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Results for “Likelihood Functions”

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PubMed1994

A stable, multivariate extension of the log-normal survival model.

When applied to survival data from a population of cancer patients, the log-normal model provides estimates of three important parameters: cured fraction, mean log survival time, and standard deviation log survival time. In the original model, however, these parameters are unrelated to prognostic covariates. Furthermore, the original algorithm is computationally unstable and highly dependent on initial parameter estimates. We have developed an extension of the log-normal model that stabilizes computation and expresses survival parameters as functions of prognostic covariates. We have also developed an ancillary algorithm that provides reliable initial estimates.

Algorithms↗

PubMed2004

Genotype-by-sex and environment-by-sex interactions influence variation in serum levels of bone-specific alkaline phosphatase in adult baboons (Papio hamadryas).

While more than 77% of the people in the US with osteoporosis are women, the contributions of genotype-by-sex (G x S) and environment-by-sex interactions to sex differences in osteoporosis risk factors have not been studied. To address this issue, we conducted a statistical genetic analysis of serum concentrations of bone-specific alkaline phosphatase (Bone ALP), a highly specific marker of osteoblast function that is elevated in persons with conditions like osteoporosis characterized by excessive bone turnover or rapid bone loss. We assayed Bone ALP from 657 pedigreed baboons using a commercially available ELISA kit. Using a maximum likelihood variance decomposition approach, we treated sex as an environmental milieu in which genes influencing Bone ALP levels are expressed. We modeled the genetic covariance in Bone ALP between all relative pairs conditional on their sex so that the covariance is the product of the kinship, the genetic correlation between trait levels in the two sexes, and the genetic variances in the two sexes. Sex-specific maximum likelihood estimates (MLE) of residual heritability for Bone ALP were greater for females than for males (h2 = 0.44 vs. h2 = 0.26, respectively), but likelihood ratio tests revealed only a marginally significant difference in sex-specific genetic variances (P = 0.057). In contrast, the between-sex genetic correlation (rhoG = 0.43) was significantly less than 1.0 (P = 0.037), and the difference in sex-specific environmental variances was highly significant (P = 0.00006). We report the first evidence for G x S interactions influencing variation in an osteoporosis risk factor. The diminished between-sex genetic correlation implies that different genes influence Bone ALP levels in the two sexes. The significant differences between environmental variances suggest that unmeasured factors, including those from the internal, biological environments of the two sexes, account for a greater proportion of the Bone ALP variation in males.

Alkaline Phosphatase↗

PubMed2026

Statistical test to compare the linkage model and the admixture model based on central limit results.

In the Admixture Model, the probability that an individual carries a certain allele at a specific marker depends on the allele frequencies in K ancestral populations and the proportion of the individual's genome originating from these populations. The markers are assumed to be independent. The Linkage Model is a Hidden Markov Model that extends the Admixture Model by incorporating linkage between neighboring loci. We prove consistency and asymptotic normality of maximum likelihood estimators for the ancestry of individuals in the Linkage Model, complementing earlier results by (Pfaff et al., 2004; Pfaffelhuber and Rohde, 2022; Heinzel, 2025) for the Admixture Model. These results are used to prove that a statistical test that allows for model selection between the Admixture Model and the Linkage Model is an asymptotic level-α-test. Finally, we demonstrate the practical relevance of our results by applying the test to real-world data from The 1000 Genomes Project Consortium (2015).

Genetic Linkage↗

PubMed2006

The admixture linkage disequilibrium and genetic linkage inference on the gradual admixture population.

Through the theoretical analysis of the admixture linkage disequilibrium (ALD) in the gradual admixture (GA) model, in which admixture occurs in every generation, the ALD is found to be proportional to the difference in marker allele frequencies, P1 - P2, between two subpopulations. Based on this property, we can employ a strict monotonic function (delta(ker) = delta/(P1-P2), where delta denotes the linkage disequilibrium (LD)) of the recombination fraction between the marker locus and the disease locus to infer the true genetic linkage. We construct a quasi likelihood ratio test (LRT) for the case-only data utilizing the information of unlinked markers in the human genome. The simulation results show that our tests can be used to fine map a disease locus. The effects of parameter values in the ALD mapping are also discussed.

Black or African American↗

PubMed2001

Mathematical modeling for functional divergence after gene duplication.

In this paper, I present a statistical framework for modeling the functional divergence after gene duplication. A rate-component model to describe the rate covariation among homologous genes of a gene family is implemented when a phylogenetic tree is known. The Markov chain model is rigorous but may require a huge amount of computational time when the number of sequences is large. On the other hand, the Poisson-based model is mathematically analytical so that computation is very fast even for a large dataset. Moreover, under the posterior framework, we have developed a site-specific profile for predicting important amino acid residues responsible for these functional differences between member genes of a gene family. Our study may have great potential for functional genomics because it is cost-effective, and these predictions can be further tested by biological experimentation.

