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PubMed1991

Experimental design for drug development: a Bayesian approach.

The Bayesian approach to inference and decision making provides an integrated way of addressing the various aspects of drug development, from the early preclinical study of compounds through the clinical and postmarketing phases. In particular, it provides a natural, convenient way for choosing among experimental designs. An essential aspect of the process of evaluating design strategies is the ability to calculate predictive probabilities of potential results. I describe a Bayesian approach to experimental design and illustrate it by considering a particular type of clinical trial. Also, I compare Bayesian and classical statistical attitudes toward design.

Bayes Theorem↗

PubMed2006

Differentiation among populations with migration, mutation, and drift: implications for genetic inference.

Populations may become differentiated from one another as a result of genetic drift. The amounts and patterns of differentiation at neutral loci are determined by local population sizes, migration rates among populations, and mutation rates. We provide exact analytical expressions for the mean, variance, and covariance of a stochastic model for hierarchically structured populations subject to migration, mutation, and drift. In addition to the expected correlation in allele frequencies among populations in the same geographic region, we demonstrate that there is a substantial correlation in allele frequencies among regions at the top level of the hierarchy. We propose a hierarchical Bayesian model for inference of Wright's F-statistics in a two-level hierarchy in which we estimate the among-region correlation in allele frequencies by substituting replication across loci for replication across time. We illustrate the approach through an analysis of human microsatellite data, and we show that approaches ignoring the among-region correlation in allele frequencies underestimate the amount of genetic differentiation among major geographic population groups by approximately 30%. Finally, we discuss the implications of these results for the use and interpretation of F-statistics in evolutionary studies.

Animal Migration↗

PubMed1995

A Bayesian framework for understanding texture segmentation in the primary visual cortex.

This paper presents a mathematical theory for understanding the computations involved in texture segmentation in the primary visual cortex. We propose that texture segmentation is a part of the early visual system's overall strategy to infer surfaces of objects in a visual scene. Based on this insight, we use the Bayesian inference paradigm to formulate the texture segmentation problem into a maximum a posteriori surface inference problem. The dynamical system for finding the optimal solution of this problem can be characterized by two concurrent and interactive processes: a gradual sharpening of the boundary signals and a simultaneous smoothing of the surface signals. The behavior of these dynamical processes was studied using both analytical and computational methods. We present some computational results and mathematical predictions. This theory suggests a novel framework for understanding the functional roles of the complex cells in the primary visual cortex.

Bayes Theorem↗

PubMed1999

Meta-analysis: formulating, evaluating, combining, and reporting.

Meta-analysis involves combining summary information from related but independent studies. The objectives of a meta-analysis include increasing power to detect an overall treatment effect, estimation of the degree of benefit associated with a particular study treatment, assessment of the amount of variability between studies, or identification of study characteristics associated with particularly effective treatments. This article presents a tutorial on meta-analysis intended for anyone with a mathematical statistics background. Search strategies and review methods of the literature are discussed. Emphasis is focused on analytic methods for estimation of the parameters of interest. Three modes of inference are discussed: maximum likelihood; restricted maximum likelihood, and Bayesian. Finally, software for performing inference using restricted maximum likelihood and fully Bayesian methods are demonstrated. Methods are illustrated using two examples: an evaluation of mortality from prophylactic use of lidocaine after a heart attack, and a comparison of length of hospital stay for stroke patients under two different management protocols.

Anti-Arrhythmia Agents↗

PubMed1998

Hailfinder. Tools for and experiences with Bayesian normative modeling.

Bayes Nets (BNs) and Influence Diagrams (IDs), new tools that use graphic user interfaces to facilitate representation of complex inference and decision structures, will be the core elements of new computer technologies that will make the 21st century the Century of Bayes. BNs are a way of representing a set of related uncertainties. They facilitate Bayesian inference by separating structural information from parameters. Hailfinder is a BN that predicts severe summer weather in Eastern Colorado. Its design led to a number of novel ideas about how to build such BNs. Issues addressed included representation of spatial location, categorization of days, system boundaries, pruning, and methods for eliciting and checking on the appropriateness of conditional probabilities. The technology of BNs is improving rapidly. Especially important is the emergence of ways of reusing fragments of BNs. BNs and IDs are not just important design tools; they also represent a major enhancement of the understanding about how important intellectual tasks typically performed by people should and can be performed.

