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Risk of HIV infection as a function of the duration of intravenous drug use: a non-parametric Bayesian approach.

We analyse the elapsed time between intravenous (IV) drug initiation and HIV infection in a cohort of 972 injecting drug users attending a hospital detoxification unit. We use the time of seroconversion instead of the time of HIV infection because the date of HIV infection is rarely known and the gap between these two times is negligible (around one to three months). Although seroconversion time cannot be determined exactly, it can be inferred at least to within an interval. This seroconversion interval is determined from the dates of HIV antibody tests, if available. The data is consequently interval-censored. We estimate the distribution function of the elapsed time from IV drug initiation to seroconversion as well as the risk of seroconversion by means of a non-parametric Bayesian approach. The analysis is conducted according to the following four calendar periods: before or at 1980; between 1981 and 1985; between 1986 and 1991; after or at 1992 where the IV drug use was initiated. The methodology used is based on an alternating conditional sampling algorithm. The Bayesian approach allows not only the incorporation of prior beliefs about the distribution function, but also the analysis of the risk of seroconversion without assuming restrictive parametric models. Furthermore, the estimator for the distribution function is smooth and thus differences between groups can be easily interpreted.

Adolescent↗

Country specific cost comparisons from multinational clinical trials using empirical Bayesian shrinkage estimation: the Canadian ASSENT-3 economic analysis.

The growing number of multinational clinical trials in which patient-level health care resource data are collected have raised the issue of which is the best approach for making inference for individual countries with respect to the between-treatment difference in mean cost. We describe and discuss the relative merits of three approaches. The first uses the random effects pooled estimate from all countries to estimate the difference for any particular country. The second approach estimates the difference using only the data from the specific country in question. Using empirical Bayes estimation a third approach estimates the country-specific difference using a variance-weighted linear sum of the estimates provided by the other two approaches. The approaches are illustrated and compared using the data from the ASSENT-3 trial.

Abciximab↗

Inferring haplotypes at the NAT2 locus: the computational approach.

BACKGROUND: Numerous studies have attempted to relate genetic polymorphisms within the N-acetyltransferase 2 gene (NAT2) to interindividual differences in response to drugs or in disease susceptibility. However, genotyping of individuals single-nucleotide polymorphisms (SNPs) alone may not always provide enough information to reach these goals. It is important to link SNPs in terms of haplotypes which carry more information about the genotype-phenotype relationship. Special analytical techniques have been designed to unequivocally determine the allocation of mutations to either DNA strand. However, molecular haplotyping methods are labour-intensive and expensive and do not appear to be good candidates for routine clinical applications. A cheap and relatively straightforward alternative is the use of computational algorithms. The objective of this study was to assess the performance of the computational approach in NAT2 haplotype reconstruction from phase-unknown genotype data, for population samples of various ethnic origin. RESULTS: We empirically evaluated the effectiveness of four haplotyping algorithms in predicting haplotype phases at NAT2, by comparing the results with those directly obtained through molecular haplotyping. All computational methods provided remarkably accurate and reliable estimates for NAT2 haplotype frequencies and individual haplotype phases. The Bayesian algorithm implemented in the PHASE program performed the best. CONCLUSION: This investigation provides a solid basis for the confident and rational use of computational methods which appear to be a good alternative to infer haplotype phases in the particular case of the NAT2 gene, where there is near complete linkage disequilibrium between polymorphic markers.

Algorithms↗

Demographic history of HIV-1 subtypes B and F in Brazil.

The reconstruction of the epidemic history of several HIV populations, by using methods that infer the population history from sampled gene sequence data, has revealed important subtype-specific and regional-specific differences in patterns of epidemic growth. Here, we employ Bayesian coalescent-based methods to compare the population history of the HIV-1 subtype B and F1 epidemics in Brazil from non-contemporary env and pol gene sequences. Our results suggest that after the introduction of the subtypes B and F1 into Brazilian population, around mid to late 1960s and late 1970s, respectively, these subtypes experienced an initial period of exponential growth with similar epidemic growth rates ( approximately 0.5-0.6year(-1)). Later, the spreading rate of both subtypes seems to have slowed-down since mid to late 1980s. This demographic pattern is very similar to that reported for the subtype B epidemics in high-income countries where HIV was initially transmitted through homosexual intercourse and injecting drug use, as in Brazil; suggesting that the characteristics of transmission networks may be a key determinant of the HIV epidemic growth pattern. It is important to note that most of the subtype B and F1 sequences used in this study come from the Southeast region that has been the most affected by the AIDS epidemic in Brazil, being responsible for around 63% of all AIDS cases reported since the early eighties; but may not represent the demographic trend of the HIV-1 epidemic in other Brazilian regions.

