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PubMed2001

[Count on your beliefs. Bayes' theorem in diagnosis].

Bayesian analysis of data finds increasing use in medical statistics, diagnostic evaluation and decision analysis. The central element in bayesian analysis is a set of mathematical rules for integrated evaluation of prior knowledge and new information. In many situations this approach has superior ability to deliver dependable updated knowledge and to provide an optimal probability basis for decisions. This article (the first of two) presents Bayes' theorem and its application in diagnostic work. It is explained how likelihood ratios of diagnostic tests interact with the outcome of such tests in the conversion of initial information (prior odds) to enhanced information (posterior odds).

Bayes Theorem↗

PubMed2001

Bayesian oligogenic analysis of quantitative and qualitative traits in general pedigrees.

A Bayesian method for multipoint oligogenic analysis of quantitative and qualitative traits is presented. This method can be applied to general pedigrees, which do not necessarily have to be "peelable" and can have large numbers of markers. The number of quantitative/qualitative trait loci (QTL), their map positions in the genome, and phenotypic effects (mode of inheritances) are all estimated simultaneously within the same framework. The summaries of the estimated parameters are based on the marginal posterior distributions that are obtained through Markov chain Monte Carlo (MCMC) methods. The method uses founder alleles together with segregation indicators in order to determine the genotypes of the trait loci of all individuals in the pedigree. To improve mixing properties of the sampler, we propose (1) joint sampling of map position and segregation indicators, (2) omitting data augmentation for untyped or uninformative markers (homozygous parent), and (3) updating several markers jointly within a single block. The performance of the method was tested with two replicate GAW10 data sets (considering two levels of available marker information). The results were concordant and similar to those presented earlier with other methods. These analyses clearly illustrate the utility and wide applicability of the method.

Algorithms↗

PubMed2006

Identifying differentially expressed genes in meta-analysis via Bayesian model-based clustering.

A Bayesian model-based clustering approach is proposed for identifying differentially expressed genes in meta-analysis. A Bayesian hierarchical model is used as a scientific tool for combining information from different studies, and a mixture prior is used to separate differentially expressed genes from non-differentially expressed genes. Posterior estimation of the parameters and missing observations are done by using a simple Markov chain Monte Carlo method. From the estimated mixture model, useful measure of significance of a test such as the Bayesian false discovery rate (FDR), the local FDR (Efron et al., 2001), and the integration-driven discovery rate (IDR; Choi et al., 2003) can be easily computed. The model-based approach is also compared with commonly used permutation methods, and it is shown that the model-based approach is superior to the permutation methods when there are excessive under-expressed genes compared to over-expressed genes or vice versa. The proposed method is applied to four publicly available prostate cancer gene expression data sets and simulated data sets.

Algorithms↗

PubMed2001

Bayesian segregation analysis of production traits in two strains of laying chickens.

A bayesian marker-free segregation analysis was applied to search for evidence of segregating genes affecting production traits in two strains of laying hens under long-term selection. The study used data from 6 generations of Leghorn (H77) and New Hampshire (N88) breeding nuclei. Estimation of marginal posterior means of variance components and parameters of a single autosomal locus was performed by use of the Gibbs sampler. The results showed evidence for a mixed major gene: -polygenic inheritance of BW and age at sexual maturity (ASM) in both strains. Single genes affecting BW and ASM explained one-third of the genetic variance. For ASM large overdominance effect at single locus was estimated. Initial egg production (IEP) and average egg weight (EW) showed a polygenic model of inheritance. The polygenic heritability estimates for BW, ASM, IEP, and EW were 0.32, 0.25, 0.23, and 0.08 in Strain H77 and 0.25, 0.24, 0.11, and 0.38 in Strain N88, respectively.

Age Factors↗

PubMed2002

Datamining protein structure databanks for crystallization patterns of proteins.

