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Combining location and expression data for principled discovery of genetic regulatory network models.

We develop principled methods for the automatic induction (discovery) of genetic regulatory network models from multiple data sources and data modalities. Models of regulatory networks are represented as Bayesian networks, allowing the models to compactly and robustly capture probabilistic multivariate statistical dependencies between the various cellular factors in these networks. We build on previous Bayesian network validation results by extending the validation framework to the context of model induction, leveraging heuristic simulated annealing search algorithms and posterior model averaging. Using expression data in isolation yields results inconsistent with location data so we incorporate genomic location data to guide the model induction process. We combine these two data modalities by allowing location data to influence the model prior and expression data to influence the model likelihood. We demonstrate the utility of this approach by discovering genetic regulatory models of thirty-three variables involved in S. cerevisiae pheromone response. The models we automatically generate are consistent with the current understanding regarding this regulatory network, but also suggest new directions for future experimental investigation.

Bayes Theorem↗

Hierarchical modelling of small area and hospital variation in short-term prognosis after acute myocardial infarction. A longitudinal study of 35- to 74-year-old men in Denmark between 1978 and 1997.

Models for analysis of trends in hospital and small area variation in case fatality after acute myocardial infarction are presented. The data are from administrative registries in Denmark. Hierarchical modelling in a logistic regression with a Bayesian approach is used. Model selection is undertaken using the deviance and the Bayesian information criteria. There is a modest trend for hospital variation in case-fatality rates that coincides with the introduction of new treatment strategies. This hospital variation is considerably larger than the variation at the area level. There is no trend for variation of the case-fatality rates at the area level. Unstructured random effects slightly outperform spatially correlated random effects at the area level. Somewhat high correlations over time within hospitals and within areas were detected for the case-fatality rates. Heavy-tailed distributions (T-distributions) could be an alternative for the random effect distribution in data from administrative registries and compete in the model selection with the normal distribution in this study.

Adult↗

A limited sampling method to estimate methotrexate pharmacokinetics in patients with rheumatoid arthritis using a Bayesian approach and the population data modeling program P-PHARM.

This paper describes a methodology to calculate methotrexate (MTX) pharmacokinetic parameters after intramuscular administration using two samples and the population parameters. Total and free MTX were measured over a 36-h period in 56 rheumatoid arthritis patients; 14 patients were studied after a two-dose scheme at 15-day intervals. The Hill equation was used to relate the free MTX to the total MTX changes in plasma concentrations, and a two-compartment open model was used to fit the total MTX plasma concentrations. A non-linear mixed effect procedure was used to estimate the population parameters and to explore the interindividual variability in relation to the following covariables: age, weight, height, haemoglobin, erythrocyte sedimentation rate, platelet count, creatinine clearance, rheumatoid factor, C-reactive protein, swelling joint count, and Ritchie's articular index. Population parameters were evaluated for 40 patients using a three-step approach. The population average parameters and the interindividual variabilities expressed as coefficients of variation (CV%) were: CL, 6.94 l center dot h-1 (20.5%); V, 34.8 l (32.2%); k12, 0.0838 h-1 (47.7%); k21, 0.0769 h-1 (61.6%); ka, 4.31 h-1 (58%); Emax, 1.12 mu mol center dot l-1 (19.7%); gamma, 0.932 (12.3%); and EC50, 2.14 mu mol center dot l-1 (27.3%). Thirty additional data sets (16 new patients and 14 patients of the previous population but treated on a separate occasion) were used to evaluate the predictive performance of the population parameters. Twelve blood samples were collected from each individual in order to calculate individual parameters using standard fitting procedures. These values were compared to the ones estimated using a Bayesian approach with population parameters as a priori information together with two samples, selected from the individual observations. The results show that the bias was not statistically different from zero and the precision of these parameters was excellent.

Adult↗

[Bayesian estimates of unknown parameters of mathematical models of the dynamics of the mutation process and changes in the ratio of cells having passed different numbers of divisions in a culture].

