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Results for “Likelihood Functions”

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PubMed1999

Fitting the psychometric function.

A constrained generalized maximum likelihood routine for fitting psychometric functions is proposed, which determines optimum values for the complete parameter set--that is, threshold and slope--as well as for guessing and lapsing probability. The constraints are realized by Bayesian prior distributions for each of these parameters. The fit itself results from maximizing the posterior distribution of the parameter values by a multidimensional simplex method. We present results from extensive Monte Carlo simulations by which we can approximate bias and variability of the estimated parameters of simulated psychometric functions. Furthermore, we have tested the routine with data gathered in real sessions of psychophysical experimenting.

Bayes Theorem↗

PubMed1999

Monotonic algorithms for transmission tomography.

We present a framework for designing fast and monotonic algorithms for transmission tomography penalized-likelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the log likelihood. Due to the form of the log-likelihood function it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log likelihood that arises due to background events, such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified at each iteration, the CPU time is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity, and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real and simulated PET transmission scans.

Algorithms↗

PubMed2002

A semiparametric model for the analysis of recurrent-event panel data.

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.

Animals↗

PubMed2005

A powerful and robust method for mapping quantitative trait loci in general pedigrees.

The variance-components model is the method of choice for mapping quantitative trait loci in general human pedigrees. This model assumes normally distributed trait values and includes a major gene effect, random polygenic and environmental effects, and covariate effects. Violation of the normality assumption has detrimental effects on the type I error and power. One possible way of achieving normality is to transform trait values. The true transformation is unknown in practice, and different transformations may yield conflicting results. In addition, the commonly used transformations are ineffective in dealing with outlying trait values. We propose a novel extension of the variance-components model that allows the true transformation function to be completely unspecified. We present efficient likelihood-based procedures to estimate variance components and to test for genetic linkage. Simulation studies demonstrated that the new method is as powerful as the existing variance-components methods when the normality assumption holds; when the normality assumption fails, the new method still provides accurate control of type I error and is substantially more powerful than the existing methods. We performed a genomewide scan of monoamine oxidase B for the Collaborative Study on the Genetics of Alcoholism. In that study, the results that are based on the existing variance-components method changed dramatically when three outlying trait values were excluded from the analysis, whereas our method yielded essentially the same answers with or without those three outliers. The computer program that implements the new method is freely available.

Chromosome Mapping↗

PubMed2003

Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations.

MOTIVATION: Most scoring functions used in protein fold recognition employ two-body (pseudo) potential energies. The use of higher-order terms may improve the performance of current algorithms. METHODS: Proteins are represented by the side chain centroids of amino acids. Delaunay tessellation of this representation defines all sets of nearest neighbor quadruplets of amino acids. Four-body contact scoring function (log likelihoods of residue quadruplet compositions) is derived by the analysis of a diverse set of proteins with known structures. A test protein is characterized by the total score calculated as the sum of the individual log likelihoods of composing amino acid quadruplets. RESULTS: The scoring function distinguishes native from partially unfolded or deliberately misfolded structures. It also discriminates between pre- and post-transition state and native structures in the folding simulations trajectory of Chymotrypsin Inhibitor 2 (CI2).

Algorithms↗

PubMedDate not supplied

Reoperative neurosurgery in dogs with thoracolumbar disc disease.

