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Results for “likelihood”

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PubMed1995

The comparison of injury severity instrument performance using likelihood ratio and ROC curve analyses.

BACKGROUND: The relative merits of injury severity instruments are often difficult to determine because the statistical techniques, study populations, and outcomes used in trauma research tend to obscure rather than elucidate differences in performance. OBJECTIVE: To describe the advantages of likelihood ratio and receiver operator characteristic (ROC) curve analyses and to demonstrate them using study populations and outcomes that facilitate instrument discrimination. MATERIALS AND METHODS: Previously published data on the performance of the "Injury Severity Score" and of four triage instruments in the prediction of mortality; paired comparison of two instruments in a previously unpublished trauma registry dataset; use of likelihood ratio and ROC analyses. MEASUREMENTS AND MAIN RESULTS: In a comparison of triage instruments this study clearly showed that CRAMS, PHI, and RTI, which contain nonphysiological information, have higher performance levels than the Revised Trauma Score (RTS), which is restricted to physiological information. Absolute performance gains of these instruments over the RTS ranged from 5.9% to 43.5%. This study also noted that the ISS performs equally well for blunt and penetrating trauma, and affirms concerns about the adequacy of its performance. CONCLUSIONS: Likelihood ratio and ROC curve analyses demonstrate differences in injury severity instrument performance that were obscured by less rigorous methods of comparison.

Humans↗

PubMed1998

Type of health care coverage and the likelihood of being screened for cancer.

OBJECTIVES: This study explored whether type of outpatient health coverage affected the likelihood of men and women aged 20 to 64 years receiving recommended cancer screening procedures. METHODS: Data from the 1989 and 1990 California Behavioral Risk Factor Surveillance Surveys were used to compare Pap smear, mammogram, fecal occult blood test, and proctoscopic examination rates for adults with three different types of private health care coverage (Group/staff model health maintenance organization, Independent Practice Association Model health maintenance organization, indemnity plan) and no outpatient health insurance. Logistic regression models were used to control for sociodemographic and health characteristics and whether individuals had a usual health care provider. RESULTS: Individuals with Group Model health maintenance organization coverage were significantly more likely than those with indemnity plans to have had recent cervical, breast, and colorectal cancer screening, whereas screening likelihood for those with Independent Practice Association model health maintenance organization coverage did not differ substantially from those with indemnity plans. Individuals with no outpatient coverage were less likely to be screened than those with outpatient coverage. The most consistently significant predictor across cancer screening procedures for both men and women was having a usual doctor who knew their medical history. CONCLUSIONS: Adults who had private outpatient insurance were more likely to undergo recommended cancer detection procedures than those who did not. Adults who belonged to a health maintenance organization, which emphasizes and pays for a broader spectrum preventive care, were more likely to receive Pap smears, mammograms, and fecal occult blood tests than those covered by indemnity plans. Receiving care primarily from one doctor significantly increased the likelihood of having screening procedures, irrespective of type of health plan.

Adult↗

PubMed2003

Identifying patients with type 2 diabetes with a higher likelihood of erectile dysfunction: the role of the interaction between clinical and psychological factors.