Bayes Theorem↗

Phylogenetic relationships among clonal groups of extraintestinal pathogenic Escherichia coli as assessed by multi-locus sequence analysis.

The evolutionary origins of extraintestinal pathogenic Escherichia coli (ExPEC) remain uncertain despite these organisms' relevance to human disease. A valid understanding of ExPEC phylogeny is needed as a framework against which the observed distribution of virulence factors and clinical associations can be analyzed. Accordingly, phylogenetic relationships were defined by multi-locus sequence analysis among 44 representatives of selected ExPEC clonal groups and the E. coli Reference (ECOR) collection. Recombination, which significantly obscured the phylogenetic signal for several strains, was dealt with by excluding strains or specific sequences. Conflicting overall phylogenies, and internal phylogenies for virulence-associated phylogenetic group B2, were inferred depending on the specific dataset (i.e., how extensively purged of recombination), outgroup (Salmonella enterica and/or Escherichia fergusonii), and analysis method (neighbor joining, maximum parsimony, maximum likelihood, or Bayesian likelihood). Nonetheless, the major E. coli phylogenetic groups A, B1, and B2 were consistently well resolved, as was a major sub-component of group D and an ECOR 37-O157:H7 clade. Moreover, nine important ExPEC clonal groups within groups B2 and D, characterized by serotypes O6:K2:H1, O18:K1:H7, O6:H31, and O4:K+:H+ (from group B2), and O1:K1:H-, O7:K1:H-, O157:K+:H (non-7), O15:K52:H1, and O11/17/77:K52:H18 ("clonal group A") (from group D), were consistently well resolved, regardless of clinical background (cystitis, pyelonephritis, neonatal meningitis, sepsis, or fecal), host group, geographical origin, and virulence profile. Among the group B2-derived clonal groups the O6:K2:H1 clade appeared basal. Within group D, "clonal group A" and the O15:K52:H1 clonal group were consistently placed with ECOR 47 and ECOR 44, respectively, as nearest neighbors. These findings clarify phylogenetic relationships among key ExPEC clonal groups but also emphasize that recombination appears to obscure the oldest evolutionary relationships, despite extensive targeted sequencing and use of a wide range of analysis techniques.

Animals↗

Performance of maximum parsimony and likelihood phylogenetics when evolution is heterogeneous.

All inferences in comparative biology depend on accurate estimates of evolutionary relationships. Recent phylogenetic analyses have turned away from maximum parsimony towards the probabilistic techniques of maximum likelihood and bayesian Markov chain Monte Carlo (BMCMC). These probabilistic techniques represent a parametric approach to statistical phylogenetics, because their criterion for evaluating a topology--the probability of the data, given the tree--is calculated with reference to an explicit evolutionary model from which the data are assumed to be identically distributed. Maximum parsimony can be considered nonparametric, because trees are evaluated on the basis of a general metric--the minimum number of character state changes required to generate the data on a given tree--without assuming a specific distribution. The shift to parametric methods was spurred, in large part, by studies showing that although both approaches perform well most of the time, maximum parsimony is strongly biased towards recovering an incorrect tree under certain combinations of branch lengths, whereas maximum likelihood is not. All these evaluations simulated sequences by a largely homogeneous evolutionary process in which data are identically distributed. There is ample evidence, however, that real-world gene sequences evolve heterogeneously and are not identically distributed. Here we show that maximum likelihood and BMCMC can become strongly biased and statistically inconsistent when the rates at which sequence sites evolve change non-identically over time. Maximum parsimony performs substantially better than current parametric methods over a wide range of conditions tested, including moderate heterogeneity and phylogenetic problems not normally considered difficult.