OBJECTIVE: To characterize the subset of dogs in our neurosurgical practice that underwent spinal surgery for thoracolumbar (TL) disc herniation and subsequently underwent additional decompressive TL surgery. STUDY DESIGN: A retrospective case series. SAMPLE POPULATION: Thirty dogs that underwent reoperation for TL disc herniation. A comparison group of Dachshunds that underwent only one decompressive TL disc surgery was also studied. METHODS: Dogs that underwent reoperation were divided into two groups based on the interval between their first and second surgery. The early reoperation group included those dogs having a second surgery less than 4 weeks after the initial operation. The late reoperation group included those dogs having a second surgery more than 4 weeks after the initial operation. For each Dachshund in the late reoperation group, two Dachshunds that underwent only one decompressive TL disc surgery were selected and formed the comparison group. Dogs in the comparison group were matched with reoperated cases based on the severity of preoperative neurologic deficit and site of disc herniation. These two groups were compared to determine: (1) if age and body weight were risk factors for reoperation, and (2) if dogs had a poorer functional outcome after their second decompressive surgery than did those in the comparison group after their first (and only) decompressive surgery. RESULTS: A total of 30 of 467 (6.4%) dogs that underwent decompressive TL disc surgery were reoperated. In the early reoperative cases (n = 5 dogs), the inciting cause in all cases was residual compression from disc material at the site of the initial surgery. In the late reoperation group, 22 of 25 (88%) cases had a second disc herniation at a site distinct from the initial lesion. Dachshunds had a significantly higher risk for late reoperation (odds ratio and 95% CI = 3.67, 1.46 to 10.03); other small and medium-sized breeds (<20 kg) were underrepresented. Age and body weight were not significant predictors for reoperation. A total of 21 of 23 (91%) dogs had functional recovery after late reoperation. Complete sensorimotor loss was a significant negative predictor of functional recovery in the late reoperative cases (P = .01). Likelihood of functional recovery in dogs after their second decompressive surgery was identical to the functional recovery of dogs in the comparison group. CONCLUSIONS AND CLINICAL RELEVANCE: Our results show that a second disc herniation occurring at a site distinct from the initial lesion is the most common cause for reoperation and that Dachshunds have a significantly greater risk than other breeds.

Animals↗

PubMed2004

Ischemic cardiomyopathy: value of different MRI techniques for prediction of functional recovery after revascularization.

OBJECTIVE: The purpose of this study was to compare the value of different MRI techniques for the assessment of myocardial viability. SUBJECTS AND METHODS. Eighteen infarct patients (mean age +/- SD, 62 +/- 8 years) with myocardial ischemia were examined using MRI before and after revascularization. The MRI study before treatment consisted of an evaluation of first-pass perfusion, contractile function at rest and during dobutamine stress, and delayed hyperenhancement. Findings were correlated with segmental and global cardiac function after revascularization. RESULTS: In initially dysfunctional segments, the likelihood of functional recovery after revascularization was 91% for segments without delayed hyperenhancement, 43% for segments with delayed hyperenhancement with transmural extent of 75% or less, and 8% for segments with delayed hyperenhancement with transmural extent of more than 75% (p < 0.05). Improved function at dobutamine stress MRI indicated functional recovery in 87%, whereas functional recovery was observed in only 30% of segments not responding at dobutamine stress MRI (p < 0.05). No significant correlation was found between the results of first-pass perfusion MRI and functional recovery. The ejection fraction after revascularization was best predicted by the MRI-derived infarct volume (p < 0.001, R(2) = 0.63). CONCLUSION: A simple protocol consisting of baseline contractility and delayed enhancement MRI studies is adequate to differentiate dysfunctional but viable from nonviable myocardium. Dobutamine stress and perfusion MRI studies offer little or no additional information.

Aged↗

PubMed1996

Order-restricted tests for stratified comparisons of binomial proportions.

The data set presented relates a binomial response to ordered levels of an explanatory variable, representing doses of a drug, with data collected at several centers. A study goal is to test independence of the response and the ordinal factor, assuming under the alternative only that the binomial parameter is a monotonically increasing function of the ordinal predictor. We present two likelihood-ratio tests that are sensitive to order-restricted alternatives. Simulating the exact distributions of the test statistics yields nearly exact P-values. We also discuss related analyses for comparing two groups on an ordinal response, and we propose a test that is sensitive to a stochastic ordering alternative.

Binomial Distribution↗

PubMed2001

Regression splines for threshold selection in survival data analysis.

The Cox proportional hazards model restricts the hazard ratio to be linear in the covariates. A survival model based on data from a clinical trial is developed using spline functions with variable knots to estimate the log hazard function. Moreover, the main point of the method is that a knot, seen as free parameters for a piecewise linear spline, represents a break point in the log hazard function which may be interpreted as a threshold value. The likelihood ratio test is used to select the final model and to determine the threshold number for a covariate. Confidence intervals for these threshold values are computed by bootstrapping the data. Two examples illustrate the method.