PURPOSE: We estimated the prevalence of erectile dysfunction in patients with type 2 diabetes and identified subgroups of patients in which the interaction among clinical, psychological and sociodemographic characteristics determined an increased likelihood of erectile dysfunction. MATERIALS AND METHODS: The presence of erectile dysfunction was based on patient self-reporting. Clinical information was collected by participating physicians. The severity of depressive symptoms was investigated using the Center for Epidemiological Studies Depression scale. To evaluate interactions among the variables investigated and identify distinct, homogeneous subgroups of patients with different odds ratios for erectile dysfunction a tree growing technique was used. RESULTS: In the 1,460 patients studied the prevalence of severe and mild-moderate erectile dysfunction was 34% and 24%, respectively. While severe erectile dysfunction was mainly related to the severity of diabetes, mild-moderate dysfunction was independent of clinical variables and only associated with the severity of depressive symptoms. The tree growing technique led to the identification of 6 classes characterized by a marked difference in the prevalence of severe erectile dysfunction of between 19% and 65%. Patients on diet alone showed the lowest prevalence of erectile dysfunction and were considered the reference category, while patients treated with insulin who had neuropathy represented the subgroup with the highest likelihood of erectile dysfunction (OR = 7.2, 95% CI 3.9 to 13.2). In patients treated with oral agents the odds ratio for erectile dysfunction was 2.7 (95% CI 1.8 to 3.9) for those with severe depressive symptoms and 1.9 (95% CI 1.3 to 2.7) for current/former smokers with low depressive symptoms. Patient age, retinopathy and cardiac-cerebrovascular disease were globally predictive variables associated with an increased likelihood of erectile dysfunction. CONCLUSIONS: Our data illustrate the interplay of clinical and psychological factors in determining the risk of erectile dysfunction in type 2 diabetes and can help identify those for whom much greater attention is needed to detect erectile problems.

Aged↗

PubMed2003

Estimation of weights and validation: a marginal likelihood approach.

The estimation of weights is quite an important aspect of the restrained refinement of macromolecular structures and related procedures such as the estimation of coordinate errors and structure validation using geometrical criteria. In principle, the method of maximum likelihood can be used for estimation of both atomic and weighting parameters. However, the low observation-to-parameter ratio in macromolecular refinement makes this kind of estimate of weighting parameters seriously biased; thus, the weighting parameters have traditionally been estimated separately from atomic parameters using a special technique, such as minimizing the free R factor. However, the variance of the latter estimate is large, as only a small portion of all data is used. In this work, an estimator of weights is proposed which is based on an approximation of a marginal likelihood function of the weighting parameters and which uses all the X-ray data. There is a known true value for the overall scaling coefficient for distance variances in restrained refinement and therefore the (maximum-likelihood) estimator for this coefficient may be used as a validation statistic.

Crystallography, X-Ray↗

PubMed2001

Likelihood maximization for list-mode emission tomographic image reconstruction.

The maximum a posteriori (MAP) Bayesian iterative algorithm using priors that are gamma distributed, due to Lange, Bahn and Little, is extended to include parameter choices that fall outside the gamma distribution model. Special cases of the resulting iterative method include the expectation maximization maximum likelihood (EMML) method based on the Poisson model in emission tomography, as well as algorithms obtained by Parra and Barrett and by Huesman et al. that converge to maximum likelihood and maximum conditional likelihood estimates of radionuclide intensities for list-mode emission tomography. The approach taken here is optimization-theoretic and does not rely on the usual expectation maximization (EM) formalism. Block-iterative variants of the algorithms are presented. A self-contained, elementary proof of convergence of the algorithm is included.

Algorithms↗

PubMedDate not supplied

A short proof that phylogenetic tree reconstruction by maximum likelihood is hard.

Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum likelihood tree is NP-hard by exploiting a connection between likelihood and parsimony observed by Tuffley and Steel.

Algorithms↗

PubMed2006

Pattern generation using likelihood inference for cellular automata.

Cellular automata are discrete dynamical systems which evolve on a discrete grid. Recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns. We develop likelihood-based methods for estimating rules of cellular automata aimed at the re-generation of observed regular patterns. Under noisy data, our approach is equivalent to estimating the local map of a stochastic cellular automaton. Direct computations of the maximum likelihood estimates are possible for regular binary patterns. The likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool. We illustrate our method with a series of examples using binary images.

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↗

PubMed2005

Maximum-likelihood techniques for joint segmentation-classification of multispectral chromosome images.

