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PubMed1998

Strategy and cost in investigating solitary pulmonary nodules.

OBJECTIVE: To compare the probability of cancer in a solitary pulmonary nodule using standard criteria with Bayesian analysis and result of 2-[F-18] fluoro-2-deoxy-D-glucose-positron emission tomographic (FDG-PET) scan. SETTING: A university hospital and a teaching Veteran Affairs Medical Center. METHODS: Retrospective analysis of 52 patients who had undergone both CT scan of the chest and a FDG-PET scan for evaluation of a solitary pulmonary nodule. FDG-PET scan was classified as abnormal or normal. Utilizing Bayesian analysis, the probability of cancer using "standard criteria" available in the literature, based on patient's age, history of previous malignancy, smoking history, size and edge of nodule, and presence or absence of calcification were calculated and compared to the probability of cancer based on an abnormal or normal FDG-PET scan. Histologic study of the nodules was the gold standard. RESULTS: The likelihood ratios for malignancy in a solitary pulmonary nodule with an abnormal FDG-PET scan was 7.11 (95% confidence interval [CI], 6.36 to 7.96), suggesting a high probability for malignancy, and 0.06 (95% CI, 0.05 to 0.07) when the PET scan was normal, suggesting a high probability for benign nodule. FDG-PET scan as a single test alone was more accurate than the standard criteria and standard criteria plus PET scan in correctly classifying nodules as malignant or benign. CONCLUSION: FDG-PET scan as a single test was a better predictor of malignancy in solitary pulmonary nodules than the standard criteria using Bayesian analysis. FDG-PET scan can be a useful adjunct test in the evaluation of solitary pulmonary nodules.

Cost-Benefit Analysis↗

PubMed2001

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12.

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.

Bayes Theorem↗

PubMed1997

Large sample Bayesian inference on the parameters of the proportional hazard models.

This paper considers large sample Bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function. We use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution. The suggested approach is much simpler than alternative Bayesian analyses previously suggested for the proportional hazards models. Using simulated data we compare estimates obtained from the Bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination. We show that under a wider range of assumptions, the Bayesian analysis provides reduced estimation errors and improved rejection of noise variables. Finally, we illustrate the methodology using data from a large study of prognostic markers in breast cancer.

Bayes Theorem↗

PubMed1984

Bayesian probability analysis: a prospective demonstration of its clinical utility in diagnosing coronary disease.

One hundred fifty-four patients referred for coronary arteriography were prospectively studied with stress electrocardiography, stress thallium scintigraphy, cine fluoroscopy (for coronary calcifications), and coronary angiography. Pretest probabilities of coronary disease were determined based on age, sex, and type of chest pain. These and pooled literature values for the conditional probabilities of test results based on disease state were used in Bayes' theorem to calculate posttest probabilities of disease. The results of the three noninvasive tests were compared for statistical independence, a necessary condition for their simultaneous use in Bayes' theorem. The test results were found to demonstrate pairwise independence in patients with and those without disease. Some dependencies that were observed between the test results and the clinical variables of age and sex were not sufficient to invalidate application of the theorem. Sixty-eight of the study patients had at least one major coronary artery obstruction of greater than 50%. When these patients were divided into low-, intermediate-, and high-probability subgroups according to their pretest probabilities, noninvasive test results analyzed by Bayesian probability analysis appropriately advanced 17 of them by at least one probability subgroup while only seven were moved backward. Of the 76 patients without disease, 34 were appropriately moved into a lower probability subgroup while 10 were incorrectly moved up. We conclude that posttest probabilities calculated from Bayes' theorem more accurately classified patients with and without disease than did pretest probabilities, thus demonstrating the utility of the theorem in this application.

Angiography↗

PubMed2001

The empirical bias of estimates by restricted maximum likelihood, Bayesian method, and method R under selection for additive, maternal, and dominance models.

Bayesian analysis via Gibbs sampling, restricted maximum likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.

Animals↗

PubMed2004

Phylogenetic relationships among early-diverging eudicots based on four genes: were the eudicots ancestrally woody?