With the help of Bayesian methods, the conditions of solving experimental data samples and their divisions were established, equivalence of estimations of unknown linear dynamic models parameters proved, the estimations having been worked out by both accounting calculation errors and using their compensations with additional noise in the original model's discrete analog. The results are used in mathematical modeling of changing intensity of the process of hereditary pathology frequencies, and the process of changing the ratio of cells having passed different numbers of divisions in the culture.

Bayes Theorem↗

Inference of gene regulatory networks by means of dynamic differential Bayesian networks and nonparametric regression.

We propose a dynamic differential Bayesian networks (DDBNs) and nonparametric regression model. This model is an extended model of traditional dynamic Bayesian networks (DBNs), which can incorporate temporal information in a natural way and directly handle real-valued data obtained from microarrays without any transformation. In addition, it can cope with differential information between gene expression levels, without any loss to the traditional advantage, i.e., the capability of estimating non-linear relationships between genes. We apply DDBNs to analyze simulated data and real data, i.e., Saccharomyces cerevisiae cell cycle gene expression data. We have confirmed the effectiveness of our approach in the sense that some edges have been successfully detected only by DDBNs, not by DBNs.

Algorithms↗

Automatic detection of interictal spikes using data mining models.

A prospective candidate for epilepsy surgery is studied both the ictal and interictal spikes (IS) to determine the localization of the epileptogenic zone. In this work, data mining (DM) classification techniques were utilized to build an automatic detection model. The selected DM algorithms are: Decision Trees (J 4.8), and Statistical Bayesian Classifier (naïve model). The main objective was the detection of IS, isolating them from the EEG's base activity. On the other hand, DM has an attractive advantage in such applications, in that the recognition of epileptic discharges does not need a clear definition of spike morphology. Furthermore, previously 'unseen' patterns could be recognized by the DM with proper 'training'. The results obtained showed that the efficacy of the selected DM algorithms is comparable to the current visual analysis used by the experts. Moreover, DM is faster than the time required for the visual analysis of the EEG. So this tool can assist the experts by facilitating the analysis of a patient's information, and reducing the time and effort required in the process.

Action Potentials↗

Fast LROC analysis of Bayesian reconstructed emission tomographic images using model observers.

Lesion detection and localization is an important task in emission computed tomography. Detection and localization performance with signal location uncertainty may be summarized by a scalar figure of merit, the area under the localization receiver operating characteristic (LROC) curve, A(LROC). We consider model observers to compute A(LROC) for two-dimensional maximum a posteriori (MAP) reconstructions. Model observers may be used to rapidly prototype studies that use human observers. We address the case background-known-exactly (BKE) and signal known except for location. Our A(LROC) calculation makes use of theoretical expressions for the mean and covariance of the reconstruction and, unlike conventional methods that also use model observers, does not require computation of a large number of sample reconstructions. We validate the results of the procedure by comparison to A(LROC) obtained using a gold-standard Monte Carlo method employing a large set of reconstructed noise samples. Under reasonable simulation conditions, our theoretical calculation is about one to two orders of magnitude faster than the conventional Monte Carlo method.

Algorithms↗

Dependence among sites in RNA evolution.

Although probabilistic models of genotype (e.g., DNA sequence) evolution have been greatly elaborated, less attention has been paid to the effect of phenotype on the evolution of the genotype. Here we propose an evolutionary model and a Bayesian inference procedure that are aimed at filling this gap. In the model, RNA secondary structure links genotype and phenotype by treating the approximate free energy of a sequence folded into a secondary structure as a surrogate for fitness. The underlying idea is that a nucleotide substitution resulting in a more stable secondary structure should have a higher rate than a substitution that yields a less stable secondary structure. This free energy approach incorporates evolutionary dependencies among sequence positions beyond those that are reflected simply by jointly modeling change at paired positions in an RNA helix. Although there is not a formal requirement with this approach that secondary structure be known and nearly invariant over evolutionary time, computational considerations make these assumptions attractive and they have been adopted in a software program that permits statistical analysis of multiple homologous sequences that are related via a known phylogenetic tree topology. Analyses of 5S ribosomal RNA sequences are presented to illustrate and quantify the strong impact that RNA secondary structure has on substitution rates. Analyses on simulated sequences show that the new inference procedure has reasonable statistical properties. Potential applications of this procedure, including improved ancestral sequence inference and location of functionally interesting sites, are discussed.

