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PubMed1998

Maximum likelihood estimation of population divergence times and population phylogenies under the infinite sites model.

In this paper, a maximum likelihood estimator of population divergence time based on the infinite sites model is developed. It is demonstrated how this estimator may be applied to obtain maximum likelihood estimates of the topology of population phylogenies. This approach addresses several classical problems occurring in the inference of the phylogenetic relationship of populations, most notably the problem of shared ancestral polymorphisms. The method is applied to previously published data sets of human African populations and of Caribbean hawksbill turtles.

Animals↗

PubMed1992

Likelihood-based analyses of longitudinal twin and family data: experiences with pedigree-based approaches.

Substantial progress has been made recently in analyses of longitudinal twin and family data, principally for two reasons. The first is the continuing development of more refined models for describing longitudinal data; the second is the widespread availability of analytic methods (e.g. LISREL) with which to implement these models. Computational restrictions have limited likelihood-based analyses of longitudinal genetic data to analyses of covariance matrices or mean squares; however, advances in computer technology now make it feasible to conduct likelihood analyses of longitudinal pedigree data. We consider potential advantages of using pedigree-based methods. Our initial experiences with the application of these methods to simulated twin data, using the FISHER (Lange, K.L., et al., Genet. Epidemiol. 5:471, 1988) quantitative genetics package, are discussed, with particular attention to practical details such as running times on several computers. Preliminary results of the pedigree-based analyses, including robust estimation methods, convincingly demonstrate the failure of methods assuming the multivariate normal distribution for simulated twin data provided by Carey (this issue).

Adolescent↗

PubMed1996

Likelihood ratios for mixed stains when the number of donors cannot be agreed.

Suppose that part of the prosecution's evidence in some crime case is analysis of a blood stain, and that the traits E discovered in the stain suggest multiple donors. Then the prosecution will probably allege some specific inculpatory hypothesis H0 about the sources of the stain, and P (E [symbol: see text] H0) can be calculated. It is desirable to use this as the numerator of a likelihood ratio. However, in general the obvious denominator P (E [symbol: see text] approximately H0) cannot be calculated, so unless the defense is sufficiently obliging as to stipulate to a specific choice among the potentially infinite number of more or less exculpatory alternative hypotheses, the desired likelihood ratio can't be evaluated. We show that nonetheless, in most cases there is an adequate inequality.

Blood Donors↗

PubMed1995

The effect of relatedness on likelihood ratios and the use of conservative estimates.

DNA profiling can be used to identify criminals through their DNA matching that left at the scene of a crime. The strength of the evidence supplied by a match in DNA profiles is given by the likelihood ratio. This, in turn, depends upon the probability that a match would be produced if the suspect is innocent. This probability could be strongly affected by the possibility of relatedness between the suspect and the true source of the scene-of-crime DNA profile. Methods are shown that allow for the possibility of such relatedness, arising either through population substructure or through a family relationship. Uncertainties about the likelihood ratio have been taken as grounds for the use of very conservative estimates of this quantity. The use of such conservative estimates can be shown to be neither necessary nor harmless.

Alleles↗

PubMed2002

Gene conversion and the evolution of euryarchaeal chaperonins: a maximum likelihood-based method for detecting conflicting phylogenetic signals.

Recombination is well known as a complicating factor in the interpretation of molecular phylogenies. Here we describe a maximum likelihood sliding window method based on a likelihood ratio test for scanning DNA sequence alignments for regions of incongruent phylogenetic signals, such as those influenced by recombination. Using this method, we identify several instances of gene conversion between paralogous chaperonin genes in euryarchaeote Archaea, many of which are not detected by two other widely used methods. In the Thermococcus/Pyrococcus lineage, where a gene duplication producing a and b paralogues predates the divergence of Thermococcus strains KS-1 and KS-8, gene conversion has homogenized portions of the a and b genes in KS-8 since the divergence of these two strains. A region near the 3' end of the a and b paralogues in the methanogen Methanobacterium thermoautotrophicum also appears to have undergone gene conversion. We apply the method to two additional test data sets, the argF gene of Neisseria and a set of actin paralogues in maize, and show that it successfully identifies all the recombinant regions that were previously detected with other methods. Our approach is relatively insensitive to the presence of divergent sequences in the alignment, making it ideal for detecting recombination between both closely and distantly related genes.