Based on analyses of combined data sets of three genes (18S rDNA, rbcL, and atpB), phylogenetic relationships among the early-diverging eudicot lineages (Ranunculales, Proteales, Trochodendraceae, Sabiaceae, and Buxaceae) remain unclear, as are relationships within Ranunculales, especially the placement of Eupteleaceae. To clarify relationships among these early-diverging eudicot lineages, we added entire sequences of 26S rDNA to the existing three-gene data set. In the combined analyses of four genes based on parsimony, ML, and Bayesian analysis, Ranunculales are strongly supported as a clade and are sister to other eudicots. Proteales appear as sister to the remaining eudicots, which are weakly (59%) supported as a clade. Relationships among Trochodendraceae, Buxaceae (including Didymeles), Sabiaceae, and Proteales remain unclear. Within Ranunculales, Eupteleaceae are sister to all other Ranunculales, with bootstrap support of 70% in parsimony analysis and with posterior probability of 1.00 in Bayesian analysis. Our character reconstructions indicate that the woody habit is ancestral, not only for the basal angiosperms, but also for the eudicots. Furthermore, Ranunculales may not be ancestrally herbaceous, as long maintained. The woody habit appears to have been ancestral for several major clades of eudicots, including Caryophyllales, and asterids.

Bayes Theorem↗

PubMed2003

Association of African genetic admixture with resting metabolic rate and obesity among women.

OBJECTIVE: To investigate the role of genetic admixture in explaining phenotypic variation in obesity-related traits in a sample of African-American women (n = 145) and to determine significant associations between obesity traits and admixture genetic markers. RESEARCH METHODS AND PROCEDURES: Associations between genetic admixture and BMI, resting metabolic rate, fat mass, fat-free mass, and bone mineral density were tested using linear regression considering the estimation of admixture by 1) a maximum-likelihood approach (MLA) and 2) a Bayesian analysis. RESULTS: Both the conservative MLA and the Bayesian approach support an association between African genetic admixture and BMI. Evidence for the associations of African genetic admixture with fat mass and fat-free mass was supported by the Bayesian analysis; the MLA supported an association with bone mineral density. When the individual ancestry informative markers that were used to estimate admixture were tested for associations with BMI, significant associations were identified in chromosomes 1, 11, and 12. DISCUSSION: These results provide evidence supporting the application of admixture mapping methods to the identification of genes that result in higher levels of obesity among African-American women. Further research is needed to replicate and further explore these findings.

Apolipoprotein A-I↗

PubMed2004

Maximum entropy and Bayesian data analysis: Entropic prior distributions.

The problem of assigning probability distributions which reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of maximum (relative) entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is inspired and guided by intuition gained from the successful use of ME methods in statistical mechanics. For experiments that cannot be repeated the resulting "entropic prior" is formally identical with the Einstein fluctuation formula. For repeatable experiments, however, the expected value of the entropy of the likelihood turns out to be relevant information that must be included in the analysis. The important case of a Gaussian likelihood is treated in detail.

Journal Article↗

PubMed1994

Bayesian hierarchical analysis of within-units variances in repeated measures experiments.

We develop hierarchical Bayesian models for biomedical data that consist of multiple measurements on each individual under each of several conditions. The focus is on investigating differences in within-subject variation between conditions. We present both population-level and individual-level comparisons. We extend the partial likelihood models of Chinchilli et al. with a unique Bayesian hierarchical framework for variance components and associated degrees of freedom. We use the Gibbs sampler to estimate posterior marginal distributions for the parameters of the Bayesian hierarchical models. The application involves a comparison of two cholesterol analysers each applied repeatedly to a sample of subjects. Both the partial likelihood and Bayesian approaches yield similar results, although confidence limits tend to be wider under the Bayesian models.

Algorithms↗

PubMed1998

Predicting hospitalisation of patients with diabetes mellitus. An application of the Bayesian discriminant analysis.