Animals↗

Bayesian approach for the calibration of models: application to an urban stormwater pollution model.

In environmental modelling, estimating the confidence level in conceptual model parameters is necessary but difficult. Having a realistic estimation of the uncertainties related to the parameters is necessary i) to assess the possible origin of the calibration difficulties (correlation between model parameters for instance), and ii) to evaluate the prediction confidence limits of the calibrated model. In this paper, an application of the Metropolis algorithm, a general Monte Carlo Markov chain sampling method, for the calibration of a four-parameter lumped urban stormwater quality model is presented. Unlike traditional optimisation approaches, the Metropolis algorithm identifies not only a "best parameter set", but a probability distribution of parameters according to measured data. The studied model includes classical formulations for the pollutant accumulation during dry weather period and their washoff during a rainfall event. Results indicate mathematical shortcomings in the pollutant accumulation formulation used.

Algorithms↗

Bayesian approach for a nonlinear growth model.

Nonlinear least squares methods are currently used for fitting a well-known growth model, namely the Jenss model, to the length measurements of a child followed throughout the first six years of life. An empirical Bayes approach is developed for fitting the model, and the prior distribution of the growth-model parameters is estimated from a large sample of least squares parameters. An expression which is proportional to the posterior distribution is derived so that the posterior mode can be estimated. Given the observations on a child, this posterior mode provides Bayes estimates of the Jenss curve parameters for the child.

Bayes Theorem↗

Modelling human immunodeficiency virus infection and acquired immune deficiency syndrome cases in Scotland: data sources, prior information and Bayesian estimation.

"The paper describes the methodology developed to carry out predictions of the acquired immune deficiency syndrome (AIDS) epidemic in Scotland. Information on the human immunodeficiency virus (HIV) epidemic comes from formal case reports of AIDS cases and HIV positive tests, reports from surveillance schemes and from special studies. These sources of information, up to the end of 1994, are reviewed.... A simple model of the HIV epidemic in Scotland is proposed and the information is summarized in terms of this model. Bayesian methodology, using Markov chain Monte Carlo methods, is described and used to predict future cases of AIDS in Scotland and people who will be living with AIDS in the years 1995-1999."

Acquired Immunodeficiency Syndrome↗

Database search based on Bayesian alignment.

The size of protein sequence database is getting larger each day. One common challenge is to predict protein structures or functions of the sequences in databases. It is easy when a sequence shares direct similarity to a well-characterized protein. If there is no direct similarity, we have to rely on a third sequence or a model as intermediate to link two proteins together. We developed a new model based method, called Bayesian search, as a means to connect two distantly related proteins. We compared this Bayesian search model with pairwise and multiple sequence comparison methods on structural databases using structural similarity as the criteria for relationship. The results show that the Bayesian search can link more distantly related sequence pairs than other methods, collectively and consistently over large protein families. If each query made one error on average against SCOP database PDB40D-B, Bayesian search found 36.5% of related pairs, PSI-Blast found 32.6%, and Smith-Waterman method found 25%. Examples are presented to show that the alignments predicted by the Bayesian search agree well with structural alignments. Also false positives found by Bayesian search at low cutoff values are analyzed.

Algorithms↗

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

Asthma↗

Semiparametric regression in capture-recapture modeling.

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in survival may be explained by incorporating relevant covariates. We propose nonparametric and semiparametric regression methods for estimating survival in capture-recapture models. A fully Bayesian approach using Markov chain Monte Carlo simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adélie.

Animals↗

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↗

A compartmental pharmacokinetic model of cyclosporin and its predictive performance after Bayesian estimation in kidney and simultaneous pancreas-kidney transplant recipients.

