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PubMed2006

Statistical evaluation of ion-channel gating models based on distributions of log-likelihood ratios.

The distributions of log-likelihood ratios (DeltaLL) obtained from fitting ion-channel dwell-time distributions with nested pairs of gating models (Xi, full model; Xi(R), submodel) were studied both theoretically and using simulated data. When Xi is true, DeltaLL is asymptotically normally distributed with predictable mean and variance that increase linearly with data length (n). When Xi(R) is true and corresponds to a distinct point in full parameter space, DeltaLL is Gamma-distributed (2DeltaLL is chi-square). However, when data generated by an l-component multiexponential distribution are fitted by l+1 components, Xi(R) corresponds to an infinite set of points in parameter space. The distribution of DeltaLL is a mixture of two components, one identically zero, the other approximated by a Gamma-distribution. This empirical distribution of DeltaLL, assuming Xi(R), allows construction of a valid log-likelihood ratio test. The log-likelihood ratio test, the Akaike information criterion, and the Schwarz criterion all produce asymmetrical Type I and II errors and inefficiently recognize Xi, when true, from short datasets. A new decision strategy, which considers both the parameter estimates and DeltaLL, yields more symmetrical errors and a larger discrimination power for small n. These observations are explained by the distributions of DeltaLL when Xi or Xi(R) is true.

Computer Simulation↗

PubMed2005

A composite-likelihood approach for detecting directional selection from DNA sequence data.

We present a novel composite-likelihood-ratio test (CLRT) for detecting genes and genomic regions that are subject to recurrent natural selection (either positive or negative). The method uses the likelihood functions of Hartl et al. (1994) for inference in a Wright-Fisher genic selection model and corrects for nonindependence among sites by application of coalescent simulations with recombination. Here, we (1) characterize the distribution of the CLRT statistic (Lambda) as a function of the population recombination rate (R=4Ner); (2) explore the effects of bias in estimation of R on the size (type I error) of the CLRT; (3) explore the robustness of the model to population growth, bottlenecks, and migration; (4) explore the power of the CLRT under varying levels of mutation, selection, and recombination; (5) explore the discriminatory power of the test in distinguishing negative selection from population growth; and (6) evaluate the performance of maximum composite-likelihood estimation (MCLE) of the selection coefficient. We find that the test has excellent power to detect weak negative selection and moderate power to detect positive selection. Moreover, the test is quite robust to bias in the estimate of local recombination rate, but not to certain demographic scenarios such as population growth or a recent bottleneck. Last, we demonstrate that the MCLE of the selection parameter has little bias for weak negative selection and has downward bias for positively selected mutations.

Base Sequence↗

PubMed2005

An efficient Monte Carlo method for estimating Ne from temporally spaced samples using a coalescent-based likelihood.

This article presents an efficient importance-sampling method for computing the likelihood of the effective size of a population under the coalescent model of Berthier et al. Previous computational approaches, using Markov chain Monte Carlo, required many minutes to several hours to analyze small data sets. The approach presented here is orders of magnitude faster and can provide an approximation to the likelihood curve, even for large data sets, in a matter of seconds. Additionally, confidence intervals on the estimated likelihood curve provide a useful estimate of the Monte Carlo error. Simulations show the importance sampling to be stable across a wide range of scenarios and show that the N(e) estimator itself performs well. Further simulations show that the 95% confidence intervals around the N(e) estimate are accurate. User-friendly software implementing the algorithm for Mac, Windows, and Unix/Linux is available for download. Applications of this computational framework to other problems are discussed.

Algorithms↗

PubMed2006

Clinical value of MDCT in the diagnosis of coronary artery disease in patients with a low pretest likelihood of significant disease.