Bayes Theorem↗

Molecular phylogenetics and evolution of maternal care in Membracine treehoppers.

The treehopper subfamily Membracinae (Insecta: Hemiptera: Membracidae) comprises the majority of genera and species diversity in the New World tropics. These treehoppers exhibit a wide range of social behaviors, making them an excellent group for studying patterns of social evolution in insects. However, to date the tribal and generic relationships have remained unclear. We reconstructed the phylogeny of the Membracinae using a combined mitochondrial (COI, COII, tRNA-Leu, and 12S) and nuclear (Wg) gene data set. A total of 2608 aligned nucleotide sites were obtained for 112 species, representing 25 of 38 currently recognized genera and all four tribes. A strict consensus of five equally parsimonious trees recovered the subfamily and three of its four tribes. The majority rule consensus tree derived from the Bayesian analyses based on the GTR+I+G and mixed-models recovered many clades shared with the parsimony trees and is identical to the single best tree inferred from maximum likelihood analysis, aside from the rearrangement of one node. A comparison of mitochondrial and nuclear genes indicated that Wg provided higher consistency index (CI), data decisiveness (DD), partitioned Bremer support (PBS) than any of the mitochondrial genes analyzed. The combined mitochondrial and nuclear DNA provide strong support for the monophyly of the subfamily and three of its four tribes (Aconophorini, Hoplophorionini, and Hypsoprorini). Membracini is paraphyletic with respect to Hoplophorionini and contains two lineages, the Membracini sensu strictu and the newly resurrected tribe Bolbonotini. Our analyses show that there is a strong phylogenetic component to the evolution of maternal care. Given the widespread occurrence of maternal care within the subfamily, this trait is estimated to have < or = 3 origins, two reversals, and one loss. Our results suggest that the evolution of maternal care in insects may not be as evolutionarily labile as previously thought.

Animals↗

High intron sequence conservation across three mammalian orders suggests functional constraints.

Several studies have demonstrated high levels of sequence conservation in noncoding DNA compared between two species (e.g., human and mouse), and interpreted this conservation as evidence for functional constraints. If this interpretation is correct, it suggests the existence of a hidden class of abundant regulatory elements. However, much of the noncoding sequence conserved between two species may result from chance or from small-scale heterogeneity in mutation rates. Stronger inferences are expected from sequence comparisons using more than two taxa, and by testing for spatial patterns of conservation in addition to primary sequence similarity. We used a Bayesian local alignment method to compare approximately 10 kb of intron sequence from nine genes in a pairwise manner between human, whale, and seal to test whether the degree and pattern of conservation is consistent with neutral divergence. Comparison of the three sets of conserved gapless pairwise blocks revealed the following patterns: The proportion of identical intron nucleotides averaged 47% in pairwise comparisons and 28% across the three taxa. Proportions of conserved sequence were similar in unique sequence and general mammalian repetitive elements. We simulated sequence evolution under a neutral model using published estimates of substitution rate heterogeneity for noncoding DNA and found pairwise identity at 33% and three-taxon identity at 16% of nucleotide sites. Spatial patterns of primary sequence conservation were also nonrandomly distributed within introns. Overall, segments of intron sequence closer to flanking exons were significantly more conserved than interior intron sequence. This level of intron sequence conservation is above that expected by chance and strongly suggests that intron sequences are playing a larger functional role in gene regulation than previously realized.

Animals↗

Parental and sib likelihoods in genealogy reconstruction.

Estimation of genealogical relationships from genetic data provides an approach to answering many questions of population biology. In this estimation problem, previous work has shown that bilateral relatives such as full sibs may be more likely parents than the true parent individuals. This paper investigates the source of this paradox, and the circumstances under which it may arise. Alternative approaches to inferring parentage are proposed; these involve analysis of the distributions of log-likelihood statistics and of the bivariate distribution of sib and parent log-likelihoods. A Bayesian approach may also be superposed on the likelihood analysis, enabling any prior knowledge of the population to be incorporated.

Alleles↗

Clinical simulation using context-sensitive temporal probability models.