A study of 345 protein structures selected among 1,500 structures determined by nuclear magnetic resonance (NMR) methods, revealed useful correlations between crystallization properties and several parameters for the studied proteins. NMR methods of structure determination do not require the growth of protein crystals, and hence allow comparison of properties of proteins that have or have not been the subject of crystallographic approaches. One- and two-dimensional statistical analyses of the data confirmed a hypothesized relation between the size of the molecule and its crystallization potential. Furthermore, two-dimensional Bayesian analysis revealed a significant relationship between relative ratio of different secondary structures and the likelihood of success for crystallization trials. The most immediate result is an apparent correlation of crystallization potential with protein size. Further analysis of the data revealed a relationship between the unstructured fraction of proteins and the success of its crystallization. Utilization of Bayesian analysis on the latter correlation resulted in a prediction performance of about 64%, whereas a two-dimensional Bayesian analysis succeeded with a performance of about 75%.

Bayes Theorem↗

PubMed2005

Comparison of statistical analysis and Bayesian Networks in the evaluation of dissolution performance of BCS Class II model drugs.

This project compared the effect of formulation variables on the dissolution performance of model Biopharmaceutics Classification System (BCS) Class II drugs from hard gelatin capsules using statistical analysis and Bayesian networks. The drugs chosen for this study were carbamazepine (CAR), chlorpropamide (CHL), diazepam (DIA), ketoprofen (KET), and naproxen (NAP). Formulations contained anhydrous lactose, microcrystalline cellulose, sodium stearyl fumerate, sodium lauryl sulfate, and croscarmellose sodium. A Box-Behnken experimental design was used in the statistical analysis. The weakly acidic drugs were tested using USP apparatus II with capsule sinkers in 0.1M pH 6.8 Potassium Phosphate buffer. The weakly basic drugs were tested using USP apparatus I in 0.1N HCl buffer. Mean dissolution profiles were compared via calculation of the similarity factor. The Box-Behnken experimental design was found to be useful in assessing primary and secondary excipient effects on dissolution. The Bayesian Network developed for the dataset mirrored the key excipient effects on dissolution performance.

Bayes Theorem↗

PubMed1998

Comparing a mass-balance algorithm with a Bayesian regression analysis computer program for predicting serum phenytoin concentrations.

The ability of a mass-balance algorithm to predict non-steady-state phenytoin concentrations in neurosurgery patients was compared with that of Phenda, a computerized Bayesian regression analysis program. Fifty neurosurgery patients who had had two or more initial phenytoin serum concentrations measured at least 60 hours apart and at least 1 hour after any i.v. doses, with the second concentration being not more than twice and not less than half of the first, and who had had a third or final phenytoin measurement (for use in a prediction analysis) were evaluated. The patients' maximum rates of metabolism were calculated by using the two initial phenytoin concentrations and a mass-balance algorithm, and the third phenytoin concentration was predicted. The patients' demographics and phenytoin dosages and concentrations were entered into Phenda, which was used to predict the third phenytoin concentration. The ability of the two methods to predict the third concentration was evaluated by the method of Sheiner and Beal. Fifty observations from 48 patients were evaluated. The mass-balance algorithm had a positive prediction bias of 2.52 mg/L and a precision error of 5.08 mg/L, compared with 2.30 and 5.30, respectively, for Phenda. The difference in the results between the two methods was not significant. There was no significant difference between the mass-balance algorithm and Phenda in the ability to predict phenytoin concentrations.

Algorithms↗

PubMed2001

Ethical dilemmas in a randomized trial of asthma treatment: can Bayesian statistical analysis explain the results?