Bayes Theorem↗

PubMed2004

RPB2 gene phylogeny in flowering plants, with particular emphasis on asterids.

Two, apparently functional, paralogues of the RPB2 gene, which encodes the second largest subunit of RNA polymerase II, are shown to be present in two major groups of asterid plants. Although all other land plants surveyed so far have been found to have only one of these two copies, the RPB2 gene phylogeny inferred from the 3' half of the gene for 35 angiosperm taxa and six other land plants indicates that the duplication of the RPB2 gene occurred earlier than the time for origin of the asterid group, probably near the origin of "core eudicots." The d copy is present in all plants which are unambiguously assigned to the core eudicots, whereas the I copy is retained only in the lamiid clade, Ericales, and Escallonia, all belonging to the asterid group of plants. Both parsimony and likelihood analyses of sequences from the 3' half of the gene give strong bootstrap support for these conclusions. There is no support for monophyly of the taxa having both copies. Thus, numerous losses of one of the copies must be inferred. Structurally, both paralogues appear functional, and transcription is demonstrated for both copies. In the lamiid group, the d copy has lost introns 18-23. The well supported phylogenetic relationships implied by the RPB2 gene phylogeny are largely congruent with well supported phylogenetic hypotheses based on other sequence data. However, Ilex, usually assigned to the campanuliid clade, is instead supported as being a member of the lamiid clade, both from sequence data and the presence of an I copy as well as the loss of introns 18-23 in the d copy. Escallonia, supported as a member of the campanuliid clade both by RPB2-d-sequences and previously published DNA sequence data, has all the introns 18-23 in its d copy, as do all other members studied from the campanuliid group. We used the Markov Chain Monte Carlo (MCMC) approach of the MrBayes program to implement Maximum Likelihood bootstrapping. Under the same model of evolution, bootstrapping frequencies are significantly lower than the Bayesian posterior probabilities inferred from the MCMC chain.

Gene Dosage↗

PubMed1996

Bayesian imputation of predictive values when covariate information is available and gold standard diagnosis is unavailable.

We suggest a conceptually simple Bayesian approach to inferences about the conditional probability of a specimen being infection-free given the outcome of a diagnostic test and covariate information. The approach assumes that the infection state of a specimen is not observable but uses the outcomes of a second test in conjunction with those of the first, that is, dual testing data. Dual testing procedures are often employed in clinical laboratories to assure that samples are not contaminated or to increase the likelihood of correct diagnoses. Using the CD4 count and a proxy for risk behavior as covariates, we apply the method to obtain inferences about the conditional probability of an individual being HIV-1 infection-free given the individual's covariates and a negative outcome with the standard enzyme-linked immunoad-sorbent assay/Western blotting test for HIV-1 detection. Inferences combine data from two studies where specimens were tested with the standard and with the more sensitive polymerase chain reaction test.

Algorithms↗

PubMed2005

Analysing child mortality in Nigeria with geoadditive discrete-time survival models.

Child mortality reflects a country's level of socio-economic development and quality of life. In developing countries, mortality rates are not only influenced by socio-economic, demographic and health variables but they also vary considerably across regions and districts. In this paper, we analysed child mortality in Nigeria with flexible geoadditive discrete-time survival models. This class of models allows us to measure small-area district-specific spatial effects simultaneously with possibly non-linear or time-varying effects of other factors. Inference is fully Bayesian and uses computationally efficient Markov chain Monte Carlo (MCMC) simulation techniques. The application is based on the 1999 Nigeria Demographic and Health Survey. Our method assesses effects at a high level of temporal and spatial resolution not available with traditional parametric models, and the results provide some evidence on how to reduce child mortality by improving socio-economic and public health conditions.

Adolescent↗

PubMed2006

Estimating measures of diagnostic accuracy when some covariate information is missing.