Biological Evolution↗

PubMed2000

Probabilistic modeling of single-trial fMRI data.

This paper describes a probabilistic framework for modeling single-trial functional magnetic resonance (fMR) images based on a parametric model for the hemodynamic response and Markov random field (MRF) image models. The model is fitted to image data by maximizing a lower bound on the log likelihood. The result is an approximate maximum a posteriori estimate of the joint distribution over the model parameters and pixel labels. Examples show how this technique can used to segment two-dimensional (2-D) fMR images, or parts thereof, into regions with different characteristics of their hemodynamic response.

Brain↗

PubMed2005

Effects of variance-function misspecification in analysis of longitudinal data.

The approach of generalized estimating equations (GEE) is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within-subject correlations. The variance is often assumed to be a known function of the mean. This article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses. Our numerical studies indicate that (1) correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified; (2) misspecification of the variance function impacts much more on estimators for within-cluster covariates than for cluster-level covariates; and (3) if the variance function is misspecified, correct choice of the correlation structure may not necessarily improve estimation efficiency. We illustrate impacts of different variance functions using a real data set from cow growth.

Animals↗

PubMed2000

Current and residual functional disability associated with psychopathology: findings from the Netherlands Mental Health Survey and Incidence Study (NEMESIS).

BACKGROUND: Few population studies have investigated the functional disabilities that accompany specific psychiatric diagnoses. This study assesses the nature and strength of current and residual impairments in various functional domains of life. METHODS: Data were derived from the Netherlands Mental Health Survey and Incidence Study (NEMESIS), a prospective study in the Dutch general population aged 18 to 64 (N = 7147). Psychiatric diagnoses were based on the Composite International Diagnostic Interview; functional disability was assessed on the basis of the Short-Form-36 and the number of disability days. RESULTS: Psychopathology was associated with increased disability in social, emotional and physical domains of life. Disability levels varied by psychiatric diagnosis, with mood disorders showing the poorest levels of functioning, especially for vitality and social functioning; alcohol-related disorders were associated with few disabilities. Co-morbidity strongly aggravated the disability. The effect of contextual factors on disability was limited, although somatic ill health, unemployment and adverse youth history increased the likelihood of functional disability. The findings indicate that psychopathology can also have residual debilitating effects. CONCLUSIONS: Mental health care providers should be aware that the extent and the type of disability may vary with the different types of disorders and among different groups within the population. Since recovery from functional limitations may not be complete or may take more time than the remission of the psychiatric symptomatology, non-psychiatric follow-up care is needed. The high number of lost work days is relevant from an economic perspective. There is a need for illness-specific disability assessment instruments.

Activities of Daily Living↗

PubMed1997

Weighing the evidence for hypotheses with small samples of right-censored exponential data.

The p-value evidence for an alternative to a null hypothesis regarding the mean lifetime can be unreliable if based on asymptotic approximations when there is only a small sample of right-censored exponential data. However, a guarded weight of evidence for the alternative can always be obtained without approximation, no matter how small the sample, and has some other advantages over p-values. Weights of evidence are defined as estimators of 0 when the null hypothesis is true and 1 when the alternative is true, and they are judged on the basis of the ensuing risks, where risk is mean squared error of estimation. The evidence is guarded in that a pre-assigned bound is placed on the risk under the hypothesis. Practical suggestions are given for choosing the bound and for interpreting the magnitude of the weight of evidence. Acceptability profiles are obtained by inversion of a family of guarded weights of evidence for two-sided alternatives to point hypotheses, just as confidence intervals are obtained from tests; these profiles are arguably more informative than confidence intervals, and are easily determined for any level and any sample size, however small. They can help understand the effects of different amounts of censoring. They are found for several small size data sets, including a sample of size 12 for post-operative cancer patients. Both singly Type I and Type II censored examples are included. An examination of the risk functions of these guarded weights of evidence suggests that if the censoring time is of the same magnitude as the mean lifetime, or larger, then the risks in using a guarded weight of evidence based on a likelihood ratio are not much larger than they would be if the parameter were known.

Confidence Intervals↗

PubMed2004

Two-sample statistics for testing the equality of survival functions against improper semi-parametric accelerated failure time alternatives: an application to the analysis of a breast cancer clinical trial.

This paper presents two-sample statistics suited for testing equality of survival functions against improper semi-parametric accelerated failure time alternatives. These tests are designed for comparing either the short- or the long-term effect of a prognostic factor, or both. These statistics are obtained as partial likelihood score statistics from a time-dependent Cox model. As a consequence, the proposed tests can be very easily implemented using widely available software. A breast cancer clinical trial is presented as an example to demonstrate the utility of the proposed tests.