OBJECTIVES: The original objective was to determine whether the use of bilevel positive airway pressure (BiPAP) ventilation would reduce the need for endotracheal intubation, the length of hospital stay, and hospital charges in patients with status asthmaticus. The development of physician treatment bias made patient enrollment difficult. The article subsequently describes the use of Bayesian statistics to explain study results when this bias occurs. METHODS: This study was a prospective, randomized controlled clinical trial conducted over a 34.5-month period at an urban university hospital with an emergency department census of 94,000 annual visits. Patients remaining in status asthmaticus after initial standard treatment with inhaled beta-agonists and steroids were randomized to receive BiPAP ventilation plus standard treatment versus standard treatment alone (non-BiPAP), with intubation for either group as needed. Patients with concurrent cardiac or other pulmonary diseases were excluded. The primary outcome measures were endotracheal intubation rate and length of hospital stay. Secondary outcome measures included vital signs (respiratory rate, pulse rate, blood pressure), changes in expiratory peak flow, changes in pulse oximetry values, and hospital charges. Data were analyzed using Fisher's exact test, Mann-Whitney tests, and Bayesian statistics. For patients enrolled in the study more than once, data analysis was performed on the first enrollment only. RESULTS: Nineteen patients were enrolled in the BiPAP group and 16 patients in the non-BiPAP group. Patients were frequently enrolled more than once and the data from the subsequent enrollments were excluded from the analysis. A marked decrease in enrollment, due to physician treatment bias, led to a premature termination of the study. Demographics showed that the groups were similar in age, sex, initial peak flow rate, and arterial blood gas measurements. There was a 7.3% increase (95% CI = -22 to +45) in the intubation rate in the non-BiPAP group (n = 2) compared with that for the BiPAP group (n = 1). No significant difference was seen in length of hospital stay or hospital charges, although there was a favorable trend toward the BiPAP group. Complications encountered in the BiPAP group included one patient with discomfort associated with the nasal BiPAP mask. Bayesian analysis demonstrated that in order for the collected data to be convincing at the 95% confidence level, the prior conviction among treating physicians that BiPAP was a successful treatment modality would have had to be 98.9%. CONCLUSIONS: In this study, BiPAP appeared to have no deleterious effects in patients with status asthmaticus, with a trend toward decreased endotracheal intubation rate, decreased length of hospital stay, and decreased hospital charges. Although further study with more patients is needed to determine the clinical and statistical significance of this intervention, ethical concerns regarding withholding BiPAP treatment from the patients in the control group forced a premature termination of the study in the authors' institution.

Adult↗

PubMedDate not supplied

Bayesian approaches in pharmacokinetic decision making.

The theory of Bayesian analysis and its application to therapeutic and pharmacokinetic decision making are discussed. Diagnostic and therapeutic decisions are commonly based on institution, experience, and laboratory information; these decisions reflect varying degrees of uncertainty. Bayesian analysis quantifies the decision process by attaching probabilities to the likelihood of accuracy of each of these decision-making factors to achieve an overall estimate of decision quality. Using Bayesian principles to quantify the probability of efficacy and toxicity associated with serum drug concentrations represents one application of Bayesian theory to enhance therapeutic decisions. The Bayesian approach in pharmacokinetics involves the prediction of pharmacokinetic values, dosage regimens, and serum concentrations for drugs. Beginning with mean population pharmacokinetic parameters, one uses observed serum concentrations in individual patients to modify these parameters through Bayesian analysis to improve the accuracy of future serum concentration predictions. As more clinical pharmacokinetic laboratories and consultation services become familiar with the procedure, Bayesian forecasting promises to expand markedly the sophistication of therapeutic drug monitoring.

Decision Making↗

PubMed2002

Bayesian phylogenetic analysis supports monophyly of ambulacraria and of cyclostomes.

Vertebrates are part of the phylum Chordata, itself part of a three-phylum group known as the deuterostomes. Despite extensive phylogenetic analysis of the deuterostome animals, several unresolved relationships remain. These include the relationship between the three deuterostome phyla (chordates, echinoderms and hemichordates), and the monophyletic or paraphyletic origin of the cyclostomes (hagfish and lampreys). Using robust Bayesian statistical analysis of 18S ribosomal DNA, mitochondrial genes and nuclear protein-coding DNA, we find strong support for a hemichordate-echinoderm clade, and for monophyly of the cyclostomes.

Animals↗

PubMed2006

Bayesian spatial analysis and disease mapping: tools to enhance planning and implementation of a schistosomiasis control programme in Tanzania.

OBJECTIVE: To predict the spatial distributions of Schistosoma haematobium and S. mansoni infections to assist planning the implementation of mass distribution of praziquantel as part of an on-going national control programme in Tanzania. METHODS: Bayesian geostatistical models were developed using parasitological data from 143 schools. RESULTS: In the S. haematobium models, although land surface temperature and rainfall were significant predictors of prevalence, they became non-significant when spatial correlation was taken into account. In the S. mansoni models, distance to water bodies and annual minimum temperature were significant predictors, even when adjusting for spatial correlation. Spatial correlation occurred over greater distances for S. haematobium than for S. mansoni. Uncertainties in predictions were examined to identify areas requiring further data collection before programme implementation. CONCLUSION: Bayesian geostatistical analysis is a powerful and statistically robust tool for identifying high prevalence areas in a heterogeneous and imperfectly known environment.

