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A new summarization method for Affymetrix probe level data.

MOTIVATION: We propose a new model-based technique for summarizing high-density oligonucleotide array data at probe level for Affymetrix GeneChips. The new summarization method is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. Thereafter, the RNA concentration is estimated from the model. In contrast to previous methods our new method called 'Factor Analysis for Robust Microarray Summarization (FARMS)' supplies both P-values indicating interesting information and signal intensity values. RESULTS: We compare FARMS on Affymetrix's spike-in and Gene Logic's dilution data to established algorithms like Affymetrix Microarray Suite (MAS) 5.0, Model Based Expression Index (MBEI), Robust Multi-array Average (RMA). Further, we compared FARMS with 43 other methods via the 'Affycomp II' competition. The experimental results show that FARMS with default parameters outperforms previous methods if both sensitivity and specificity are simultaneously considered by the area under the receiver operating curve (AUC). We measured two quantities through the AUC: correctly detected expression changes versus wrongly detected (fold change) and correctly detected significantly different expressed genes in two sets of arrays versus wrongly detected (P-value). Furthermore FARMS is computationally less expensive then RMA, MAS and MBEI. AVAILABILITY: The FARMS R package is available from http://www.bioinf.jku.at/software/farms/farms.html. SUPPLEMENTARY INFORMATION: http://www.bioinf.jku.at/publications/papers/farms/supplementary.ps

Algorithms↗

Development and evaluation of a Bayesian pharmacokinetic estimator and optimal, sparse sampling strategies for ceftazidime.

Data were gathered during an activity-controlled trial in which seriously ill, elderly patients were randomized to receive intravenous ceftazidime or ciprofloxacin and for which adaptive feedback control of drug concentrations in plasma and activity profiles was prospectively performed. The adaptive feedback control algorithm for ceftazidime used an initial population model, a maximum a posteriori (MAP)-Bayesian pharmacokinetic parameter value estimator, and an optimal, sparse sampling strategy for ceftazidime that had been derived from data in the literature obtained from volunteers. Iterative two-stage population pharmacokinetic analysis was performed to develop an unbiased MAP-Bayesian estimator and updated optimal, sparse sampling strategies. The final median values of the population parameters were follows: the volume of distribution of the central compartment was equal to 0.249 liter/kg, the volume of distribution of the peripheral compartment was equal to 0.173 liter/kg, the distributional clearance between the central and peripheral compartments was equal to 0.2251 liter/h/kg, the slope of the total clearance (CL) versus the creatinine clearance (CLCR) was equal to 0.000736 liter/h/kg of CL/1 ml/min/1.73 m2 of CLCR, and nonrenal clearance was equal to + 0.00527 liter/h/kg. Optimal sampling times were dependent on CLCR; for CLCR of > or = 30 ml/min/1.73 m2, the optimal sampling times were 0.583, 3.0, 7.0, and 16.0 h and, for CLCR of < 30 ml/min/1.73 m2, optimal sampling times were 0.583, 4.15, 11.5, and 24.0 h. The study demonstrates that because pharmacokinetic information from volunteers may often not be reflective of specialty populations such as critically ill elderly individuals, iterative two-stage population pharmacokinetic analysis, MAP-Bayesian parameter estimation, and optimal, sparse sampling strategy can be important tools in characterizing their pharmacokinetics.

Adult↗

Inference in linkage analysis of multifactorial traits using recombinant inbred strains of mice.

Recombinant inbred strains have been shown to be important tools for segregation and linkage analysis of multifactorial traits. Tests of association have been used as robust methods of linkage detection, however, guidelines for forming inferences from significance levels have not been generally available. In this paper, lessons learned from a Bayesian statistical approach to linkage analysis of Mendelian traits have been applied to studies of multifactorial traits. Criteria for detection of linkage based on Bonferroni's correction for multiple testing are also discussed.

Animals↗

Analysis of DNA multilocus profiles in a paternity case in which the child's profile may be partial.