Carcinoma, Small Cell↗

PubMed2005

Cortical activation during Pavlovian fear conditioning depends on heart rate response patterns: an MEG study.

In the present study, we examined stimulus-driven neuromagnetic activity in a delayed Pavlovian aversive conditioning paradigm using steady state visual evoked fields (SSVEF). Subjects showing an accelerative heart rate (HR) component to the CS+ during learning trials exhibited an increased activation in sensory and parietal cortex due to CS+ depiction in the extinction block. This was accompanied by a selective orientation response (OR) to the CS+ during extinction as indexed by HR deceleration. However, they did not show any differential cortical activation patterns during acquisition. In contrast, subjects not showing an accelerative HR component but rather unspecific HR changes during learning were characterized by greater activity in left orbito-frontal brain regions in the acquisition block but did not show differential SSVEF patterns during extinction. The results suggest that participants expressing different HR responses also differ in their stimulus-driven neuromagnetic response pattern to an aversively conditioned stimulus.

Adult↗

PubMed2003

Estimation of a change point in a hazard function based on censored data.

The hazard function plays an important role in reliability or survival studies since it describes the instantaneous risk of failure of items at a time point, given that they have not failed before. In some real life applications, abrupt changes in the hazard function are observed due to overhauls, major operations or specific maintenance activities. In such situations it is of interest to detect the location where such a change occurs and estimate the size of the change. In this paper we consider the problem of estimating a single change point in a piecewise constant hazard function when the observed variables are subject to random censoring. We suggest an estimation procedure that is based on certain structural properties and on least squares ideas. A simulation study is carried out to compare the performance of this estimator with two estimators available in the literature: an estimator based on a functional of the Nelson-Aalen estimator and a maximum likelihood estimator. The proposed least squares estimator tums out to be less biased than the other two estimators, but has a larger variance. We illustrate the estimation method on some real data sets.

Bias↗

PubMed2002

Do you know your total cholesterol (TC) number?

Total cholesterol (TC) measurements are subject to errors primarily because of temporal variations in cholesterol levels within each individual. These errors make it difficult to estimate the proportion of study subjects with true (error-free) TC in a specific range, an extremely important parameter to policy makers in health care management. To properly address this issue, it is key to accurately estimate the distribution function of the true TC, which typically deviates from the normal distribution. To better approximate the distribution function of the true TC, we propose a constrained maximum likelihood estimator based on a mixture-of-normals model. A simulation study illustrates that the proposed estimator performs better than an estimator based on the normality assumption that is frequently used in the literature to address the same issue. Finally, the proposed estimator is applied to data from a study, and its performance is once again compared with that of an estimator based on the normality assumption.

Algorithms↗

PubMed1995

Irritable bowel syndrome in a community: symptom subgroups, risk factors, and health care utilization.

The clinical relevance of subdividing the irritable bowel syndrome (IBS) into subgroups based on bowel habit is largely unknown. We therefore obtained an age- and sex-stratified random sample of Olmsted County, Minnesota, residents aged 20-95 years. All subjects were mailed a valid self-report questionnaire during the years 1988-1993; the response rate was 74% (n = 3,022). Among subjects with IBS (n = 536), four symptom-based subgroups of similar size were identified: constipation predominant, diarrhea predominant, alternating constipation and diarrhea, and neither. The prevalence of IBS was significantly greater in females, primarily because of a higher prevalence of constipation-predominant IBS in women. Of persons > or = 60 years of age, 23% reported the initial onset of IBS in the previous year compared with 10% in younger subjects; the age at onset of IBS was similar among the subgroups. Marital status, education level, smoking, and alcohol use were not significantly different among the subgroups. Of those with IBS, 25% reported visiting a physician for abdominal pain or disturbed defecation in the prior year compared with only 8% of persons without IBS. Female sex, an increased number of Manning's symptom criteria, and the individual IBS subgroups were not associated with higher rates of physician visits. We conclude that the onset of IBS may not be limited to early adulthood and that subgroups of IBS based on bowel patterns may not identify clinically distinct entities.

Adult↗

PubMed2003

A probability model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies.