OBJECTIVE: The aim of this study was to evaluate the clinical value of MDCT in the diagnosis of coronary artery disease in a population having a low pretest likelihood of significant disease. SUBJECTS AND METHODS: Sixty-four patients with suspected coronary artery disease and a low pretest likelihood of significant disease according to the criteria of the American Heart Association underwent both MDCT of the heart and quantitative conventional coronary angiography (QCA). MDCT examinations were performed on a 16-MDCT scanner. CT data sets were evaluated on a per-patient basis and a per-segment basis and were classified as indicating no disease, nonsignificant disease (stenoses </= 50%), or significant disease (stenoses > 50%). Sensitivity, specificity, negative predictive value (NPV), and positive predictive value (PPV) of 16-MDCT in the detection or exclusion of significant and nonsignificant coronary artery disease were evaluated on both per-patient and per-segment bases. RESULTS: Regarding the success rate of 16-MDCT, 94% (60/64) of patients and 92% (388/420) of vessel segments were of sufficient quality for diagnosis. In the remaining 60 patients evaluated, QCA revealed significant coronary artery disease, nonsignificant disease, and no disease in 8.3% (5/60), 75.0% (45/60), and 16.7% (10/60) of cases, respectively, on a per-patient basis, and in 1.3% (5/388), 23.2% (90/388), and 75.5% (293/388) of cases, respectively, on a per-segment basis. The sensitivity, specificity, NPV, and PPV of 16-MDCT for the detection of significant coronary artery disease were 80.0%, 94.5%, 98.1%, and 57.1%, respectively, on a per-patient basis, and 80.0%, 99.2%, 99.7%, and 57.1% on a per-segment basis. CONCLUSION: In a population having a low pretest likelihood of significant coronary artery disease, 16-MDCT shows a moderate to high sensitivity and high NPV for the detection or exclusion of significant disease, but has a somewhat reduced PPV compared with QCA.

Adult↗

PubMed1993

Sequential transformation for multiple traits for estimation of (co)variance components with a derivative-free algorithm for restricted maximum likelihood.

Transformation of multiple-trait records that undergo sequential selection can be used with derivative-free algorithms to maximize the restricted likelihood in estimation of covariance matrices as with derivative methods. Data transformation with appropriate parts of the Choleski decomposition of the current estimate of the residual covariance matrix results in mixed-model equations that are easily modified from round to round for calculation of the logarithm of the likelihood. The residual sum of squares is the same for transformed and untransformed analyses. Most importantly, the logarithm of the determinant of the untransformed coefficient matrix is an easily determined function of the Choleski decomposition of the residual covariance matrix and the determinant of the transformed coefficient matrix. Thus, the logarithm of the likelihood for any combination of covariance matrices can be determined from the transformed equations. Advantages of transformation are 1) the multiple-trait mixed-model equations are easy to set up, 2) the least squares part of the equations does not change from round to round, 3) right-hand sides change from round to round by constant multipliers, and 4) less memory is required. An example showed only a slight advantage of the transformation compared with no transformation in terms of solution time for each round (1 to 5%).

Algorithms↗

PubMed1992

Power of likelihood ratio tests for heterogeneity of intraclass correlation and variance in balanced half-sib designs.

Statistical power of likelihood ratio tests was investigated for detection of heterogeneous variances and intraclass correlation in balanced half-sib designs. Powers of likelihood ratio tests were obtained from simulations. For half-sib designs of sires nested within herds, true intraclass correlations and phenotypic variances, and estimates thereof, were repeatedly sampled, and likelihood ratio tests were conducted. The power for detecting heterogeneity of intraclass correlations was low, but the power for detecting heterogeneous phenotypic variances was nearly always 100%. For balanced cross-classified designs, sires had progeny in all herds, and data were simulated by assuming that heterogeneity of between- and within-sire components was the result of a herd-dependent scale effect. Using this model, the power to detect heterogeneous between-sire components was substantially higher than the corresponding power to detect heterogeneous intraclass correlations in the nested design. It seems unlikely that reliable inference about heterogeneity of genetic variances or heritabilities between individual herds from daily cattle field data can be made.

Analysis of Variance↗

PubMed1997

Likelihood-ratio decision strategy for independent observations in the same-different task: an approximation to the detection-theoretic model.

An optimal decision strategy for deciding whether two things are the same or different is to adopt a likelihood-ratio criterion. The parametric equations for the receiver operating characteristic (ROC) based on the likelihood-ratio strategy when observations are independent are complicated; they require the numerical evaluation of a double integral. An approximation to the parametric equations for the likelihood-ratio strategy was developed. This approximation takes the form of a pair of equations that describe ROCs virtually indistinguishable from those of the full model.