Actins↗

PubMed2004

Likelihood analysis of the chalcone synthase genes suggests the role of positive selection in morning glories (Ipomoea).

Chalcone synthase (CHS) is a key enzyme in the biosynthesis of flavonoides, which are important for the pigmentation of flowers and act as attractants to pollinators. Genes encoding CHS constitute a multigene family in which the copy number varies among plant species and functional divergence appears to have occurred repeatedly. In morning glories (Ipomoea), five functional CHS genes (A-E) have been described. Phylogenetic analysis of the Ipomoea CHS gene family revealed that CHS A, B, and C experienced accelerated rates of amino acid substitution relative to CHS D and E. To examine whether the CHS genes of the morning glories underwent adaptive evolution, maximum-likelihood models of codon substitution were used to analyze the functional sequences in the Ipomoea CHS gene family. These models used the nonsynonymous/synonymous rate ratio (omega = d(N)/ d(S)) as an indicator of selective pressure and allowed the ratio to vary among lineages or sites. Likelihood ratio test suggested significant variation in selection pressure among amino acid sites, with a small proportion of them detected to be under positive selection along the branches ancestral to CHS A, B, and C. Positive Darwinian selection appears to have promoted the divergence of subfamily ABC and subfamily DE and is at least partially responsible for a rate increase following gene duplication.

Acyltransferases↗

PubMed2005

Accuracy and power of the likelihood ratio test for comparing evolutionary rates among genes.

Sequences for multiple protein-coding genes are now commonly available from several, often closely related species. These data sets offer intriguing opportunities to test hypotheses regarding whether different types of genes evolve under different selective pressures. Although maximum likelihood (ML) models of codon substitution that are suitable for such analyses have been developed, little is known about the statistical properties of these tests. We use a previously developed fixed-sites model and computer simulations to examine the accuracy and power of the likelihood ratio test (LRT) in comparing the nonsynonymous-to-synonymous substitution rate ratio (omega = dN/dS) between two genes. Our results show that the LRT applied to fixed-sites models may be inaccurate in some cases when setting significance thresholds using a chi(2) approximation. Instead, we use a parametric bootstrap to describe the distribution of the LRT statistic for fixed-sites models and examine the power of the test as a function of sampling variables and properties of the genes under study. We find that the power of the test is high (>80%) even when sampling few taxa (e.g., six species) if sequences are sufficiently diverged and the test is largely unaffected by the tree topology used to simulate data. Our simulations show fixed-sites models are suitable for comparing substitution parameters among genes evolving under even strong evolutionary constraint (omega approximately 0.05), although relative rate differences of 25% or less may be difficult to detect.

Biological Evolution↗

PubMed2004

A maximum likelihood method for detecting functional divergence at individual codon sites, with application to gene family evolution.

The tailoring of existing genetic systems to new uses is called genetic co-option. Mechanisms of genetic co-option have been difficult to study because of difficulties in identifying functionally important changes. One way to study genetic co-option in protein-coding genes is to identify those amino acid sites that have experienced changes in selective pressure following a genetic co-option event. In this paper we present a maximum likelihood method useful for measuring divergent selective pressures and identifying the amino acid sites affected by divergent selection. The method is based on a codon model of evolution and uses the nonsynonymous-to-synonymous rate ratio (omega) as a measure of selection on the protein, with omega = 1, < 1, and > 1 indicating neutral evolution, purifying selection, and positive selection, respectively. The model allows variation in omega among sites, with a fraction of sites evolving under divergent selective pressures. Divergent selection is indicated by different omega's between clades, such as between paralogous clades of a gene family. We applied the codon model to duplication followed by functional divergence of (i) the epsilon and gamma globin genes and (ii) the eosinophil cationic protein (ECP) and eosinophil-derived neurotoxin (EDN) genes. In both cases likelihood ratio tests suggested the presence of sites evolving under divergent selective pressures. Results of the epsilon and gamma globin analysis suggested that divergent selective pressures might be a consequence of a weakened relationship between fetal hemoglobin and 2,3-diphosphoglycerate. We suggest that empirical Bayesian identification of sites evolving under divergent selective pressures, combined with structural and functional information, can provide a valuable framework for identifying and studying mechanisms of genetic co-option. Limitations of the new method are discussed.