We present a language for representing context-sensitive temporal probabilistic knowledge. Context constraints allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language and an implemented algorithm (BNG) that generates Bayesian networks to compute the posterior probabilities of queries. We illustrate the use of the BNG system by applying it to the problem of modeling the effects of medications and other interventions on the condition of a patient in cardiac arrest.

Artificial Intelligence↗

An introduction to Bayesian hierarchical models with an application in the theory of signal detection.

Although many nonlinear models of cognition have been proposed in the past 50 years, there has been little consideration of corresponding statistical techniques for their analysis. In analyses with nonlinear models, unmodeled variability from the selection of items or participants may lead to asymptotically biased estimation. This asymptotic bias, in turn, renders inference problematic. We show, for example, that a signal detection analysis of recognition memory data leads to asymptotic underestimation of sensitivity. To eliminate asymptotic bias, we advocate hierarchical models in which participant variability, item variability, and measurement error are modeled simultaneously. By accounting for multiple sources of variability, hierarchical models yield consistent and accurate estimates of participant and item effects in recognition memory. This article is written in tutorial format; we provide an introduction to Bayesian statistics, hierarchical modeling, and Markov chain Monte Carlo computational techniques.

Bayes Theorem↗

A molecular phylogeny of eurytomid wasps inferred from DNA sequence data of 28S, 18S, 16S, and COI genes.

Using partial DNA sequence data from nuclear 28S and 18S genes and mitochondrial 16S and COI genes, we reconstructed a phylogeny of the family Eurytomidae. Both maximum parsimony and Bayesian methods were employed. The analysis revealed a significant incongruence between the mitochondrial genes and the nuclear genes, and we chose the results from the nuclear genes as our preferred hypothesis. Our phylogeny suggested that the family Eurytomidae is not a monophyletic group; neither are the genera Eurytoma and Bruchophagus. The monophyly of genera Sycophila and Plutarchia was well supported, as was the close association of the genera Aiolomorphus, Tenuipetiolus, Bephratelloides, and Phylloxeroxenus. Our phylogeny also revealed an anticipated pattern, in which species groups from the genera Eurytoma and Bruchophagus are often more closely related to other small genera than to other species groups of the same genus. Subsequent taxonomic revisions include elevating the subfamily Rileyinae to a family status and the divisions of the genera Eurytoma and Bruchophagus.

Animals↗

Assessing the combined effect of asbestos exposure and smoking on lung cancer: a Bayesian approach.

We review the literature on the combined association between lung cancer and two environmental exposures, asbestos exposure and smoking, and explore a Bayesian approach to assess evidence of interaction between the exposures. The meta-analysis combines separate indices of additive and multiplicative relationships and multivariate relative risk estimates. By making inferences on posterior probabilities we can explore both the form and strength of interaction. This analysis may be more informative than providing evidence to support one relation over another on the basis of statistical significance. Overall, we find evidence for a more than additive and less than multiplicative relation.

Asbestos↗

Evidence-based sample size calculations based upon updated meta-analysis.

Meta-analyses of randomized controlled trials (RCTs) provide the highest level of evidence regarding the effectiveness of interventions and as such underpin much of evidence-based medicine. Despite this, meta-analyses are usually produced as observational by-products of the existing literature, with no formal consideration of future meta-analyses when individual trials are being designed. Basing the sample size of a new trial on the results of an updated meta-analysis which will include it, may sometimes make more sense than powering the trial in isolation. A framework for sample size calculation for a future RCT based on the results of a meta-analysis of the existing evidence is presented. Both fixed and random effect approaches are explored through an example. Bayesian Markov Chain Monte Carlo simulation modelling is used for the random effects model since it has computational advantages over the classical approach. Several criteria on which to base inference and hence power are considered. The prior expectation of the power is averaged over the prior distribution for the unknown true treatment effect. An extension to the framework allowing for consideration of the design for a series of new trials is also presented. Results suggest that power can be highly dependent on the statistical model used to meta-analyse the data and even very large studies may have little impact on a meta-analysis when there is considerable between study heterogeneity. This raises issues regarding the appropriateness of the use of random effect models when designing and drawing inferences across a series of studies.