Decision Making↗

PubMed1991

Screening for alcohol abuse using CAGE scores and likelihood ratios.

OBJECTIVE: To assess the performance of the CAGE (acronym referring to four questions, see below) questionnaire in discriminating between medicine outpatients with and without an alcohol abuse or dependence disorder. DESIGN: A cross-sectional design of a sample of consecutive patients who received both the alcohol module of the diagnostic interview schedule and the CAGE (Cut down, Annoyed, Guilty, Eye-opener) screening questionnaire. SETTING: The outpatient medical practice of an urban university teaching hospital. PATIENTS: All patients 18 years or older who signed a consent form approved by the university's institutional review board. MEASUREMENT: Calculation of the sensitivity, specificity, receiver operating characteristic (ROC) curve, and likelihood ratio for CAGE scores of 0 to 4. RESULTS: Thirty-six percent of the sample group met criteria for a history of alcohol abuse or dependence. A CAGE score of 2 or more was associated with a sensitivity and specificity of 74% and 91%. The calculated area under the ROC curve was 0.89, whereas the likelihood ratios for CAGE scores of 0 to 4 were 0.14, 1.5, 4.5, 13, and 100, respectively. These ratios were associated with posterior probabilities for an abuse or dependence disorder of 7%, 46%, 72%, 88%, and 98%, respectively. CONCLUSION: Clinicians can improve their ability to estimate a patient's risk for an alcohol abuse or dependence disorder using likelihood ratios for CAGE scores.

Adult↗

PubMed2001

Maximum likelihood analysis of adaptive evolution in HIV-1 gp120 env gene.

Every functional protein appears to have some conserved amino acids which are critically important to the basic structure and function of the protein and thus under purifying selection. Some proteins also have variable amino acids which, when changed, offer a selective advantage, and thus undergo adaptive evolution. These amino acids are also important to the structure and function of the protein, although in a different way. It seems that the selective pressure in every protein varies among sites. Maximum likelihood models developed recently for comparison of silent and replacement nucleotide substitution rates allow for variable selective pressures among amino acid sites, and provide a powerful approach to studying the evolutionary process of protein-coding genes. This paper applies the likelihood models to analyze a data set of 186 HIV-1 gp120 env gene sequences for comparison with a previous analysis of the same data set. The maximum likelihood analysis identified a number of sites under positive selection, some in the conserved regions of the protein.

Adaptation, Physiological↗

PubMed2001

[Roaming through methodology. XXXVI. Likelihood ratios and Bayes' rule].

In practice, the terms 'sensitivity' and 'specificity' are often used in a different sense to that found in textbooks. Their value depends on the composition of the groups in which the test was applied. It is rarely recognised that sensitivity and specificity change during the course of a disease. The interpretation of their value appears to be difficult. The likelihood ratio combines sensitivity and specificity, and is therefore associated with the same problems. The likelihood ratio is Bayes' rule in its simplest form: how does a given probability (in this case that of a particular disease being present) change with the addition of a single new fact (i.e., the result of a diagnostic test)? The Bayesian approach is applied in various fields but rarely in clinical practice, because the prior probability of a diagnosis is difficult to quantify. Likelihood ratios are useful when studying the diagnostic process and when teaching the diagnostic thought process. They can also be applied in the statistical interpretation of clinical trial results.

Bayes Theorem↗

PubMed2003

Does having an outpatient visit after hospital discharge reduce the likelihood of readmission?

