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Results for “Bayesian analysis”

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PubMed1999

Bayesian inference analysis of ellipsometry data.

Variable angle spectroscopic ellipsometry is a nondestructive technique for accurately determining the thicknesses and refractive indices of thin films. Experimentally, the ellipsometry parameters psi and Delta are measured, and the sample structure is then determined by one of a variety of approaches, depending on the number of unknown variables. The ellipsometry parameters have been inverted analytically for only a small number of sample types. More general cases require either a model-based numerical technique or a series of approximations combined with a sound knowledge of the test sample structure. In this paper, the combinatorial optimization technique of simulated annealing is used to perform least-squares fits of ellipsometry data (both simulated and experimental) from both a single layer and a bilayer on a semi-infinite substrate using what is effectively a model-free system, in which the thickness and refractive indices of each layer are unknown. The ambiguity inherent in the best-fit solutions is then assessed using Bayesian inference. This is the only way to consistently treat experimental uncertainties along with prior knowledge. The Markov chain Monte Carlo algorithm is used. Mean values of unknown parameters and standard deviations are determined for each and every solution. Rutherford backscattering spectrometry is used to assess the accuracy of the solutions determined by these techniques. With our computer analysis of ellipsometry data, we find all possible models that adequately describe that data. We show that a bilayer consisting of a thin film of poly(styrene) on a thin film of silicon dioxide on a silicon substrate results in data that are ambiguous; there is more than one acceptable description of the sample that will result in the same experimental data.

Journal Article↗

PubMed2003

Geographic variation of pediatric burn injuries in a metropolitan area.

OBJECTIVES: To use a geographic information system (GIS) and spatial statistics to describe the geographic variation of burn injuries in children 0-14 years of age in a major metropolitan area. METHODS: The authors reviewed patient records for burn injuries treated during 1995 at the two children's hospitals in St. Louis. Patient addresses were matched to block groups using a GIS, and block group burn injury rates were calculated. Mapping software and Bayesian analysis were used to create maps of burn injury rates and risks in the city of St. Louis. RESULTS: Three hundred eleven children from the city of St. Louis were treated for burn injuries in 1995. The authors identified an area of high incidence for burn injuries in North St. Louis. The filtered rate contour was 6 per 1,000 children at risk, with block group rates within the area of 0 to 58.8 per 1,000 children at risk. Hierarchical Bayesian analysis of North St. Louis burn data revealed a relative risk range of 0.8771 to 1.182 for census tracts within North St. Louis, suggesting that there may be pockets of high risk within an already identified high-risk area. CONCLUSIONS: This study shows the utility of geographic mapping in providing information about injury patterns within a defined area. The combination of mapping injury rates and spatial statistical analysis provides a detailed level of injury surveillance, allowing for identification of small geographic areas with elevated rates of specific injuries.

Adolescent↗

PubMed1988

The accuracy and stability of Bayesian theophylline predictions.

Pharmacokinetic parameters for theophylline were determined in 33 patients (3 women), mean age 61.2 years and weight 74.6 kg using the following three methods: (a) standard one-compartmental model calculations, assuming 100% bioavailability, after a single dose of theophylline syrup (mean dose 413 mg); (b) drug nomogram; and (c) Bayesian analysis. Patients entered a randomised study of three two-monthly dosage regimens using low, medium, and high theophylline twice daily doses. These doses produced mean (+/- SE) steady-state serum theophylline concentrations of 6.3 (+/- 0.4), 12.1 (+/- 0.3) and 18.3 (+/- 0.5) mg/L, respectively. A fourth period of placebo (2-month duration) was also included. At the end of each treatment period the measured serum theophylline concentration of each patient was compared with those predicted by each of the above three methods. The revised estimates derived from Bayesian analysis produced the least biased [mean prediction error (ME)] and most precise (mean squared prediction error) predictions for all three dosage periods. Statistical analysis of relative performance demonstrated that the difference in precision between the revised estimates and those of the other two methods was significant (p less than 0.05) with the magnitude of the difference increasing with dose. The revised estimates were also found to be less biased (p less than 0.05) than those of the nomogram. The ME (+/- SE) of the revised estimates for the low, medium, and high dosage periods was 0.34 (+/- 0.30), -0.02 (+/- 0.22) and -0.48 (+/- 0.31) mg/L, respectively.