Many biomedical data sets are concerned with relating the result of screening procedure(s) for a clinical event to the occurrence of that event. The effect of risk factors on measures of accuracy such as positive predictive value and negative predictive value is of great interest for clinicians. In this paper we propose a generic approach to estimate these measures of accuracy in the setting where an explanatory model has been fitted to the joint screening and event outcome data but information on one or more risk factors in the model is not available. We refer to these as conditional rates, i.e. rates conditioned on only a subset of risk factors. We argue that, based upon the joint distribution of the event outcome, the screening result and the risk factor occurrence, a formal expression for such a rate can be obtained. This expression is a function of model parameters and thus can be estimated once the model has been fitted. Inference within the Bayesian framework is particularly attractive since simulation based model fitting straightforwardly yields samples from the posterior distribution of any conditional rate of interest. We perform a simulation study to compare these estimated conditional rates with frequently used ad hoc estimates. Differences can be substantial. We also illustrate the proposed methodology to compute conditional positive predictive value for a screening mammography data set. The proposed approach is also applicable when there are multiple diagnostic screening test outcomes.

Bayes Theorem↗

PubMed2005

The complete mitochondrial genome of a tree frog, Polypedates megacephalus (Amphibia: Anura: Rhacophoridae), and a novel gene organization in living amphibians.

In this study, we have determined the complete sequence of the mitochondrial genome of an Old World tree frog Polypedates megacephalus (Anura: Rhacophoridae) by using a long polymerase chain reaction (PCR) technique and shotgun strategy of sequencing. The entire mtDNA sequence is 16,473 nt long with a novel mitogenomic gene organization in amphibians. Unlike other neobatrachian frogs, the transfer ribonucleic acid (tRNA)-Leu(CUN) and tRNA-Thr genes exchange their positions in P. megacephalus and form a Thr-Leu(CUN)-Pro-Phe tRNA gene tetrad. Moreover, we found that the ATP8 gene was replaced by a noncoding sequence of 853 nt long and that the ND5 gene was absent in the new mitogenome. These peculiar features of P. megacephalus mtDNA were further studied among related anuran species by PCR amplification. The new sequence data was used to assess the phylogenetic relationships of the three living amphibian orders using neighbor-joining, maximum likelihood, and Bayesian methods. In agreement with most morphological studies, phylogenetic analyses of a whole mitochondrial genome data set suggest a close relationship between salamanders and frogs. Moreover, using a molecular clock-independent Bayesian approach for inferring dating information from molecular phylogenies, we have provided a rough timescale for living amphibian evolution. This timescale provides a working framework for future paleontological researches on amphibian evolution and improves our understanding of the evolutionary history of modern amphibians.

Animals↗

PubMed2026

Lineage-specific transmission and spatial clustering of Mycobacterium tuberculosis in Kaohsiung, Taiwan, in 2019-23: a population-based genomic study.