Breast Neoplasms↗

PubMed2004

Gene conversion and functional divergence in the beta-globin gene family.

Different models of gene family evolution have been proposed to explain the mechanism whereby gene copies created by gene duplications are maintained and diverge in function. Ohta proposed a model which predicts a burst of nonsynonymous substitutions following gene duplication and the preservation of duplicates through positive selection. An alternative model, the duplication-degeneration-complementation (DDC) model, does not explicitly require the action of positive Darwinian selection for the maintenance of duplicated gene copies, although purifying selection is assumed to continue to act on both copies. A potential outcome of the DDC model is heterogeneity in purifying selection among the gene copies, due to partitioning of subfunctions which complement each other. By using the d(N)/ d(S) (omega) rate ratio to measure selection pressure, we can distinguish between these two very different evolutionary scenarios. In this study we investigated these scenarios in the beta-globin family of genes, a textbook example of evolution by gene duplication. We assembled a comprehensive dataset of 72 vertebrate beta-globin sequences. The estimated phylogeny suggested multiple gene duplication and gene conversion events. By using different programs to detect recombination, we confirmed several cases of gene conversion and detected two new cases. We tested evolutionary scenarios derived from Ohta's model and the DDC model by examining selective pressures along lineages in a phylogeny of beta-globin genes in eutherian mammals. We did not find significant evidence for an increase in the omega ratio following major duplication events in this family. However, one exception to this pattern was the duplication of gamma-globin in simian primates, after which a few sites were identified to be under positive selection. Overall, our results suggest that following gene duplications, paralogous copies of beta-globin genes evolved under a nonepisodic process of functional divergence.

Animals↗

PubMed2002

Sensitivity analysis for healthcare models fitted to data by statistical methods.

After fitting complex models to data using statistical methods, a sensitivity analysis can be carried out. This determines which parts of a model are causing the bulk of the uncertainty in the model predictions (model "output"), and is a decision-support tool for the modeller who contemplates refining a model further or collecting additional data. A simple methodology for carrying out a sensitivity analysis is described. It is envisaged that such a relatively quick insight-generating step would precede the use of a more formal decision-theoretic approach that would address specific questions. Its use is illustrated using a model for breast cancer screening previously published in this journal. A simpler 3-parameter screening model is used in a simulation study of the error of the method as a function of sample size.

Breast Neoplasms↗

PubMed2007

Copulation, genital damage and early death in Callosobruchus maculatus.

Antagonistic sexual coevolution stems from the notion that male and female interests over reproduction are in conflict. Such conflicts appear to be particularly obvious when male genital armature inflicts damage to the female reproductive tract resulting in reduced female longevity. However, studies of mating frequency, genital damage and female longevity are difficult to interpret because females not only sustain more genital damage, but also receive more seminal fluid when they engage in multiple copulations. Here, we attempt to disentangle the effects of genital damage and seminal fluid transfer on female longevity in the beetle Callosobruchus maculatus (Coleoptera: Bruchidae). Males copulating for the sixth time in succession inflicted greater levels of genital damage, but transferred smaller ejaculates in comparison with virgin males. The number of copulations performed by males was negatively related to female fecundity and positively related to female longevity, suggesting a trade-off between fecundity and longevity. However, inclusion of fecundity as a covariate revealed sperm and/or seminal fluid transfer to have a negative impact on female longevity above that caused by the fecundity-longevity trade-off. The consequences of multiple copulations on female longevity were examined. Females that mated twice laid more eggs and died sooner than those that mated once. However, incorporation of fecundity as a covariate into our statistical model removed the effect of female mating frequency on female longevity, indicating that double-mated females suffer greater mortality owing to the trade-off between fecundity and longevity. Males of this species are known to transfer very large ejaculates (up to 8% of their body weight), which may represent a significant nutritional benefit to females. However, the receipt of large ejaculates appears to carry costs. Thus, the interpretation of multiple mating experiments on female longevity and associated functional explanations of polyandry in this species are likely to be complex.

Animals↗

PubMed2006

The high prevalence of anemia in diabetes is linked to functional erythropoietin deficiency.

Anemia is a common finding in diabetes, particularly in patients with albuminuria or renal impairment. We recently showed that at least 1 in 5 outpatients with type 1 or type 2 diabetes in tertiary clinics have anemia, in whom it constitutes a significant additional burden. Anemia is associated strongly with an increased risk of diabetic complications including nephropathy, retinopathy, and heart failure. Although a number of factors contribute to an increased prevalence of anemia in diabetes, an uncoupling of hemoglobin concentration and renal erythropoietin synthesis associated with tubular dysfunction appears to be the dominant factor. In our patients with diabetes and anemia, more than three quarters had functional erythropoietin deficiency. This association was most pronounced in patients with renal impairment, in whom nearly half of all patients had anemia. However, 70% of anemic patients without renal impairment also had inappropriately low erythropoietin levels. Consequently, the likelihood of functional erythropoietin deficiency, as a cause of anemia in patients with diabetes, is not dependent on the severity of renal impairment. Although there is a clear rationale for correction of anemia in diabetes, it remains to be established whether this will lead to improved outcomes. Some small studies suggest improvement in cardiac outcomes and hospitalization. It is anticipated that large ongoing studies will help define the optimal approach to the management of anemia in diabetes.