Bayes Theorem↗

PubMed1991

An assessment of population-based and Bayesian methods to individualize digoxin doses shortly after the start of therapy for atrial fibrillation.

The accuracy of population-based methods and of Bayesian analysis to predict individual digoxin pharmacokinetic variables have been evaluated by their ability to predict a measured peak and trough serum digoxin concentration. We studied 13 digitalized patients (three women) whose mean (range) age and weight was 65.8 (60-78) years and 76.6 (68-101.6) kg and who had stable renal function. The population-based methods (using a clearance of 48.87 + 0.87 x creatinine clearance in ml/h/kg and volume of distribution, in litres, of either 7.3 x weight (kg) or 269 + 3.12 x creatinine clearance) were more than adequate for clinical purposes. The mean prediction errors of a measured steady-state peak concentration from these two population methods were -0.074 and 0.013 microgram/l respectively, whilst those of a measured trough concentration were -0.058 and 0.005 microgram/l. Bayesian analysis, using a sample drawn 11 h after the dose on day five of therapy, gave overall the least biased and most precise of the revised estimates. The mean prediction errors of peak and trough values using this sample were 0.069 and -0.005 microgram/l respectively. As expected, the closer the sample was drawn to the time of the trough concentration the more precise were the Bayesian-derived predictions. The value of the Bayesian technique to individualize digoxin doses could not be validated because it was not possible to distinguish between this and the population methods.(ABSTRACT TRUNCATED AT 250 WORDS)

Aged↗

PubMed2005

Bayesian decomposition analysis of bacterial phylogenomic profiles.

BACKGROUND: The past two decades have seen the appearance of new infectious diseases and the reemergence of old diseases previously thought to be under control. At the same time, the effectiveness of the existing antibacterials is rapidly decreasing due to the spread of multidrug-resistant pathogens. AIM: The aim of this study was to the identify candidate molecular targets (e.g. enzymes) within essential metabolic pathways specific to a significant subset of bacterial pathogens as the first step in the rational design of new antibacterial drugs. METHODS: We constructed a dataset of phylogenomic profiles (vectors that encode the similarity, measured by BLAST scores, of a gene across many species) for a series of 31 pathogenic bacteria of interest with 1073 genes taken from the reference organisms Escherichia coli and Mycobacterium tuberculosis. We applied Bayesian Decomposition, a matrix decomposition algorithm, to identify functional metabolic units comprising overlapping sets of genes in this dataset. RESULTS: Although no information on phylogeny was provided to the system, Bayesian Decomposition retrieved the known bacteria phylogenic relationships on the basis of the proteins necessary for survival. In addition, a set of genes required by all bacteria was identified, as well as components and enzymes specific to subsets of bacteria. CONCLUSION: The use of phylogenomic profiles and Bayesian Decomposition provide important insights for the design of new antibacterial therapeutics.

Algorithms↗

PubMed1993

Computer dosing program for the initiation of vancomycin therapy.

The predictive performance of a computer dosing program used for initiating vancomycin therapy was studied. Initial serum vancomycin concentrations in 31 adult patients receiving vancomycin were estimated by using a computer program (T.D.M.S.) incorporating a two-compartment open model. Sixty-two serum vancomycin concentrations at steady state (Css) were obtained before and after one-hour infusions and compared with estimated Css values. Bias and precision were evaluated by calculating median error (ME) and median absolute error (MAE), respectively. Population-based estimates of volume of distribution (V) and clearance (CL) were compared with those obtained by fitting each patient's data set by using Bayesian analysis (BA) and non-linear least-squares regression (NLLS). Median (mean +/- S.D.) bias and precision for peak Css were 7.7 (10.2 +/- 10.8) and 7.7 (10.6 +/- 10.5) mg/L, and for trough Css were 7.4 (7.7 +/- 7.6) and 7.4 (8.8 +/- 6.2) mg/L. The medians were significantly different from zero. Estimated median (mean +/- S.D.) V, CL, and half-life were 0.72 L/kg, 0.60 (0.67 +/- 0.21) mL/min/kg, and 11.59 (12.87 +/- 3.91) hours. Median (mean +/- S.D.) CL values determined by BA and NLLS were 0.86 (0.89 +/- 0.32) and 0.85 (0.92 +/- 0.34) mL/min/kg, respectively. Both CL values were significantly greater than the population-based estimate. However, median V values determined by BA and NLLS did not differ from the population-based estimate. A revised clearance model derived from Bayesian analysis of data for the first 21 patients was tested in the 10 other patients and appeared to improve the predictive performance of the a priori model.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed1991

The prediction of steady-state plasma phenobarbitone concentrations (following low-dose phenobarbitone) to refine its use as an indicator of compliance.