Amino Acids↗

PubMed2000

Maximum likelihood estimation on large phylogenies and analysis of adaptive evolution in human influenza virus A.

Algorithmic details to obtain maximum likelihood estimates of parameters on a large phylogeny are discussed. On a large tree, an efficient approach is to optimize branch lengths one at a time while updating parameters in the substitution model simultaneously. Codon substitution models that allow for variable nonsynonymous/synonymous rate ratios (omega = d(N)/d(S)) among sites are used to analyze a data set of human influenza virus type A hemagglutinin (HA) genes. The data set has 349 sequences. Methods for obtaining approximate estimates of branch lengths for codon models are explored, and the estimates are used to test for positive selection and to identify sites under selection. Compared with results obtained from the exact method estimating all parameters by maximum likelihood, the approximate methods produced reliable results. The analysis identified a number of sites in the viral gene under diversifying Darwinian selection and demonstrated the importance of including many sequences in the data in detecting positive selection at individual sites.

Algorithms↗

PubMed2006

A classical likelihood based approach for admixture mapping using EM algorithm.

Several disease-mapping methods have been proposed recently, which use the information generated by recent admixture of populations from historically distinct geographic origins. These methods include both classic likelihood and Bayesian approaches. In this study we directly maximize the likelihood function from the hidden Markov Model for admixture mapping using the EM algorithm, allowing for uncertainty in model parameters, such as the allele frequencies in the parental populations. We determined the robustness of the proposed method by examining the ancestral allele frequency estimate and individual marker-location specific ancestry when the data were generated by different population admixture models and no learning sample was used. The proposed method outperforms a widely used Bayesian MCMC strategy for data generated from various population admixture models. The multipoint information content for ancestry was derived based on the map provided by Smith et al. (2004) and the associated statistical power was calculated. We examined the distribution of admixture LD across the genome for both real and simulated data and established a threshold for genome wide significance applicable to admixture mapping studies. The software ADMIXPROGRAM for performing admixture mapping is available from authors.

Algorithms↗

PubMed2006

Likelihood ratio tests in behavioral genetics: problems and solutions.

The likelihood ratio test of nested models for family data plays an important role in the assessment of genetic and environmental influences on the variation in traits. The test is routinely based on the assumption that the test statistic follows a chi-square distribution under the null, with the number of restricted parameters as degrees of freedom. However, tests of variance components constrained to be non-negative correspond to tests of parameters on the boundary of the parameter space. In this situation the standard test procedure provides too large p-values and the use of the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for model selection is problematic. Focusing on the classical ACE twin model for univariate traits, we adapt existing theory to show that the asymptotic distribution for the likelihood ratio statistic is a mixture of chi-square distributions, and we derive the mixing probabilities. We conclude that when testing the AE or the CE model against the ACE model, the p-values obtained from using the chi(2)(1 df) as the reference distribution should be halved. When the E model is tested against the ACE model, a mixture of chi(2)(0 df), chi(2)(1 df) and chi(2)(2 df) should be used as the reference distribution, and we provide a simple formula to compute the mixing probabilities. Similar results for tests of the AE, DE and E models against the ADE model are also derived. Failing to use the appropriate reference distribution can lead to invalid conclusions.

Analysis of Variance↗

PubMed1994

Sensitivity and specificity of diagnostic tests in acute maxillary sinusitis determined by maximum likelihood in the absence of an external standard.