Anemia↗

PubMed2003

Alignment and phylogenetic analysis of beta-fibrinogen intron 7 sequences among avian orders reveal conserved regions within the intron.

We sequenced beta-fibrinogen intron 7 (beta-fibint 7) from 28 species of birds, representing 18 families in nine orders. Although the antiquity of the avian orders is estimated to be 55 to 90 Myr, and numerous indels have accrued among diverging lineages, the intron sequences were not difficult to align. However, alignment of avian sequences with mammal or snake sequences was difficult, and the residual phylogenetic signal was weak. beta-fibint 7 is an AT-rich intron, and its base composition varies little over the diversity of birds represented by our sample. Alignment of these anciently diverged sequences reveals at least five clusters of conserved nucleotides; at least two clusters appear to be in excess of the minimal set usually associated with intron excision, but their functions are unknown. Two equally most-parsimonious (MP) trees were found when indels were not included in the phylogenetic analysis, and six such trees were found when indels were included. The Neighbor-Joining and maximum-likelihood trees were identical to each other and to one of the MP trees in each MP analysis. Indels, as well as nucleotide substitutions, are phylogenetically informative, and bootstrap support exceeded 90% for 21 of 24 inferred nodes when indels were included in the MP analysis. All traditional orders represented by two or more species appear monophyletic. Relationships among avian orders are strongly supported with the exception of an inferred sister-group relationship between Caprimulgiformes and Columbiformes. A relatively close relationship between Piciformes and Passeriformes is inferred, at odds with earlier DNA-DNA hybridization studies but consistent with traditional classifications. Among Passeriformes, the traditional perspective of a sister-group relationship of suboscines and oscines is supported, as is the subsequent split of the oscines into a lineage representative of the Corvida before the diversification of the Passerida. The four species of owls divide into two strongly supported clades, corresponding to the widely accepted bifurcation of owls into two families, Tytonidae and Strigidae. A sister-group relationship between gallinaceous birds and waterfowl, the Galloanserae, is also strongly supported.

Animals↗

PubMed1998

Modelling cure rates using the Gompertz model with covariate information.

We extend the modified Gompertz hazard function, first used by Cantor and Shuster for estimation of cure rates from pediatric clinical trials, by including covariate effects. The extended model provides a convenient method for estimation of the cure rate as a function of treatments and covariates.

Algorithms↗

PubMed2000

Assessing an unknown evolutionary process: effect of increasing site-specific knowledge through taxon addition.

Assessment of the evolutionary process is crucial for understanding the effect of protein structure and function on sequence evolution and for many other analyses in molecular evolution. Here, we used simulations to study how taxon sampling affects accuracy of parameter estimation and topological inference in the absence of branch length asymmetry. With maximum-likelihood analysis, we find that adding taxa dramatically improves both support for the evolutionary model and accurate assessment of its parameters when compared with increasing the sequence length. Using a method we call "doppelgänger trees," we distinguish the contributions of two sources of improved topological inference: greater knowledge about internal nodes and greater knowledge of site-specific rate parameters. Surprisingly, highly significant support for the correct general model does not lead directly to improved topological inference. Instead, substantial improvement occurs only with accurate assessment of the evolutionary process at individual sites. Although these results are based on a simplified model of the evolutionary process, they indicate that in general, assuming processes are not independent and identically distributed among sites, more extensive sampling of taxonomic biodiversity will greatly improve analytical results in many current sequence data sets with moderate sequence lengths.

Evolution, Molecular↗

PubMed2005

Weighted expectation maximization reconstruction algorithms for thermoacoustic tomography.

Thermoacoustic tomography (TAT) is an emerging imaging technique with potential for a wide range of biomedical imaging applications. In this correspondence, we propose an infinite family of weighted expectation maximization (EM) algorithms for reconstruction of images from temporally truncated TAT measurement data. The weighted EM algorithms are equivalent mathematically to the conventional EM algorithm, but are shown to propagate data inconsistencies in different ways. Using simulated and experimental TAT measurement data, we demonstrate that suitable choices of weighted EM algorithms can effectively mitigate image artifacts that are attributable to temporal truncation of the TAT data function.

Acoustics↗