BACKGROUND: The epidemiology of tuberculosis in Taiwan has been influenced by the introduction of multiple Mycobacterium tuberculosis lineages and by the ageing of the population. We conducted a population-based study to investigate M tuberculosis transmission in Kaohsiung, a city in southern Taiwan. METHODS: In this study, we performed whole-genome sequencing (WGS) of M tuberculosis isolates from all culture-positive cases of tuberculosis notified in Kaohsiung between Jan 1, 2019 and Dec 31, 2023. We obtained routine epidemiological data for each case collected through the national tuberculosis control programme. We characterised the lineage composition of the isolate collection and evaluated genomic clustering of isolates, defined as a difference of 12 or fewer single-nucleotide polymorphisms. Univariable and multivariable logistic regression analyses were performed to estimate the odds of a case belonging to a genomic cluster based on host factors (age, sex, sputum smear status, and residential region) and pathogen factors (drug resistance status and strain lineage). Spatial aggregation of large genomic clusters (including greater than or equal to ten isolates) was assessed using a non-parametric statistical clustering method. We used a Bayesian transmission tree inference method to explore the patterns of age-dependent transmission. FINDINGS: During the study period, 5667 tuberculosis cases were notified in Kaohsiung, 4916 (86·7%) of which were culture-positive. Of these 4916 cases, whole-genome sequencing was successfully performed for 4168 (84·8%) isolates. 1219 (29·2%) of 4168 individuals were female and 2947 (70·7%) were male; the median age was 69·7 years (IQR 57·4-80·7). The dominant lineages were lineage 1 (1749 [42·0%] of 4168 isolates), lineage 2 (1510 [36·2%]), and lineage 4 (905 [21·7%]). 1069 (25·6%) of 4168 were genomically linked and formed 287 clusters. Lineage 2 isolates had higher odds (aOR 2·15 [95% CI 1·80-2·52]) than lineage 1 isolates of genomic clustering across all regions, whereas lineage 4 isolates had a significantly higher risk (2·75 [1·16-6·89]) of genomic clustering than lineage 1 only in the rural northeast region, inhabited primarily by indigenous populations. Spatial clustering analysis corroborated these lineage-region interactions. Although younger adults (<35 years) had the highest individual-level odds (5·64 [4·16-7·68]) of clustering in the logistic regression analysis compared with those aged 80 years or older, the transmission inference indicated that individuals aged 55-74 years were responsible for a greater proportion of inferred transmission events, contributing 50·8% of all transmission events. INTERPRETATION: This sequencing study revealed that older adults (aged ≥65 years) might have played a substantial and under-recognised role in the transmission of tuberculosis in Taiwan. The lineage-specific clustering and spatial patterns suggested that both pathogen characteristics and host demographics shaped tuberculosis transmission dynamics. These findings support the use of integrated genomic surveillance to guide precision tuberculosis control and motivate further research on age-specific transmission pathways and targeted interventions to advance tuberculosis elimination efforts. FUNDING: Taiwan National Health Research Institutes and Taiwan National Science and Technology Council.

Mycobacterium tuberculosis↗

PubMed2005

Bayesian fMRI time series analysis with spatial priors.

We describe a Bayesian estimation and inference procedure for fMRI time series based on the use of General Linear Models (GLMs). Importantly, we use a spatial prior on regression coefficients which embodies our prior knowledge that evoked responses are spatially contiguous and locally homogeneous. Further, using a computationally efficient Variational Bayes framework, we are able to let the data determine the optimal amount of smoothing. We assume an arbitrary order Auto-Regressive (AR) model for the errors. Our model generalizes earlier work on voxel-wise estimation of GLM-AR models and inference in GLMs using Posterior Probability Maps (PPMs). Results are shown on simulated data and on data from an event-related fMRI experiment.

Bayes Theorem↗

PubMed2006

Spatial epidemiology of human schistosomiasis in Africa: risk models, transmission dynamics and control.

This paper reviews recent studies on the spatial epidemiology of human schistosomiasis in Africa. The integrated use of geographical information systems, remote sensing and geostatistics has provided new insights into the ecology and epidemiology of schistosomiasis at a variety of spatial scales. Because large-scale patterns of transmission are influenced by climatic conditions, an increasing number of studies have used remotely sensed environmental data to predict spatial distributions, most recently using Bayesian methods of inference. Such data-driven approaches allow for a more rational implementation of intervention strategies across the continent. It is suggested that improved incorporation of transmission dynamics into spatial models and assessment of uncertainties inherent in data and modelling approaches represent important future research directions.

Africa↗

PubMed2003

A comparison of bayesian methods for haplotype reconstruction from population genotype data.

In this report, we compare and contrast three previously published Bayesian methods for inferring haplotypes from genotype data in a population sample. We review the methods, emphasizing the differences between them in terms of both the models ("priors") they use and the computational strategies they employ. We introduce a new algorithm that combines the modeling strategy of one method with the computational strategies of another. In comparisons using real and simulated data, this new algorithm outperforms all three existing methods. The new algorithm is included in the software package PHASE, version 2.0, available online (http://www.stat.washington.edu/stephens/software.html).

Algorithms↗

PubMed2006

Longitudinal population analysis of dual infection with recombination in two strains of HIV type 1 subtype B in an individual from a Phase 3 HIV vaccine efficacy trial.