Traditional chromosome imaging has been limited to grayscale images, but recently a 5-fluorophore combinatorial labeling technique (M-FISH) was developed wherein each class of chromosomes binds with a different combination of fluorophores. This results in a multispectral image, where each class of chromosomes has distinct spectral components. In this paper, we develop new methods for automatic chromosome identification by exploiting the multispectral information in M-FISH chromosome images and by jointly performing chromosome segmentation and classification. We (1) develop a maximum-likelihood hypothesis test that uses multispectral information, together with conventional criteria, to select the best segmentation possibility; (2) use this likelihood function to combine chromosome segmentation and classification into a robust chromosome identification system; and (3) show that the proposed likelihood function can also be used as a reliable indicator of errors in segmentation, errors in classification, and chromosome anomalies, which can be indicators of radiation damage, cancer, and a wide variety of inherited diseases. We show that the proposed multispectral joint segmentation-classification method outperforms past grayscale segmentation methods when decomposing touching chromosomes. We also show that it outperforms past M-FISH classification techniques that do not use segmentation information.

Algorithms↗

PubMed2006

Monotonic penalized-likelihood image reconstruction for X-ray fluorescence computed tomography.

In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed.

Algorithms↗

PubMed1999

Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies.

This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.

Analysis of Variance↗

PubMed1999

Simulated likelihood methods for complex double-platform line transect surveys.

The conventional line transect approach of estimating effective search width from the perpendicular distance distribution is inappropriate in certain types of surveys, e.g., when an unknown fraction of the animals on the track line is detected, the animals can be observed only at discrete points in time, there are errors in positional measurements, and covariate heterogeneity exists in detectability. For such situations a hazard probability framework for independent observer surveys is developed. The likelihood of the data, including observed positions of both initial and subsequent observations of animals, is established under the assumption of no measurement errors. To account for measurement errors and possibly other complexities, this likelihood is modified by a function estimated from extensive simulations. This general method of simulated likelihood is explained and the methodology applied to data from a double-platform survey of minke whales in the northeastern Atlantic in 1995.

Animals↗

PubMed2000

Mixture models, robustness, and the weighted likelihood methodology.

Problems associated with the analysis of data from a mixture of distributions include the presence of outliers in the sample, the fact that a component may not be well represented in the data, and the problem of biases that occur when the model is slightly misspecified. We study the performance of weighted likelihood in this context. The method produces estimates with low bias and mean squared error, and it is useful in that it unearths data substructures in the form of multiple roots. This in turn indicates multiple potential mixture model fits due to the presence of more components than originally specified in the model. To compute the weighted likelihood estimates, we use as starting values the method of moment estimates computed on bootstrap subsamples drawn from the data. We address a number of important practical issues involving bootstrap sample size selection, the role of starting values, and the behavior of the roots. The algorithm used to compute the weighted likelihood estimates is competitive with EM, and it is similar to EM when the components are not well separated. Moreover, we propose a new statistical stopping rule for the termination of the algorithm. An example and a small simulation study illustrate the above points.

Animals↗

PubMed2000

Estimation of multivariate frailty models using penalized partial likelihood.

There exists a growing literature on the estimation of gamma distributed multiplicative shared frailty models. There is, however, often a need to model more complicated frailty structures, but attempts to extend gamma frailties run into complications. Motivated by hip replacement data with a more complicated dependence structure, we propose a model based on multiplicative frailties with a multivariate log-normal joint distribution. We give a justification and an estimation procedure for this generally structured frailty model, which is a generalization of the one presented by McGilchrist (1993, Biometrics 49, 221-225). The estimation is based on Laplace approximation of the likelihood function. This leads to estimating equations based on a penalized fixed effects partial likelihood, where the marginal distribution of the frailty terms determines the penalty term. The tuning parameters of the penalty function, i.e., the frailty variances, are estimated by maximizing an approximate profile likelihood. The performance of the approximation is evaluated by simulation, and the frailty model is fitted to the hip replacement data.

Biometry↗

PubMed2001

A maximum likelihood-based method for mining major genes affecting a quantitative character.