Numerical chromosome abnormalities (aneuploidies) are among the most common known causes of mental retardation and the leading cause of pregnancy loss in humans. They primarily arise by the process of meiotic non-disjunction. We still know very little about the contribution of genetic and environmental causes for non-disjunction in humans. In order to increase our understanding of the epidemiology of human trisomies, it is necessary to establish the proportion of cases occurring in the first or second division of meiosis. Trisomic patients will display, in study of microsatellite typed by the polymerase chain reaction (PCR), three fragment peaks of equal intensity, two fragments at an average 2:1 dosage or one individual fragment. In this work we describe a statistical approach for estimation of the fraction of meiosis I non-disjunctions (F) in the absence of the parental information. First we determine a probability model for the number of peaks in a polymorphic microsatellite locus, which is a function of F. Based on this model, we obtain a maximum likelihood estimator for F, using the observed proportion of one, two and three allele patterns in trisomic individuals. Relying on the properties of maximum likelihood theory, we also calculate the asymptotic variance and confidence intervals for F. Owing to the fact that the samples of trisomic patients are limited in number, the use of asymptotic theory may be compromised. Thus, we employ the bootstrap technique to build confidence intervals for F and compare the results with those obtained from the normal theory. This estimator that dispenses the need to study parents opens the possibility of using archival material for comparative epidemiological studies of Down's syndrome and other aneuploidies. In this paper we propose a probability model to estimate the fraction of meiosis I non-disjunction, F, by only using the proportion of allele patterns of trisomy individuals, while traditional methods require typing pericentromeric markers from those affected and their parents.

Brazil↗

PubMed2006

Quantile regression methods for reference growth charts.

Estimation of reference growth curves for children's height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population. Age-specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods. Non-parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions. We compare estimated reference curves for height using the penalized likelihood approach of Cole and Green with quantile regression curves based on data used for modern Finnish reference charts. An advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data. Quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated.

Adolescent↗

PubMed2005

New algorithms for Luria-Delbrück fluctuation analysis.

Fluctuation analysis is the most widely used approach in estimating microbial mutation rates. Development of methods for point and interval estimation of mutation rates has long been hampered by lack of closed form expressions for the probability mass function of the number of mutants in a parallel culture. This paper uses sequence convolution to derive exact algorithms for computing the score function and observed Fisher information, leading to efficient computation of maximum likelihood estimates and profile likelihood based confidence intervals for the expected number of mutations occurring in a test tube. These algorithms and their implementation in SALVADOR 2.0 facilitate routine use of modern statistical techniques in fluctuation analysis by biologists engaged in mutation research.

Algorithms↗

PubMed2003

A latent process model for joint modeling of events and marker.

The paper formulates joint modeling of a counting process and a sequence of longitudinal measurements, governed by a common latent stochastic process. The latent process is modeled as a function of explanatory variables and a Brownian motion process. The conditional likelihood given values of the latent process at the measurement times, has been drawn using Brownian bridge properties; then integrating over all possible values of the latent process at the measurement times leads to the desired joint likelihood. An estimation procedure using joint likelihood and a numerical optimization is described. The method is applied to the study of cognitive decline and Alzheimer's disease.

Aged↗

PubMed2003

Evidence for positive selection on the floral scent gene isoeugenol-O-methyltransferase.

Isoeugenol-O-methyltransferase (IEMT) is an enzyme involved in the production of the floral volatile compounds methyl eugenol and methyl isoeugenol in Clarkia breweri (Onagraceae). IEMT likely evolved by gene duplication from caffeic acid-O-methyltransferase followed by amino acid divergence, leading to the acquisition of its novel function. To investigate the selective context under which IEMT evolved, maximum likelihood methods that estimate variable d(N)/d(S) ratios among lineages, among sites, and among a combination of both lineages and sites were utilized. Statistically significant support was obtained for a hypothesis of positive selection driving the evolution of IEMT since its origin. Subsequent Bayesian analyses identified several sites in IEMT that have experienced positive selection. Most of these positions are in the active site of IEMT and have been shown by site-directed mutagenesis to have large effects on substrate specificity. Although the selective agent is unknown, the adaptive evolution of this gene may have resulted in increased effectiveness of pollinator attraction or herbivore repellence.

Amino Acid Sequence↗