This report describes a simple approach to multilocus paternity analysis for cases where the child's sample may be inadequate leading to a partial profile. A specimen calculation is given. A previous paper described how the various band sharing configurations in the DNA multilocus profiles of a mother-child-putative father trio could be combined in a comprehensive mathematical analysis to give an overall Bayesian likelihood ratio. In that paper, it was assumed that all three members of the trio gave full DNA profiles. In some cases that assumption may not be valid but it is possible to extend the analysis to allow for partial profiles. This paper demonstrates how this may be done by considering the case where the child's profile may be partial for one reason or another. A specimen calculation is given.

Bayes Theorem↗

[Data analysis by statistical models].

The basic idea for the realization of effective statistical data analysis is illustrated with an example. The use of statistical models is explained and the feasibility of objective comparison of the models by an information criterion AIC is demonstrated. Further, the possibility of practical use of Bayesian models for complex data analysis is explained. Finally, the necessity of cooperation between the experts of respective fields and statisticians for further development of statistical data analysis is mentioned.

Adult↗

Random walk models for bayesian clustering of gene expression profiles.

The analysis of gene expression temporal profiles is a topic of increasing interest in functional genomics. Model-based clustering methods are particularly interesting because they are able to capture the dynamic nature of these data and to identify the optimal number of clusters. We have defined a new Bayesian method that allows us to cope with some important issues that remain unsolved in the currently available approaches: the presence of time dislocations in gene expression, the non-stationarity of the processes generating the data, and the presence of data collected on an irregular temporal grid. Our method, which is based on random walk models, requires only mild a priori assumptions about the nature of the processes generating the data and explicitly models inter-gene variability within each cluster. It has first been validated on simulated datasets and then employed for the analysis of a dataset relative to serum-stimulated fibroblasts. In all cases, the results have been promising, showing that the method can be helpful in functional genomics research.

Journal Article↗

Genetic analysis of the age at menopause by using estimating equations and Bayesian random effects models.

Multi-wave self-report data on age at menopause in 2182 female twin pairs (1355 monozygotic and 827 dizygotic pairs), were analysed to estimate the genetic, common and unique environmental contribution to variation in age at menopause. Two complementary approaches for analysing correlated time-to-onset twin data are considered: the generalized estimating equations (GEE) method in which one can estimate zygosity-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modelled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the freeware package BUGS.

Adult↗

Population toxicokinetic analysis of 2,3,7,8-tetrachlorodibenzo-p-dioxin using Bayesian techniques.

Understanding the kinetics of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) concentrations in humans is an important step for TCDD cancer risk assessment. In this paper longitudinal series of serum TCDD concentration measurements on U.S. veterans of the Vietnam war, who were exposed to dioxin during herbicide-spraying operations, are studied. The overall aim is to use these data to infer the dynamics of TCDD concentrations in humans. This is done by identifying a kinetic model describing the dioxin time course at the individual level. The individual toxicokinetic model is then expanded into a population model within a Bayesian hierarchical framework which allows residual variations across subjects that cannot be explained by observed covariates. Other complications in the data, such as unknown exposure histories, are also resolved implicitly through the hierarchical model. Moreover, the choice of a Bayesian approach enables the accumulation of external source of information in the form of prior distributions. The model is subjected to various diagnostic checks and analyses of sensitivity to distributional assumptions showing a good fit in terms of both the population and the kinetic features.

Bayes Theorem↗

Computational analysis of disparity modulation sensitivity: an explanation in terms of a Bayesian surface reconstruction.

Sensitivity to binocular disparity modulation has been shown to have a bandpass nature. This paper presents a computational account for the disparity modulation function (DMF) in terms of a Bayesian surface reconstruction. The Bayesian approach suggests that prior assumptions about surface structure will affect the perception of disparity modulation. Taking into account a prior constraint of surface smoothness being imposed on the perceived surfaces, we propose that computing the first derivatives of the surfaces determines the bandpass shape of the DMF. Based on this idea, we derive an analytical prediction of the DMF. It is then shown that the prediction gives a good fit to the empirical data. Implications for possible mechanisms underlying the DMF are discussed.

Depth Perception↗

Thrombotic microangiopathy after allogeneic blood and marrow transplantation is associated with dose-intensive myeloablative conditioning regimens, unrelated donor, and methylprednisolone T-cell depletion.