This study shows how to obtain maximum likelihood estimates of test sensitivities and specificities in case of lack of an external standard, using the Expectation Maximisation (EM) algorithm. This method is used to compare four diagnostic tests in patients suspected of acute maxillary sinusitis. Data were analyzed from published studies. Antral aspiration is the test with the highest diagnostic value. The diagnostic value of a positive clinical examination (according to explicit criteria) and of a positive radiograph or ultrasound are comparable. A negative radiograph is of more diagnostic value than a negative clinical examination or ultrasound. The width of the confidence intervals may be too small, due to model deviations which may give incorrect standard errors. However, the estimated likelihood ratios adequately reflect the relative value of the diagnostic tests considered, even when the assumption of independence is dropped.

Acute Disease↗

PubMed2006

A likelihood approach to analyzing clinical trial data when treatments favor different outcomes.

It is increasingly common in clinical trials to design studies for which more than one primary outcome exists. Methods that exist for more than one outcome are generally concerned with identifying one of two situations: (1) improvement in all outcomes from one treatment, as compared to the other treatment(s); or (2) improvement in a single efficacy endpoint, without an excess of toxicity. In contrast, the Colpopexy and Urinary Reduction Effort (CARE) Study is a randomized clinical trial comparing two treatments that presents a slightly different scenario. In this study, there are two outcomes, and it was anticipated by the investigators that each treatment may favor a different outcome. Few statistical methods exist to address the specific challenges encountered by this design. We designed a method to address the specific analytic issues raised in the planning of the CARE study. We developed a likelihood ratio approach to test whether or not a treatment difference exists at the end of the study by considering both the absolute treatment differences and the direction of the differences with respect to the treatments. This method involves simultaneously testing each component of a composite null hypothesis, while maintaining an overall type I error rate. A simulation study is performed to evaluate the operating characteristics of this test, in which we find that our joint likelihood-ratio test has a power as high as, or higher than, other commonly used methods for multiple outcomes, while maintaining a nominal type I error rate.

Female↗

PubMed2005

Phylogenetics by likelihood: evolutionary modeling as a tool for understanding the genome.

Molecular evolutionary studies provide a means of investigating how cells function and how organisms adapt to their environment. The products of evolutionary studies provide medically important insights to the source of major diseases, such as HIV, and hold the key to understand the developing immunity of pathogenic bacteria to antibiotics. They have also helped mankind understand its place in nature, casting light on the selective forces and environmental conditions that resulted in modern humans. The use of likelihood as a framework for statistical modeling in phylogenetics has played a fundamental role in studying molecular evolution, enabling rigorous and robust conclusions to be drawn from sequence data. The first half of this article is a general introduction to the likelihood method for inferring phylogenies, the properties of the models used, and how it can be used for statistical testing. The latter half of the article focuses on the emerging new generation of phylogenetic models that describe heterogeneity in the evolutionary process along sequences, including the recoding of protein coding sequence data to amino acids and codons, and various approaches for describing dependencies between sites in a sequence. We conclude with a detailed case study examining how modern modeling approaches have been successfully employed to identify adaptive evolution in proteins.

Animals↗

PubMed2005

A fast image reconstruction algorithm based on penalized-likelihood estimate.

Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurately modeling the counting statistics and the photon transport during acquisition. They are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to the conventional filtered back projection algorithm. But a major drawback of the statistical iterative image reconstruction is its high computational cost. In this paper, a fast algorithm is proposed as a modified OS-EM (MOS-EM) using a penalized function, which is applied to the least squares merit function to accelerate image reconstruction and to achieve better convergence. The experimental results show that the algorithm can provide high quality reconstructed images with a small number of iterations.

Algorithms↗

PubMed2005

Reduced likelihood of cancer screening among women in urban areas and with low socio-economic status: a multilevel analysis in Japan.