The objective of this study was to develop, and subsequently test, a Bayesian discrimination model for the purpose of identifying both the personal and the healthcare system characteristics predictive of hospitalisation for the treatment of patients with diabetes mellitus or commonly observed cormorbidities associated with the disease. First, a Bayesian classification framework was proposed. The model was then tested by using a logit regression technique in order to estimate the probability of one or more hospitalisation events among patients with diabetes. The study used claims data extracted from the Hawaii Medical Service Association (HMSA) Private Business Claims (PBS) files for the 1995 calendar year. Patients under 65 years were identified by paid claims with ICD-9-CM diagnosis codes of 250.xx which gave a sample size of 6841 patients. Age, gender, various pharmacotherapy variables, presence of hypertension, hyperlipidaemia, congestive heart failure, multiple cardiovascular diseases, any combination of commonly observed comorbidities, dialysis services and annual eye examination are highly predictive of 1 or more hospitalisation events. The model shows a predictive power of almost 90%. This study found that multivariate discriminant analysis using a logit regression model successfully identifies: (i) important explanatory variables predictive of hospitalisation; (ii) assigns patients into 1 of 2 mutually exclusive classes; and (iii) offers a benchmark for a comprehensive disease management strategy for patients with more complicated diabetes.

Bayes Theorem↗

PubMed2002

Bayesian subset analysis: application to studying treatment-by-gender interactions.

Evaluating treatment effects within subsets of patients plays a major part of the analysis of many major clinical trials. Clinicians are often impressed by the heterogeneity of patient populations in clinical trials and hence are interested in examining subset effects. Statisticians generally discourage subset analysis or suggest that clinicians 'do subset analysis but do not believe it'. This advice, however, is a sign of the inadequacy of the analytic methods generally used for subset analysis. Separate analysis of many subsets, and basing conclusions on whether the observed treatment difference achieves significance at the 0.05 level, is likely to yield erroneous conclusions. Making the separate analysis of subsets dependent on demonstration of a statistically significant treatment-by-subset interaction is also not an effective analytic strategy because of the limited power of interaction tests. This paper describes a Bayesian approach to subset analysis developed by Simon, Dixon and Freidlin. The method avoids many of the problems of subset analysis because it is not 'separate' analysis of subsets. Instead, subset-specific treatment effects are estimated as an average of observed within-subset differences and overall differences; the two components are weighted by the a priori estimate of the likelihood of qualitative treatment by subset interactions. Hence, the Bayesian method proposed permits subset analyses incorporating the assumption that qualitative interactions are unlikely. The methodology is applied to the problem of designing and analysing clinical trials to estimate treatment effects for males and females.

Bayes Theorem↗

PubMed1989

Bayesian derived predictions for twice daily theophylline under outpatient conditions and an assessment of optimal sampling times.

1. The accuracy of a computerised method of pharmacokinetic interpretation of a single serum theophylline concentration, employing the statistical technique of Bayesian analysis, has been evaluated for an oral slow release form of theophylline using twice daily dosing. 2. Twenty-four hour steady state serum theophylline concentration-time profiles of one Uniphyllin Continus 400 mg tablet (Napp Laboratories) every 12 h were measured in 15 patients. These profiles demonstrated a diurnal variation of theophylline absorption which was faster during the day. 3. Revised predictions of the profiles were generated by Bayesian analysis using a single serum theophylline concentration taken during a previous outpatient appointment. Comparing the predicted and measured profiles, the accuracy of the Bayesian method is considered more than adequate for clinical purposes. 4. The predictions produced by the revised estimates were statistically less biased and more precise than those derived by a theophylline algorithm using population data. 5. The mean prediction errors of the revised estimates of the day and night-peak drug concentrations were -0.55 mg l-1 and -0.21 mg l-1 whilst those of the evening and morning troughs were 1.17 mg l-1 and 0.41 mg l-1, respectively. 6. Analysis of the predictive and relative performance of the samples drawn during the profile revealed that the sample taken prior to a morning dose produced the most accurate predictions. 7. There was no statistical difference in the relative predictive performance of samples drawn up to 4 h before or 2 h after the morning dose. It is, therefore, recommended that all serum theophylline concentrations to be used in Bayesian analysis, should be drawn within this period.

Administration, Oral↗

PubMed1984

Comparison of the multivariate analysis and CADENZA systems for determination of the probability of coronary artery disease.