Adolescent↗

PubMed2002

Determination of an optimal dosage regimen using a Bayesian decision analysis of efficacy and adverse effect data.

One of the aims of Phase II clinical trials is to determine the dosage regimen(s) that will be investigated during a confirmatory Phase III clinical trial. During Phase II, pharmacodynamic data are collected that enables the efficacy and safety of the drug to be assessed. It is proposed in this paper to use Bayesian decision analysis to determine the optimal dosage regimen based on efficacy and toxicity of the drug oxybutynin used in the treatment of urinary urge incontinence. Such an approach results in a general framework allowing modeling, inference and decision making to be carried out. For oxybutynin, the repeated measurement efficacy and toxicity data were modeled using nonlinear hierarchical models and inferences were based on posterior probabilities. The optimal decision in this problem was to determine the dosage regimen that maximized the posterior expected utility given the prior information on the model parameters and the patient response data. The utility function was defined using clinical opinion on the satisfactory levels of efficacy and toxicity and then combined by weighting the relative importance of each pharmacodynamic response. Markov chain Monte Carlo (MCMC) methodology implemented in Win-BUGS 1.3 was used to obtain posterior estimates of the model parameters, probabilities and utilities.

Aged↗

PubMed2006

Combining wavelet analysis and Bayesian networks for the classification of auditory brainstem response.

The auditory brainstem response (ABR) has become a routine clinical tool for hearing and neurological assessment. In order to pick out the ABR from the background EEG activity that obscures it, stimulus-synchronized averaging of many repeated trials is necessary, typically requiring up to 2000 repetitions. This number of repetitions can be very difficult, time consuming and uncomfortable for some subjects. In this study, a method combining wavelet analysis and Bayesian networks is introduced to reduce the required number of repetitions, which could offer a great advantage in the clinical situation. 314 ABRs with 64 repetitions and 155 ABRs with 128 repetitions recorded from eight subjects are used here. A wavelet transform is applied to each of the ABRs, and the important features of the ABRs are extracted by thresholding and matching the wavelet coefficients. The significant wavelet coefficients that represent the extracted features of the ABRs are then used as the variables to build the Bayesian network for classification of the ABRs. In order to estimate the performance of this approach, stratified ten-fold cross-validation is used.

Algorithms↗

PubMed1976

Application of step-wise discriminant analysis and Bayesian classification procedure in determining prognosis of acute myocardial infarction.

A retrospective study was carried out to assess the feasibility of computer-assisted prognostication by discriminant analysis and the Bayesian classification procedure based on clinical information collected on patients with acute myocardial infarction. The overall accuracy was 94.2% in predicting hospital death but the prediction of late death after discharge was less accurate. It was found that not all of the 44 variables used for analysis were necessary to reach the same level of predictive accuracy--16 to 20 variables would result in almost the identical prediction. The Bayesian classification procedure was applied to estimate probabilities of individual patients belonging to the different prognostic categories.

Bayes Theorem↗

PubMed2006

Bayesian error analysis model for reconstructing transcriptional regulatory networks.

Transcription regulation is a fundamental biological process, and extensive efforts have been made to dissect its mechanisms through direct biological experiments and regulation modeling based on physical-chemical principles and mathematical formulations. Despite these efforts, transcription regulation is yet not well understood because of its complexity and limitations in biological experiments. Recent advances in high throughput technologies have provided substantial amounts and diverse types of genomic data that reveal valuable information on transcription regulation, including DNA sequence data, protein-DNA binding data, microarray gene expression data, and others. In this article, we propose a Bayesian error analysis model to integrate protein-DNA binding data and gene expression data to reconstruct transcriptional regulatory networks. There are two unique aspects to this proposed model. First, transcription is modeled as a set of biochemical reactions, and a linear system model with clear biological interpretation is developed. Second, measurement errors in both protein-DNA binding data and gene expression data are explicitly considered in a Bayesian hierarchical model framework. Model parameters are inferred through Markov chain Monte Carlo. The usefulness of this approach is demonstrated through its application to infer transcriptional regulatory networks in the yeast cell cycle.