OBJECTIVE: To determine whether or not having an outpatient visit after hospital discharge is associated with a lower likelihood of readmission for a statewide Medicaid population. DESIGN AND SETTING: A case-control study in the Delaware Medicaid program over a two-year period (7/1/93-6/30/95). PARTICIPANTS: 3,846 continuously enrolled patients aged 0-64 years who were hospitalized and were readmitted within 90 days (cases = 641) or not readmitted within 90 days (controls = 3,205). Subgroups included those readmitted for the same diagnosis (N = 720), for ambulatory care sensitive conditions (N = 906), or both (N = 276). MAIN OUTCOME MEASURE: Likelihood of readmission within 90 days of discharge. RESULTS: Readmission was significantly more likely when an outpatient visit was made after hospital discharge, both before and after controlling for demographic variables and case mix (adjusted odds ratio = 1.47, 95% confidence interval = 1.20-1.80). When readmission for the same diagnosis was examined, having an outpatient visit was associated with an increased likelihood of readmission before but not after controlling for demographics and case mix (adjusted odds ratio = 1.11, 95% confidence interval = 0.67-1.86). The same was for those admitted for ambulatory care sensitive conditions (adjusted odds ratio = 1.16, 95% confidence interval = 0.74-1.85) and for those readmitted for the same ambulatory care sensitive condition (adjusted odds ratio = 1.53, 95% confidence interval = 0.54-4.29). CONCLUSIONS: This study fails to demonstrate that outpatient visits after hospital discharge are associated with fewer readmissions for nonelderly Medicaid patients. This suggests that it may not be appropriate to use hospital readmission rates as an indicator of the quality of outpatient care.

Adolescent↗

PubMed1992

Likelihoods of multilocus DNA fingerprints in extended families.

A concept for the application of complex pedigree analysis to multilocus DNA fingerprinting is described. By following this approach, the extent to which the DNA fingerprints of grandparents influence the phenotype likelihoods of their offspring was determined. It was demonstrated by simulation that approximately 90% of paternity disputes can be solved if mother, child, and paternal grandparents, instead of the putative father, are tested. If only phenotype information on a single paternal sib is allowed for, true paternity will be detected with reasonable persuasive power in up to 64% of cases. Exclusion of false paternity remains possible for 40% of cases. Finally, the analysis concept is modified by reducing the number of genotype variations considered in likelihood computations. This time-saving procedure is shown to yield sufficiently accurate likelihoods in the analysis of both simulation data and multilocus DNA fingerprints obtained in two large families.

DNA Fingerprinting↗

PubMed1991

Maximum likelihood training of connectionist models: comparison with least squares back-propagation and logistic regression.

This paper presents maximum likelihood back-propagation (ML-BP), an approach to training neural networks. The widely reported original approach uses least squares back-propagation (LS-BP), minimizing the sum of squared errors (SSE). Unfortunately, least squares estimation does not give a maximum likelihood (ML) estimate of the weights in the network. Logistic regression, on the other hand, gives ML estimates for single layer linear models only. This report describes how to obtain ML estimates of the weights in a multi-layer model, and compares LS-BP to ML-BP using several examples. It shows that in many neural networks, least squares estimation gives inferior results and should be abandoned in favor of maximum likelihood estimation. Questions remain about the potential uses of multi-level connectionist models in such areas as diagnostic systems and risk-stratification in outcomes research.

Diagnosis, Computer-Assisted↗

PubMed1991

Estimating the likelihood of severe coronary artery disease.

PURPOSE: To determine which clinical characteristics obtained by a physician during an initial clinical examination are important for estimating the likelihood of severe coronary artery disease, and to determine whether estimates based on these characteristics remain valid when applied prospectively and in different patient groups. PATIENTS AND METHODS: We examined clinical characteristics predictive of severe disease in 6,435 consecutive symptomatic patients referred for suspected coronary artery disease between 1969 and 1983. RESULTS: Eleven of 23 characteristics were important for estimating the likelihood of severe coronary artery disease. A model using these characteristics accurately estimated the likelihood of severe disease in an independent sample of 2,342 patients referred since 1983. The model also accurately estimated the prevalence of severe disease in large series of patients reported in the literature. CONCLUSIONS: These findings suggest that the clinician's initial evaluation can identify patients at high or low risk of anatomically severe coronary artery disease. Cost-conscious quality care is encouraged by identifying patients at higher risk for severe coronary artery disease who are most likely to benefit from further evaluation.

Adult↗

PubMed1990

Maximum likelihood analysis of bubble incidence for mixed gas diving.