The accuracy of 2 discriminate systems for diagnosis of coronary artery disease (CAD), multivariate analysis (MVA) and Bayesian analysis (CADENZA), was evaluated in 113 patients undergoing electrocardiographic stress testing and coronary angiography. MVA uses weighting factors (F values) generated from our patient data, whereas CADENZA uses probabilities gleaned from an extensive review of the American literature. Overall accuracy was similar. MVA had a higher sensitivity for 1-vessel CAD (75 versus 33%), but CADENZA was better for determining the severity of CAD. The 2 systems provided posterior probabilities for disease that were highly correlated (r = 0.56; p less than 0.001). Both systems suggest the need for further testing based on the probability generated; herein lies their major strength. The application of such systems should help the clinician reach a diagnosis or make a decision as to management in a cost-effective manner.

Bayes Theorem↗

PubMed2003

Genetic identification of two sibling species of Lutzomyia longipalpis (Diptera: Psychodidae) that produce distinct male sex pheromones in Sobral, Ceará State, Brazil.

Lutzomyia longipalpis, the main sandfly vector for New World visceral leishmaniasis is a complex of an as yet undefined number of sibling species. At present, there is no consensus on the status (single species vs. species complex) of Brazilian populations. We applied five microsatellite loci to test the hypothesis that L. longipalpis occurs as two sympatric cryptic species in Sobral, Ceará State, Brazil as predicted by male sex pheromone chemotypes described previously for field specimens from this site [S-9-methyl-germacrene-B (9MGB) and a cembrene compound]. Abdominal spot morphology corresponds with pheromone type at this locality (9MGB in '1 spot' males and cembrene in '2 spot' males). Genotype data from 190 wild-caught L. longipalpis specimens collected in October 1999 and April 2001 were used to estimate genetic differentiation between the two sex pheromone populations and sampling dates. No significant (P > 0.05) genetic differences were found between the 1999 and 2001 9MGB samples (theta = 0.018; RST = -0.005), and genetic differentiation was low between the cembrene collections (theta = 0.037, P < 0.05; RST = -0.043, P > 0.05). By contrast, highly divergent allelic frequencies (largely at two microsatellite loci) corresponded to significant (P > 0.05) genetic differentiation (theta = 0.221; RST = 0.215) for all comparisons between samples with different pheromones. When pheromone samples were pooled across sample date, genetic differentiation was high (theta = 0.229; P < 0.001; Nem = 0.84). The allele frequency distribution at each of the five microsatellite loci was similar for males and females from the two collection years. Two of these loci showed highly divergent allele frequencies in the two sex pheromone populations. This was reflected in the highly significant genetic differentiation obtained from the male genotypes, between populations producing different pheromones (theta = 0.229-0.268; P < 0.0001 for the 2001 and theta = 0.254-0.558; P < 0.0001 for the 1999 collections, respectively). Similar results were obtained when the females, assigned to a pheromone type, were included in the analysis. Both a Bayesian analysis of the data set and a population assignment test provided strong evidence for two distinct populations corresponding to pheromone type. Given its genotype, the probability of assigning a 9MGB male to the original 9MGB population was 100% once the two years' collections were pooled. For cembrene-producing '2 spot' males this probability although still high, was lower than for 9MGB males, at 86%. This microsatellite data together with previously reported reproductive isolation between the two Sobral populations confirm that premating barriers are important in speciation of L. longipalpis.

Animals↗

PubMed2005

Bayesian network analysis of signaling networks: a primer.

High-throughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. We present a primer on the use of Bayesian networks for this task. Bayesian networks have been successfully used to derive causal influences among biological signaling molecules (for example, in the analysis of intracellular multicolor flow cytometry). We discuss ways to automatically derive a Bayesian network model from proteomic data and to interpret the resulting model.

Algorithms↗

PubMed2026

Genetic Susceptibility to Incisional Hernia Evaluation of Hernia Polygenic Risk Scores.