In this article, we present a maximum likelihood-based analytical approach for detecting a major gene of large effect on a quantitative trait in a progeny population derived from a mating design. Our analysis is based on a mixed genetic model specifying both major gene and background polygenic inheritance. The likelihood of the data is formulated by combining the information about population behaviors of the major gene during hybridization and its phenotypic distribution densities. The EM algorithm is implemented to obtain maximum likelihood estimates for population and quantitative genetic parameters of the major locus. This approach is applied to detect an overdominant gene governing stem volume growth in a factorial mating design of aspen trees. It is suggested that further molecular genetic research toward mapping single genes affecting aspen growth and production based on the same experimental data has a high probability of success.

Algorithms↗

PubMed2001

Pairwise rank-based likelihood for estimation and inference on the mixture proportion.

We consider the problem of estimation and inference on the mixture parameter in the two-sample problem when sample data from the two distributions as well as from a third population consisting of a mixture of the two are used. Under a general nonparametric model, where the relationship between the two populations is unspecified, we develop a pairwise rank-based likelihood. Simultaneous inference on the mixture proportion and a parameter representing the probability an observation from one population is greater than an observation from the other population is based on this likelihood. Under some regularity conditions, it is shown that the maximum pairwise rank likelihood estimator is consistent and has an asymptotic normal distribution. Simulation results indicate that the performance of this statistic is satisfactory. The methodology is demonstrated on a data set in prostate cancer.

Biometry↗

PubMed2004

A likelihood-based approach to estimating and testing for isolation by distance.

Simple regression of genetic similarities between pairs of populations on their corresponding geographic distances is frequently used to detect the presence of isolation by distance (IBD). However, these pairwise values are obviously not independent and there is no parametric procedure for estimating and testing for the IBD intercepts and slopes based on standard regression theory. Nonparametric tests, such as the Mantel test, and resampling techniques, such as bootstrapping, have been exploited with limited success. Here, I describe a likelihood-based analysis to allow for simultaneously detecting patterns of correlated residuals and estimating and testing for the presence of IBD. It is shown, through the analysis of two molecular datasets in pine species, that different covariance structures of the residuals exist. More over, the likelihood ratio tests under these covariance structures are less sensitive to the presence of IBD than the Mantel test and the simple regression analysis but more sensitive than the bootstrap and jackknife samples over independent populations or population pairs. Because the likelihood analysis directly models and accounts for nonindependence of residuals, it should legitimately detect the presence of IBD, thereby allowing for accurate inferences about evolutionary and demographic processes influencing the extent and patterns of IBD.

Analysis of Variance↗

PubMed2004

The maximally exposed individual--comparison of maximum likelihood estimation of high quantiles to an extreme value estimate.

The dose to human and nonhuman individuals inflicted by anthropogenic radiation is an important issue in international and domestic policy. The current paradigm for nonhuman populations asserts that if the dose to the maximally exposed individuals in a population is below a certain criterion (e.g., <10 mGy d(-1)) then the population is adequately protected. Currently, there is no consensus in the regulatory community as to the best statistical approach. Statistics, currently considered, include the maximum likelihood estimator for the 95th percentile of the sample mean and the sample maximum. Recently, the investigators have proposed the use of the maximum likelihood estimate of a very high quantile as an estimate of dose to the maximally exposed individual. In this study, we compare all of the above-mentioned statistics to an estimate based on extreme value theory. To determine and compare the bias and variance of these statistics, we use Monte Carlo simulation techniques, in a procedure similar to a parametric bootstrap. Our results show that a statistic based on extreme value theory has the least bias of those considered here, but requires reliable estimates of the population size. We recommend establishing the criterion based on what would be considered acceptable if only a small percentage of the population exceeded the limit, and hence recommend using the maximum likelihood estimator of a high quantile in the case that reliable estimates of the population size are not available.

Animals↗