BACKGROUND: Allogeneic blood and marrow transplantation (BMT)-associated thrombotic microangiopathy (TM) contributes to transplant-related morbidity and mortality. This report examines the incidence of and risk factors for allogeneic BMT-associated TM in two patient cohorts treated before and after changes in myeloablative conditioning regimen intensity (high vs. standard intensity). METHODS: Cohort 1 includes 153 consecutive allogeneic BMT patients who underwent transplantation between April 1994 and October 1997 with an allogeneic BMT-associated TM crude incidence of 12%. Cohort 2 includes 75 consecutive allogeneic BMT patients who underwent transplantation from November 1997 to November 2000 with an allogeneic BMT-associated TM crude incidence of 1%. RESULTS: In cohort 1, matched unrelated donor transplant and methylprednisolone (MP) T-cell depletion (TCD) of donor bone marrow were significantly associated with allogeneic BMT-associated TM by univariate analysis; therefore, a logistic model incorporating these effects was constructed to calculate the expected number of allogeneic BMT-associated TM cases in cohort 2. Seven cases would have been expected, but only one was observed (P = 0.003; bayesian predictive test). The multivariate analysis of both cohorts yielded MP-TCD (P<0.001), high-intensity myeloablative conditioning regimens used in cohort 1 (P = 0.02), and matched unrelated donor (P = 0.03) as significant predictors of time to allogeneic BMT-associated TM. CONCLUSION: Avoidance of high-intensity conditioning regimens may decrease the incidence of allogeneic BMT-associated TM.

Adolescent↗

Clinical feature profile of spinocerebellar ataxia type 1-8 predicts genetically defined subtypes.

An increasing number of genetically defined types of spinocerebellar ataxia (SCA) have been reported in the past decade. Phenotype--genotype correlation studies have suggested a broad overlap between SCA types. The aim of the present study was to identify patterns of clinical features that were likely to distinguish between SCA types and to test the specificity and sensitivity of these signs and symptoms using a Bayesian classifier. In total, 127 patients from 50 families with SCA types 1 to 8 were examined using a worksheet with a panel of 33 symptoms and signs. By computing the probabilities of each trait for each SCA type, we rated the predictive value of each feature for each form of ataxia and then combined the probabilities for the entire panel of traits to construct a Bayesian classifier. Results of this analysis were summarized in a simpler, more operator-based algorithm. Patients with SCA5, SCA6, and SCA8 demonstrated a predominant cerebellar syndrome, whereas patients with SCA1, SCA2, SCA3, SCA4, and SCA7 frequently had clinical features indicating an extracerebellar involvement. The Bayesian classifier predicted the SCA type in 78% of patients with sensitivities between 60 and 100% and specificities between 94 and 98.2%. The highest sensitivity to correctly predict the true SCA type was found for SCA5, SCA7, and SCA8. Sensitivities and specificities found in the present study validate the use of algorithms to help to prioritize specific SCA gene testing, which will help to reduce costs for gene testing.

Age of Onset↗

Genetic variants in migraine: a field synopsis and systematic re-analysis of meta-analyses.

OBJECTIVE: Numerous genetic variants from meta-analyses of observational studies and GWAS were reported to be associated with migraine susceptibility. However, due to the random errors in meta-analyses, the noteworthiness of the results showing statistically significant remains doubtful. Thus, we performed this field synopsis and re-analysis study to evaluate the noteworthiness using a Bayesian approach in hope of finding true associations. METHODS: Relevant meta-analyses from observational studies and GWAS examining correlation between all genetic variants and migraine risk were included in our study by a PubMed search. Identification of noteworthy associations were analyzed by false-positive rate probability (FPRP) and Bayesian false discovery probability (BFDP). Using noteworthy variants, GO enrichment analysis were conducted through DAVID online tool. Then, the PPI network and hub genes were performed using STRING database and CytoHubba software. RESULTS: As for 8 significant genetic variants from observational studies, none of which showed noteworthy at prior probability of 0.001. Out of 47 significant genetic variants in GWAS, 36 were noteworthy at prior probability of 0.000001 via FPRP or BFDP. We further found the pathways "positive regulation of cytosolic calcium ion concentration" and "inositol phosphate-mediated signaling" and hub genes including MEF2D, TSPAN2, PHACTR1, TRPM8 and PRDM16 related to migraine susceptibility. CONCLUSION: Herein, we have identified several noteworthy variants for migraine susceptibility in this field synopsis. We hope these data would help identify novel genetic biomarkers and potential therapeutic target for migraine.