OBJECTIVES: To elucidate socio-economic predictors of participation in cancer screening in Japanese women, paying attention to regional variations. METHODS: In a nationally representative sample of women aged 40--64 years (n=15,224) in Japan, the relationships of self-reported attendance at screening for stomach, colon, uterine and breast cancers with individual characteristics (marital status, occupation and household income) and regional variables (living in a metropolitan area or not, and per capita income) were examined using multilevel analysis. RESULTS: The participation rate ranged from 21.6% for colon cancer to 32.5% for uterine cancer. Being married, employed and having a higher household income were significantly associated with a higher likelihood of cancer screening for all types of cancer: the adjusted odds ratio in the lowest income quintile ranged from 0.45 for uterine cancer to 0.53 for colon cancer compared with the highest income quintile. There was significant regional variance, and living in a metropolitan area and per capita income were associated with a reduced likelihood of cancer screening. CONCLUSIONS: Women with lower socio-economic status and living in urban areas are less likely to participate in cancer screening in Japan. Cancer screening should be encouraged in urban areas, taking account of the socio-economic inequalities.

Adult↗

PubMed2006

Bayesian analysis using continuous likelihood ratios for identifying pleural exudates.

STUDY OBJECTIVES: To ascertain if equations that calculate continuous likelihood ratios (CLRs) for pleural exudates improve pleural fluid categorization, especially when false positive or false negative test results are obtained by using Light's criteria. DESIGN AND SETTING: Retrospective review of the clinical and pleural fluid data from a consecutive series of patients with pleural effusion who underwent thoracentesis at the University Hospital Arnau de Vilanova (Lleida, Spain) over an 11-year period. PATIENTS AND METHODS: A total of 1490 patients with pleural effusion (298 transudates and 1192 exudates) were recruited into the study. The presence of a transudate or exudate was established by clinical judgment. We examined the comparative diagnostic accuracy of 4 tests (i.e. pleural fluid protein and lactate dehydrogenase (LDH), and pleural fluid to serum protein and LDH ratios) for discriminating between transudates and exudates. Decision thresholds were determined by receiver operating characteristics (ROC) analysis. Equations for calculating CLRs derived from a logistic regression analysis based on a previously described method. RESULTS: Individual pleural fluid tests did not differ in their diagnostic accuracies according to ROC analysis. We calculated CLRs for the elements of Light's criteria and pleural fluid protein, and also illustrated the sequential use of CLRs for determining posttest probabilities. Overall, CLR formulas had marginal performance for the correct categorization of pleural fluid. CONCLUSIONS: CLRs provide a probabilistic statement as to the likelihood an effusion is a transudate or exudate. However, clinical judgment is little changed by the application of CLRs, and in doubtful cases a great amount of uncertainty remains. This Bayesian approach is likely to have no major impact on the clinical practice.

Bayes Theorem↗

PubMed2006

Maximum likelihood mixture estimation to determine metal background values in estuarine and coastal sediments within the European Water Framework Directive.

Some of the recently derived European Directives, such as the Water Framework and Marine Strategy, have, as ultimate aims, to achieve concentrations of hazardous substances in the marine environment near background values. Hence, the determination of natural background levels, in marine sediments, is highly relevant. The present study proposes the use of the maximum likelihood mixture estimation (MLME) to determine regional background levels and upper threshold of metal concentration, with the Basque Country as a case study (with a data set of 575 samples, from estuarine and littoral areas, including both intertidal and subtidal sediments). The heuristic procedure is applied with unimodal data distributions (Cd, Cr, Fe and Ni) and the mixture density estimations, based upon maximum likelihood, are carried out with polypopulational data distributions (As, Cu, Mn, Hg, Pb and Zn). The upper limits of the distribution are proposed, as the limits between 'High Status' and 'Good Status' (according to the Water Framework Directive terminology). The regional upper limits were 0.45 microg g(-1) for Cd, 71 microg g(-1) for Cr, 53,542 microg g(-1) for Fe, 57 microg g(-1) for Ni, 24 microg g(-1) for As, 64 microg g(-1) for Cu, 447 microg g(-1) for Mn, 0.27 microg g(-1) for Hg, 66 microg g(-1) for Pb, and 248 microg g(-1) for Zn. The results from this study can assist further in the determination of sediment reference conditions, to assess chemical status, within the above-mentioned directives; likewise, it will be studied as a useful methodology in determining regional metal backgrounds in other European countries.

Arsenic↗