death.

The medical records of 58 patients, most of whom believed they were near death during an illness or after an injury and all of whom later remembered unusual experiences occurring at the time, were examined. 28 patients were judged to have been so close to death that they would have died without medical intervention; the other 30 patients were not in danger of dying although most of them thought they were. Patients of both groups reported closely similar experiences but patients who really were close to death were more likely than those who were not to report an enhanced perception of light and enhanced cognitive powers. The claim of enhancement of cognitive functions despite the likelihood that brain function had probably become disturbed and possibly diminished, deserves further investigation.

Adolescent

Bayesian model selection and minimum description length estimation of auditory-nerve discharge rates.

Auditory-nerve fiber discharges are modeled as self-exciting point processes with intensity given by the product of a stimulus-related function and a refractory-related function. Previous methods of estimating these two functions, based on the maximum-likelihood principle, have the problem of estimating more parameters than the data can support. A new procedure, based on a Bayes criterion for choosing the complexity of the model in addition to estimating the parameters, solves the over-parametrization problem. This procedure is seen to relate asymptotically to Rissanen's minimum description length (MDL) criterion. A performance comparison of the MDL procedure with previous maximum-likelihood algorithms promotes the adoption of the MDL procedure for simultaneous estimation of the stimulus and recovery properties of auditory-nerve discharge.

Algorithms

GOFCOX: a computer program for the goodness-of-fit analysis of the Cox proportional hazards model.

GOFCOX is a user-friendly FORTRAN program for assessing the adequacy of the Cox proportional hazards model. The underlying methodology is based on the comparison of the maximum partial likelihood estimator and a weighted parameter estimator. The latter is the root to an estimation equation that assigns varying weights to the individual contributions to the partial likelihood score function. The weighted and unweighted parameter estimators have the same expectation under the Cox model, but tend to differ when the model is inappropriate. The GOFCOX program computes a rich class of weighted parameter estimators and corresponding goodness-of-fit test statistics. The program runs on both mainframe computers and microcomputers. The running time is minimal even for large data sets. A simple example is provided to illustrate the features of the program.

Computers, Mainframe

A method of non-parametric back-projection and its application to AIDS data.

The method of back-projection has been used to estimate the unobserved past incidence of infection with the human immunodeficiency virus (HIV) and to obtain projections of future AIDS incidence. Here a new approach to back-projection, which avoids parametric assumptions about the form of the HIV infection intensity, is described. This approach gives the data greater opportunity to determine the shape of the estimated intensity function. The method is based on a modification of an EM algorithm for maximum likelihood estimation that incorporates smoothing of the estimated parameters. It is easy to implement on a computer because the computations are based on explicit formulae. The method is illustrated with applications to AIDS data from Australia, U.S.A. and Japanese haemophiliacs.

Acquired Immunodeficiency Syndrome