BACKGROUND: Therapeutic drug monitoring of cyclosporin A (CsA) is an obvious necessity because of its unpredictable absorption and narrow therapeutic window. The use of limited sampling models (LSMs) has improved the estimation of the systemic exposure [area under curve (AUC)] compared with C(0h) monitoring, but these equations are rigid and not reliable in patients with an abnormal absorption profile. We developed and validated a limited sampling (t=0, 2 and 3 h) strategy, based on a compartmental population pharmacokinetic (PK) model for CsA after kidney transplantation alone (KTA) and simultaneous pancreas-kidney transplant (SPKT) recipients, a group of patients with unpredictable absorption kinetics. METHODS: A two-compartment model with lag time and first-order absorption was calculated using a PK software package from data of 20 KTA and SPKT recipients and validated prospectively in 20 KTA and 20 SPKT recipients. Calculated population PK parameters were individualized for each of the remaining 40 patients based on their CsA dosing and on one or a combination of measured CsA blood concentrations using the Bayesian fitting method. AUCs were calculated from individualized PK parameters. AUCs were also calculated using previously published LSMs. Relationships between AUCs calculated by the models and the 'golden standard' AUC (trapezoidal rule) were investigated by Pearson correlation test. RESULTS AND CONCLUSIONS: A population two-compartment model is presented to reliably estimate the CsA AUC in KTA and SPKT recipients. The performance of the model to estimate the AUC is comparable to the performance of two published LSMs in KTA patients, but markedly better in SPKT patients. Combined with Bayesian fitting, the model is very flexible since sampling times are not rigid and can be varied as long as dosing and sampling times are recorded accurately. The model has already proven to be clinically useful and is currently used to further investigate CsA in an integrated pharmacokinetic/pharmacodynamic model.

Area Under Curve↗

Comparison of neural network, Bayesian, and multiple stepwise regression-based limited sampling models to estimate area under the curve.

This study compared limited sampling methods (LSM) of estimating area under the plasma concentration versus time curve (AUC) based on a Bayesian regularized neural network, the Bayesian approach, and multiple forward stepwise regression models from selected concentration-time points. Plasma concentration versus time data sets with a linear two-compartmental pharmacokinetic model were simulated. A limited sampling method based on the forward stepwise regression model was developed and validated. Plasma concentration-time points selected by the stepwise regression model were used for neural network and Bayesian evaluation. In addition, 55 plasma concentration-time profiles from two clinical studies were used to develop and compare the predicted AUC(last) for the three approaches. From simulated data sets, mean prediction errors for AUC(last) estimation were 0.00, -5.32, and -6.06 for the neural network, Bayesian approach, and forward stepwise regression LSM, respectively. Mean square errors were 581, 588, and 618, respectively. For clinical data set, model mean prediction errors were 0.00, 3.51, and 3.87, respectively. Model mean square errors were 30.6, 109, and 76, respectively. For both simulated and clinical data sets, the neural network approach to estimate AUC(last) from selected time points was numerically more precise and significantly less biased than the other two methods.

Antiviral Agents↗

Multivariate analysis of cardiovascular reflexes applied to the diagnosis of autonomic neuropathy.

A battery of cardiovascular reflex tests is usually performed for the diagnosis of autonomic neuropathy. The tests discriminate well between normal and definitely abnormal autonomic function. However, in some patients the results are borderline and their autonomic status cannot be better defined. We performed multivariate statistical analysis of six cardiovascular autonomic tests with the aim of increasing their diagnostic efficiency. Eighty-five healthy subjects and 95 patients at risk for autonomic neuropathy were studied. Principal component analysis and two pattern recognition methods, the Bayesian technique and the SIMCA method, were applied. It was found that: (1) normal models obtained by Bayesian analysis showed very high specificity and sensitivity; (2) a battery of two tests for parasympathetic function (R-R interval variation test, deep breathing) and two tests for sympathetic function (blood pressure responses to standing and to sustained handgrip) provide an appropriate diagnostic approach, if multivariate analysis is used; (3) multivariate analysis allows a more precisely defined assessment of autonomic nervous system function in so-called borderline patients.

Adult↗