1. A model for predicting the steady-state plasma concentration of phenobarbitone following low-dose phenobarbitone used as an indicator of compliance was derived using data for 10 healthy volunteers. 2. Each volunteer was given a single 30 mg oral dose of phenobarbitone and the pharmacokinetics were described. Subsequently, volunteers were given phenobarbitone 2 mg daily for 28 days and a further pharmacokinetic profile determined during and after this period. 3. An initial predicted estimate of steady-state plasma drug concentration was made using each volunteer's demographic details. This estimate was revised by Bayesian analysis using single timed samples (24, 48, 72 or 96 h) following the single dose. 4. The model was tested on a further 10 healthy volunteers given a single 8 mg dose and who were subsequently given 2 mg daily for 28 days. 5. The revised estimate of peak steady-state plasma phenobarbitone concentration utilising the 96 h post-single dose concentration (356 ng ml-1) was least biased (mean prediction error +/- 95% CI = 10.6 +/- 19.8 ng ml-1) and most precise (root mean square error +/- 95% CI = 28.3 +/- 19.0 ng ml-1). In all cases the peak or trough steady-state drug concentration was within 13% of the predicted value. 6. The model reflected compliance accurately in a further eight volunteers with simulated partial (two-thirds) compliance. 7. The use of a predictive model using Bayesian analysis to estimate expected steady-state plasma phenobarbitone concentrations could increase further the usefulness of low-dose phenobarbitone as an indicator of compliance.

Adult↗

PubMed1983

Electrocardiographic recognition of left atrial enlargement.

The ECG is widely used as a screening test for left atrial enlargement (LAE). Surprisingly, the most widely used criterion of LAE, the P-terminal force in lead V1 (PTF-V1) has not been systematically evaluated to determine the optimal level of PTF-V1 for detection of LAE in clinical populations. Accordingly, we examined the relationship between PTF-V1 and left atrial size by echocardiogram in 361 patients and performed a Bayesian analysis of test performance in populations with a varying prevalence of LAE. As PTF-V1 increased from greater than or equal to 0.03 to greater than or equal to 0.08, sensitivity in the 82 patients with LAE (LA dimension greater than 40 mm) fell from 51% to 23%, and specificity rose from 70% to 93%. In our study population (LAE prevalence = 23%), diagnostic performance of criteria was: PTF-V1 greater than or equal to 0.03 greater than or equal to 0.04 greater than or equal to 0.05 greater than or equal to 0.06 greater than or equal to 0.08 Positive Predictive Accuracy 33 46 52 58 50 Negative Predictive Accuracy 83 83 84 83 80 Per Cent Correct Diagnosis 66 76 78 80 77 Positive predictive accuracy and per cent correct diagnosis improved progressively as PTF-V1 rose from greater than or equal to 0.03 to greater than or equal to 0.06, but fell at greater than or equal to 0.08. Applying our sensitivity and specificity data to Bayesian analysis, PTF-V1 greater than or equal to 0.06 performed best in all populations with prevalence of LAE less than or equal to 50%. We conclude that use of PTF-V1 greater than or equal to 0.06 is superior to the standard criterion of PTF-V1 greater than or equal to 0.04 for all purposes ranging from screening of a general population to evaluation of diseased individuals whose likelihood of LAE ranges up to 50%.

Adolescent↗

PubMed2004

Estimation of diagnostic test characteristics and prevalence of Giardia duodenalis in dairy calves in Belgium using a Bayesian approach.