Bayes Theorem↗

Estimation of population pharmacokinetics using the Gibbs sampler.

Quantification of the average and interindividual variation in pharmacokinetic behavior within the patient population is an important aspect of drug development. Population pharmacokinetic models typically involve large numbers of parameters related nonlinearly to sparse, observational data, which creates difficulties for conventional methods of analysis. The nonlinear mixed-effects method implemented in the computer program NONMEM is a widely used approach to the estimation of population parameters. However, the method relies on somewhat restrictive modeling assumptions to enable efficient parameter estimation. In this paper we describe a Bayesian approach to population pharmacokinetic analysis which used a technique known as Gibbs sampling to simulate values for each model parameter. We provide details of how to implement the method in the context of population pharmacokinetic analysis, and illustrate this via an application to gentamicin population pharmacokinetics in neonates.

Anti-Bacterial Agents↗

Genetic diversity within the Albugo candida complex (Peronosporales, Oomycota) inferred from phylogenetic analysis of ITS rDNA and COX2 mtDNA sequences.

Albugo candida is a destructive fungus infecting brassicaceous hosts. The genetic diversity within the A. candida complex from various host plants was investigated by sequence analysis of the internal transcribed spacer (ITS) region of rDNA and the cytochrome c oxidase subunit II (COX2) region of mtDNA. The aligned nucleotide sequences of A. candida shared significantly high distances, up to 20.4 and 8.9%, in two genes. The phylogenetic trees, obtained using the Bayesian method and maximum parsimony analysis, showed two separate groups that corresponded to the host genera. Group I included A. candida isolates infecting Arabis, Autrieta, Berteroa, Biscutella, Brassica, Cardaminopsis, Diplotaxis, Eruca, Erysimum, Heliophila, Iberis, Lunaria, Raphanus, Sinapis, Sisymbrium, and Thlaspi. Group II contained all isolates from Capsella, Descurainia, Diptychocarpus, Draba, and Lepidium. The genetic similarities between the two genes among isolates within Group I were 99.0-100% and 99.6-100%, while those within Group II were 90.4-100% and 91.1-100%, respectively, showing considerably lower values than for Group I. The A. candida isolates from Capsella bursa-pastoris in Korea are clearly separated by sequence analysis for the two genes compared to those from Wales, England, and the USA. Based on the molecular data from the two genes, we suggest the high degree of genetic diversity exhibited within A. candida complexes warrants their division into several distinct species.

Base Sequence↗

Passive smoking in the workplace: classical and Bayesian meta-analyses.

There are currently several classical and Bayesian methods of meta-analysis available for combining epidemiological results. We describe and compare these in a consistent framework, and apply them to published studies of the relative risk of lung cancer associated with exposure to environmental tobacco smoke in the workplace. We find that although all methods give reasonably similar combined estimates of relative risk of lung cancer associated with this exposure (none of which is significantly raised above unity, in either a frequentist or a Bayesian sense), the approximations arising from classical methods appear to be nonconservative and should be used with caution. The Bayesian methods, which account more explicitly for possible inhomogeneity in studies, give slightly lower estimates again of relative risk and wider posterior credible intervals, indicating that inference from the non-Bayesian approaches might be optimistic.

Bayes Theorem↗

Frequency of adverse events after vaccination with different vaccinia strains.