The method of maximum likelihood has been applied to predict the incidence of bubbling in divers for both air and helium diving. Data were obtained from 108 air man-dives and 622 helium man-dives conducted experimentally in a hyperbaric chamber. Divers were monitored for bubbles using Doppler ultrasonics during the period from surfacing until approximately 2 h after surfacing. Bubble grades were recorded according to the K-M code, and the maximum value in the precordial region for each diver was used in the likelihood analysis. Prediction models were based on monoexponential gas kinetics using one and two parallel-compartment configurations. The model parameters were of three types: gas kinetics, gas potency, and compartment gain. When the potency of the gases was not distinguished, the risk criterion used was inherently based on the gas supersaturation ratio, otherwise it was based on the potential bubble volume. The two-compartment model gave a significantly better prediction than the one-compartment model only if the kinetics of nitrogen and helium were distinguished. A further significant improvement with the two-compartment model was obtained when the potency of the two gases was distinguished, thereby making the potential bubble volume criterion a better choice than the gas pressure criterion. The results suggest that when the method of maximum likelihood is applied for the prediction of the incidence of bubbling, more than one compartment should be used and if more than one is used consideration should be given to distinguishing the potencies of the inert gases.

Atmosphere Exposure Chambers↗

PubMed1995

Model-free linkage analysis using likelihoods.

Misspecification of transmission model parameters can produce artifactually negative lod scores at small recombination fractions and in multipoint analysis. To avoid this problem, we have tried to devise a test that aims to detect a genetic effect at a particular locus, rather than attempting to estimate the map position of a locus with specified effect. Maximizing likelihoods over transmission model parameters, as well as linkage parameters, can produce seriously biased parameter estimates and so yield tests that lack power for the detection of linkage. However, constraining the transmission model parameters to produce the correct population prevalence largely avoids this problem. For computational convenience, we recommend that the likelihoods under linkage and non-linkage are independently maximized over a limited set of transmission models, ranging from Mendelian dominant to null effect and from null effect to Mendelian recessive. In order to test for a genetic effect at a given map position, the likelihood under linkage is maximized over admixture, the proportion of families linked. Application to simulated data for a wide range of transmission models in both affected sib pairs and pedigrees demonstrates that the new method is well behaved under the null hypothesis and provides a powerful test for linkage when it is present. This test requires no specification of transmission model parameters, apart from an approximate estimate of the population prevalence. It can be applied equally to sib pairs and pedigrees, and, since it does not diminish the lod score at test positions very close to a marker, it is suitable for application to multipoint data.

Chromosome Mapping↗

PubMed1994

Maximum-likelihood estimation of gene location by linkage disequilibrium.

Linkage disequilibrium, D, between a polymorphic disease and mapped markers can, in principle, be used to help find the map position of the disease gene. Likelihoods are therefore derived for the value of D conditional on the observed number of haplotypes in the sample and on the population parameter Nc, where N is the effective population size and c the recombination fraction between the disease and marker loci. The likelihood is computed explicitly for the case of two loci with heterozygote superiority and, more generally, by computer simulations assuming a steady state of constant population size and selective pressures or neutrality. It is found that the likelihood is, in general, not very dependent on the degree of selection at the loci and is very flat. This suggests that precise information on map position will not be obtained from estimates of linkage disequilibrium.

Chromosome Mapping↗

PubMed1998

Regression modelling of diagnostic likelihood ratios for the evaluation of medical diagnostic tests.

The use of diagnostic likelihood ratios has been advocated in the epidemiologic literature for the past decade. Diagnostic likelihood ratios provide valuable information about the predictive properties of a diagnostic test while having the attractive feature of being independent of the prevalence of disease in the study population. We propose a new regression method that allows for direct assessment of covariate effects on likelihood ratios for binary diagnostic tests. This may be particularly useful in assessing how factors that are under the control of the clinician can be altered to maximize the predictive ability of the test. Similarly, patient characteristics that influence the ability of the test to discriminate between diseased and nondiseased subjects may be identified using the regression model. The regression method is flexible in that it can accommodate clustered data arising from a variety of study designs. We illustrate the method with data from an audiology study.

Audiology↗