A Bayesian approach was used to determine both the test properties of three diagnostic test procedures and the prevalence of Giardia duodenalis in dairy calves in Belgium. A cross-sectional survey was conducted in the province of East Flanders, Belgium. Between September 2001 and December 2003, a total of 100 farms were visited and faecal samples were obtained rectally from 499 calves aged from newborn to 70 days. Because there is no gold standard for the diagnosis of a G. duodenalis infection in dairy calves, a subset of 235 samples obtained on the first 50 farms, was examined using three different assays: microscopical examination, an immunofluorescence assay (IFA) and an antigen detecting Elisa (ELISA). Based on the results of these three tests, Bayesian analysis indicated that the prevalence of G. duodenalis in dairy calves was 0.19 (95% Confidence Interval: 0.11-0.28) and that ELISA (Sensitivity (Se) 0.89 and Specificity (Sp): 0.90) and IFA (Se: 0.77 and Sp: 0.95) were both sensitive and specific diagnostic techniques, whereas microscopical examination was less sensitive (Se: 0.56 and Sp: 0.87). The proportion of positive farms was estimated as 0.42 (0.24-0.62). The prevalence and the cyst excretion in calves from different age categories were based on data obtained by IFA on all 499 samples. The prevalence was highest among four to five week old calves and remained high among older calves up to 10 weeks, but was lower among calves before the age of two weeks. The number of excreted cysts was estimated by IFA and ranged from 100 to 1,040,000 cysts per gram faeces, with a mean of 3516 cysts per gram faeces. The intensity of excretion peaked among four-week-old calves and remained high among calves up to the age of eight weeks. This is the first known study to use Bayesian analysis to estimate the prevalence of G. duodenalis in the faeces of dairy calves and to estimate test characteristics of diagnostic assays used for the detection of G. duodenalis.

Animals↗

PubMed2004

Multilevel linear modelling for FMRI group analysis using Bayesian inference.

Functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and/or multiple subjects. A hierarchical approach can be taken to modelling such data with a general linear model (GLM) at each level of the hierarchy introducing different random effects variance components. Inferring on these models is nontrivial with frequentist solutions being unavailable. A solution is to use a Bayesian framework. One important ingredient in this is the choice of prior on the variance components and top-level regression parameters. Due to the typically small numbers of sessions or subjects in neuroimaging, the choice of prior is critical. To alleviate this problem, we introduce to neuroimage modelling the approach of reference priors, which drives the choice of prior such that it is noninformative in an information-theoretic sense. We propose two inference techniques at the top level for multilevel hierarchies (a fast approach and a slower more accurate approach). We also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them.

Bayes Theorem↗

PubMed2005

Prior information in behavioral capture-recapture methods: demographic influences on drug injectors' propensity to be listed in data sources and their drug-related mortality.

The authors present findings from a Bayesian analysis of Scotland's four primary capture-recapture data sources for 2000 that was carried out to estimate numbers of current injecting drug users by region (Greater Glasgow vs. elsewhere in Scotland), sex (male vs. female), and age group (15-34 years vs. > or =35 years). A secondary goal of the analysis was to obtain Bayesian estimates and credible intervals for the demographic influences on Scotland's drug-related death rate per 100 current injectors. Incorporation of informative priors altered the models with highest posterior probability. Expert opinion on how demography influenced Scottish drug injectors' propensity to be listed in different data sources was taken into account, along with external information about European injectors' drug-related death rates and male:female ratios. Higher drug-related mortality was confirmed in older drug injectors and those outside of Greater Glasgow. Female injectors' lower drug-related death rate was not sustained beyond 34 years of age. The authors recommend that demographic influences be accommodated in behavioral capture-recapture estimation, especially when it is a prelude to secondary analysis, such as the analysis of drug-related death rates presented here.

Adolescent↗

PubMed2002

Incorporation of genuine prior information in cost-effectiveness analysis of clinical trial data.

The Bayesian approach to statistics has been growing rapidly in popularity as an alternative to the frequentist approach in the appraisal of healthcare technologies in clinical trials. Bayesian methods have significant advantages over classical frequentist statistical methods and the presentation of evidence to decision makers. A fundamental feature of a Bayesian analysis is the use of prior information as well as the clinical trial data in the final analysis. However, the incorporation of prior information remains a controversial subject that provides a potential barrier to the acceptance of practical uses of Bayesian methods. The purpose of this paper is to stimulate a debate on the use of prior information in evidence submitted to decision makers. We discuss the advantages of incorporating genuine prior information in cost-effectiveness analyses of clinical trial data and explore mechanisms to safeguard scientific rigor in the use of such prior information.

Bayes Theorem↗

PubMed1995