This study documents a case of coinfection (simultaneous infection of an individual with two or more strains) of two HIV-1 subtype B strains in an individual from a Phase 3 HIV-1 vaccine efficacy trial, conducted in North American and the Netherlands. We examined 86 full-length gp120 (env) gene sequences from this individual collected from nine different time points over a 20-month period. We estimated evolutionary relationships using maximum likelihood and Bayesian methods and inferred recombination breakpoints and recombinant sequences using phylogenetic and substitutional methods. These analyses identified two strongly supported monophyletic clades (clades A and B) of 14 and 69 sequences each and a small paraphyletic recombinant clade of three sequences. We then studied the genetic characteristics of these lineages by comparing estimates of genetic diversity generated by mutation and recombination and adaptive selection within a coalescent and maximum likelihood framework. Our results suggest significant differences on the evolutionary dynamics of these strains. We then discuss the implications of these results for vaccine development.

AIDS Vaccines↗

PubMed2000

Assessing the effect of an influenza vaccine in an encouragement design.

Many randomized experiments suffer from noncompliance. Some of these experiments, so-called encouragement designs, can be expected to have especially large amounts of noncompliance, because encouragement to take the treatment rather than the treatment itself is randomly assigned to individuals. We present an extended framework for the analysis of data from such experiments with a binary treatment, binary encouragement, and background covariates. There are two key features of this framework: we use an instrumental variables approach to link intention-to-treat effects to treatment effects and we adopt a Bayesian approach for inference and sensitivity analysis. This framework is illustrated in a medical example concerning the effects of inoculation for influenza. In this example, the analyses suggest that positive estimates of the intention-to-treat effect need not be due to the treatment itself, but rather to the encouragement to take the treatment: the intention-to-treat effect for the subpopulation who would be inoculated whether or not encouraged is estimated to be approximately as large as the intention-to-treat effect for the subpopulation whose inoculation status would agree with their (randomized) encouragement status whether or not encouraged. Thus, our methods suggest that global intention-to-treat estimates, although often regarded as conservative, can be too coarse and even misleading when taken as summarizing the evidence in the data for the effects of treatments.

Journal Article↗

PubMed2005

Bayesian latent variable models for mixed discrete outcomes.

In studies of complex health conditions, mixtures of discrete outcomes (event time, count, binary, ordered categorical) are commonly collected. For example, studies of skin tumorigenesis record latency time prior to the first tumor, increases in the number of tumors at each week, and the occurrence of internal tumors at the time of death. Motivated by this application, we propose a general underlying Poisson variable framework for mixed discrete outcomes, accommodating dependency through an additive gamma frailty model for the Poisson means. The model has log-linear, complementary log-log, and proportional hazards forms for count, binary and discrete event time outcomes, respectively. Simple closed form expressions can be derived for the marginal expectations, variances, and correlations. Following a Bayesian approach to inference, conditionally-conjugate prior distributions are chosen that facilitate posterior computation via an MCMC algorithm. The methods are illustrated using data from a Tg.AC mouse bioassay study.

Acrylates↗

PubMed1998

Bayesian mapping of multiple quantitative trait loci from incomplete inbred line cross data.

A novel fine structure mapping method for quantitative traits is presented. It is based on Bayesian modeling and inference, treating the number of quantitative trait loci (QTLs) as an unobserved random variable and using ideas similar to composite interval mapping to account for the effects of QTLs in other chromosomes. The method is introduced for inbred lines and it can be applied also in situations involving frequent missing genotypes. We propose that two new probabilistic measures be used to summarize the results from the statistical analysis: (1) the (posterior) QTL intensity, for estimating the number of QTLs in a chromosome and for localizing them into some particular chromosomal regions, and (2) the locationwise (posterior) distributions of the phenotypic effects of the QTLs. Both these measures will be viewed as functions of the putative QTL locus, over the marker range in the linkage group. The method is tested and compared with standard interval and composite interval mapping techniques by using simulated backcross progeny data. It is implemented as a software package. Its initial version is freely available for research purposes under the name Multimapper at URL http://www.rni.helsinki.fi/mjs.

Bayes Theorem↗