BACKGROUND: Large quantities of smallpox vaccine have been stockpiled to protect entire nations against a possible reintroduction of smallpox. Planning for an appropriate use of these stockpiled vaccines in response to a smallpox outbreak requires a rational assessment of the risks of vaccination-related adverse events, compared to the risk of contracting an infection. Although considerable effort has been made to understand the dynamics of smallpox transmission in modern societies, little attention has been paid to estimating the frequency of adverse events due to smallpox vaccination. Studies exploring the consequences of smallpox vaccination strategies have commonly used a frequency of approximately one death per million vaccinations, which is based on a study of vaccination with the New York City Board of Health (NYCBH) strain of vaccinia virus. However, a multitude of historical studies of smallpox vaccination with other vaccinia strains suggest that there are strain-related differences in the frequency of adverse events after vaccination. Because many countries have stockpiled vaccine based on the Lister strain of vaccinia virus, a quantitative evaluation of the adverse effects of such vaccines is essential for emergency response planning. We conducted a systematic review and statistical analysis of historical data concerning vaccination against smallpox with different strains of vaccinia virus. METHODS AND FINDINGS: We analyzed historical vaccination data extracted from the literature. We extracted data on the frequency of postvaccinal encephalitis and death with respect to vaccinia strain and age of vaccinees. Using a hierarchical Bayesian approach for meta-analysis, we estimated the expected frequencies of postvaccinal encephalitis and death with respect to age at vaccination for smallpox vaccines based on the NYCBH and Lister vaccinia strains. We found large heterogeneity between findings from different studies and a time-period effect that showed decreasing incidences of adverse events over several decades. To estimate death rates, we then restricted our analysis to more-recent studies. We estimated that vaccination with the NYCBH strain leads to an average of 1.4 deaths per million vaccinations (95% credible interval, 0-6) and that vaccination with Lister vaccine leads to an average of 8.4 deaths per million vaccinations (95% credible interval, 0-31). We combined age-dependent estimates of the frequency of death after vaccination and revaccination with demographic data to obtain estimates of the expected number of deaths in present societies due to vaccination with the NYCBH and Lister vaccinia strains. CONCLUSIONS: Previous analyses of smallpox vaccination policies, which rely on the commonly assumed value of one death per million vaccinations, may give serious underestimates of the number of deaths resulting from vaccination. Moreover, because there are large, strain-dependent differences in the frequency of adverse events due to smallpox vaccination, it is difficult to extrapolate from predictions for the NYCBH-derived vaccines (stockpiled in countries such as the US) to predictions for the Lister-derived vaccines (stockpiled in countries such as Germany). In planning for an effective response to a possible smallpox outbreak, public-health decision makers should reconsider their strategies of when to opt for ring vaccination and when to opt for mass vaccination.

Age Distribution↗

Some statistical and regulatory issues in the evaluation of genetic and genomic tests.

The genomics revolution is reverberating throughout the worlds of pharmaceutical drugs, genetic testing and statistical science. This revolution, which uses single nucleotide polymorphisms (SNPs) and gene expression technology, including cDNA and oligonucleotide microarrays, for a range of tests from home-brews to high-complexity lab kits, can allow the selection or exclusion of patients for therapy (responders or poor metabolizers). The wide variety of US regulatory mechanisms for these tests is discussed. Clinical studies to evaluate the performance of such tests need to follow statistical principles for sound diagnostic test design. Statistical methodology to evaluate such studies can be wide ranging, including receiver operating characteristic (ROC) methodology, logistic regression, discriminant analysis, multiple comparison procedures resampling, Bayesian hierarchical modeling, recursive partitioning, as well as exploratory techniques such as data mining. Recent examples of approved genetic tests are discussed.

Animals↗

Bayesian statistical methods in public health and medicine.

This article reviews the Bayesian statistical approach to the design and analysis of research studies in the health sciences. The central idea of the Bayesian method is the use of study data to update the state of knowledge about a quantity of interest. In study design, the Bayesian approach explicitly incorporates expressions for the loss resulting from an incorrect decision at the end of the study. The Bayesian method also provides a flexible framework for the monitoring of sequential clinical trials. We present several examples of Bayesian methods in practice including a study of disease progression in AIDS, a comparison of two therapies in a clinical trial, and a case-control study investigating the link between dietary factors and breast cancer.

Bayes Theorem↗