Algorithms↗

PubMed2006

A system for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification.

OBJECTIVE: To devise an automated system to remove artifacts from ictal scalp EEG, using independent component analysis (ICA). METHODS: A Bayesian classifier was used to determine the probability that 2s epochs of seizure segments decomposed by ICA represented EEG activity, as opposed to artifact. The classifier was trained using numerous statistical, spectral, and spatial features. The system's performance was then assessed using separate validation data. RESULTS: The classifier identified epochs representing EEG activity in the validation dataset with a sensitivity of 82.4% and a specificity of 83.3%. An ICA component was considered to represent EEG activity if the sum of the probabilities that its epochs represented EEG exceeded a threshold predetermined using the training data. Otherwise, the component represented artifact. Using this threshold on the validation set, the identification of EEG components was performed with a sensitivity of 87.6% and a specificity of 70.2%. Most misclassified components were a mixture of EEG and artifactual activity. CONCLUSIONS: The automated system successfully rejected a good proportion of artifactual components extracted by ICA, while preserving almost all EEG components. The misclassification rate was comparable to the variability observed in human classification. SIGNIFICANCE: Current ICA methods of artifact removal require a tedious visual classification of the components. The proposed system automates this process and removes simultaneously multiple types of artifacts.

Algorithms↗

PubMed1993

Cardiovascular autonomic dysfunction in multiple sclerosis is likely related to brainstem lesions.

Impairment of cardiovascular autonomic reflexes has been described in multiple sclerosis (MS), and believed reflecting dysfunction of reflex pathways located within the central nervous system. A battery of cardiovascular autonomic tests were performed in 40 patients with definite MS: R-R interval variation test, deep breathing, Valsalva manoeuvre, blood pressure and heart rate responses to standing, sustained handgrip. The results were evaluated by Bayesian analysis, a pattern recognition technique. The patients had also magnetic resonance imaging (MRI) of brain and in 19 subjects of cervical spinal cord. Deep breathing test and sustained handgrip test produced most frequently abnormal results (17.5% and 40%, respectively). However, only 4 patients (10% had two or more tests abnormal, with a very variable pattern. Evaluation by Bayesian analysis revealed 7 patients (17.5%) with definite autonomic dysfunction. A correlation was found between the confidence level obtained by Bayesian analysis, as index of autonomic function, and the Kurtzke brainstem FS score (r = 0.43, P < 0.01). There was a significant association between presence of autonomic dysfunction and clinical (P < 0.02) and MRI (P < 0.005) evidence of brainstem lesions.

Adult↗

PubMed2001

Factors influencing the prediction of steady state concentrations of digoxin.

The prediction error in the Bayesian analysis program for digoxin was evaluated in Japanese patients, and factors influencing the accuracy were investigated. Serum concentrations of digoxin were monitored two times and were compared with the predicted values obtained by using the Bayesian analysis program. The prediction error at the first time was 43.1%. Although this estimation error was reasonably restored at the second time of monitoring, the prediction error remained at 26.6%. These data suggested that unknown factors not included in the program affected the serum concentration of digoxin. Retrospective research of the digoxin serum concentrations in the patients suggested the coadministration of the drugs, which were the P-glycoprotein modulators, as well as the unexpected alteration of the serum creatinine, were the important factors influencing the prediction of the drug serum concentrations. We next examined the inhibitory effect of quinidine, verapamil and spironolactone on the transcellular transport of digoxin by using human P-glycoprotein overexpressing LLC-GA5-COL150 cells. Quinidine, verapamil and spironolactone could inhibit the transcellular transport of digoxin by 50%. In addition, the reduction of the renal clearance by 50%, which could possibly be caused by this inhibition, led to the increase of 36% in the steady state through concentrations of digoxin in the physiological pharmacokinetic model. In conclusion, the prediction of long-term serum concentration-time profiles of digoxin, based on the Bayesian analysis, will be disturbed by the coadministration of the P-glycoprotein modulators and the unexpected alteration of the serum creatinine.

Adolescent↗