Anti-Bacterial Agents↗

Biochemical networks with uncertain parameters.

The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the 'dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients.

Animals↗

Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics.

Bayesian experimental design is investigated for Bayesian analysis of nonlinear mixed-effects models. Existence of the posterior risk for parameter estimation is shown. When the same prior distribution is used for both design and inference, existence of the preposterior risk for design is also proven. If the prior distribution used in design is different from that used for inference, sufficient conditions are established for existence of the preposterior risk for design. A case study of design for an experiment in population HIV dynamics is provided.

Bayes Theorem↗

Phylogeny, biogeography, and molecular dating of cornelian cherries (Cornus, Cornaceae): tracking Tertiary plant migration.

Data from four DNA regions (rbcL, matK, 26S rDNA, and ITS) as well as extant and fossil morphology were used to reconstruct the phylogeny and biogeographic history of an intercontinentally disjunct plant group, the cornelian cherries of Cornus (dogwoods). The study tests previous hypotheses on the relative roles of two Tertiary land bridges, the North Atlantic land bridge (NALB) and the Bering land bridge (BLB), in plant migration across continents. Three approaches, the Bayesian, nonparametric rate smoothing (NPRS), and penalized likelihood (PL) methods, were employed to estimate the times of geographic isolations of species. Dispersal and vicariance analysis (DIVA) was performed to infer the sequence and directionality of biogeographic pathways. Results of phylogenetic analyses suggest that among the six living species, C. sessilis from western North America represents the oldest lineage, followed by C. volkensii from Africa. The four Eurasian species form a clade consisting of two sister pairs, C. mas-C. officinalis and C. chinensis-C. eydeana. Results of DIVA and data from fossils and molecular dating indicate that the cornelian cherry subgroup arose in Europe as early as the Paleocene. Fossils confirm that the group was present in North America by the late Paleocene, consistent with the DIVA predictions that, by the end of the Eocene, it had diversified into several species and expanded its distribution to North America via the NALB and to Africa via the last direct connection between Eurasia and Africa prior to the Miocene, or via long-distance dispersal. The cornelian cherries in eastern Asia appear to be derived from two independent dispersal events from Europe. These events are inferred to have occurred during the Oligocene and Miocene. This study supports the hypothesis that the NALB served as an important land bridge connecting the North American and European floras, as well as connecting American and African floras via Europe during the early Tertiary.

Base Sequence↗

The phylogenetic relationships among non-diplomystid catfishes as inferred from mitochondrial cytochrome b sequences; the search for the ictalurid sister taxon (Otophysi: Siluriformes).

The relationships among families of catfishes are poorly understood and have yet to be the subject of a comprehensive investigation with molecular data. Existing phylogenetic hypotheses are based on morphological data and incompletely resolved. This study analyzed complete sequences of mitochondrial gene cytochrome b for 170 species from 29 of 33 extant families, and focused on the relationships of Ictaluridae to other catfishes. In addition to previous phylogenetic studies, the fossil record, paleogeography, biogeography, and distribution of extant catfish families collectively suggest the location (if extant) of the ictalurid sister taxon to be Northern or Eastern Asia. Of the extant catfishes currently native to this area and included in this analysis, parsimony and Bayesian likelihood analyses recovered Cranoglanis bouderius as the most proximal sister taxon of Ictaluridae. Seemingly, ictalurids and cranoglanidids represent another biogeographic component linking freshwater fishes of North America and eastern Asia, e.g., catostomids and paddlefishes. The results coupled with present-day catfish distributions and inferences from the fossil record collectively suggest the ancestor of Ictaluridae to have invaded freshwaters of North America at the close of the Cretaceous through northeastern Asia and northwestern North America. Other superfamilial nodes supported the results of previous phylogenetic studies of narrower taxonomic scope. Several novel relationships were recovered (including a clade composed of Pimelodidae, Pseudopimelodidae, and Heptapteridae) and these along with sources of systematic error are discussed. A broad sampling of Bagridae permitted an examination of intergeneric relationships within this family and in light of recent morphological and molecular studies.

Animals↗