OBJECTIVES: Incisional hernia (IH) affects 13-30% of people after abdominal surgery, resulting in substantial morbidity and costs. While clinical risk factors have been studied extensively, genomic risk for IH is incompletely understood. We aimed to evaluate the impact of polygenic risk scores (PRS) on IH risk prediction. METHODS: We created and evaluated three PRS for abdominal hernia, ventral hernia and latent hernia susceptibility for prediction of IH in an institutional biobank. The primary outcome was defined as the diagnosis or repair of an IH based on ICD-9/10-CM/PCS and CPT codes. Clinical covariates included age, sex, body mass index (BMI), smoking status, index procedure type, and perioperative surgical site infection. A phenome-wide association study (PheWAS) was performed to assess clinical associations with increased PRS. We then tested the ability of the PRS to improve prediction for IH by modeling clinical covariates with and without PRS in patients who underwent abdominal surgery. Model performance was assessed using 10 iterations of 5-fold cross-validation to estimate Brier scores and area under the receiver operating characteristic curve (AUROC), which were compared using cross-model Bayesian analysis of variance. RESULTS: In 55,809 subjects, assessed PRS was significantly associated with incisional, umbilical, and ventral hernia on PheWAS, with 1.19 greater odds of developing IH per 1-SD increase in PRS (95% CI: 1.13-1.25, P < 0.001). Of 9,909 subjects who underwent qualifying abdominal surgery, 706 developed IH. In this cohort, the latent hernia susceptibility PRS was associated with a 16% increased hazard of developing IH per 1-SD increase (HR 1.16; 95% CI: 1.07-1.26; P < 0.001). Compared to a predictive model using clinical covariates (Brier score = 0.047, 95% CI: 0.046-0.048; AUROC = 0.660, 95% CI: 0.653-0.666), addition of the PRS showed similar Brier score and AUROC estimates (Brier score = 0.047, 95% CI: 0.046-0.048; AUROC: 0.667, 95% CI: 0.661-0.673) at five years. Cross-model Bayesian analysis demonstrated >99% probability of practical equivalence when trying to detect a difference of ≥ 0.02. CONCLUSION: All three PRS for hernia were independently associated with IH, suggesting that genomic factors contribute significantly to IH development. However, none of the three PRS meaningfully improved clinical IH risk prediction in patients who underwent abdominal surgery. This suggests that clinical comorbidities and surgical techniques may be equally as important as genomic architecture.

Bayesian analysis↗

PubMed2006

Predicting the effect of missense mutations on protein function: analysis with Bayesian networks.

BACKGROUND: A number of methods that use both protein structural and evolutionary information are available to predict the functional consequences of missense mutations. However, many of these methods break down if either one of the two types of data are missing. Furthermore, there is a lack of rigorous assessment of how important the different factors are to prediction. RESULTS: Here we use Bayesian networks to predict whether or not a missense mutation will affect the function of the protein. Bayesian networks provide a concise representation for inferring models from data, and are known to generalise well to new data. More importantly, they can handle the noisy, incomplete and uncertain nature of biological data. Our Bayesian network achieved comparable performance with previous machine learning methods. The predictive performance of learned model structures was no better than a naïve Bayes classifier. However, analysis of the posterior distribution of model structures allows biologically meaningful interpretation of relationships between the input variables. CONCLUSION: The ability of the Bayesian network to make predictions when only structural or evolutionary data was observed allowed us to conclude that structural information is a significantly better predictor of the functional consequences of a missense mutation than evolutionary information, for the dataset used. Analysis of the posterior distribution of model structures revealed that the top three strongest connections with the class node all involved structural nodes. With this in mind, we derived a simplified Bayesian network that used just these three structural descriptors, with comparable performance to that of an all node network.

Algorithms↗

PubMed1991

[An effective method for the estimation and comparison of the ED50 with small sample sizes].

In ED50 experiments the relationship between dose and probability of response is often modelled by the probit function. Standard statistical analysis estimates the parameters of this function by the maximum likelihood principle and derives the ED50 and its fiducial limits from these parameters. Bayesian analysis is more effective in two respects: It optionally includes prior information and in all but very few instances yields confidence intervals, whereas fiducial intervals often cannot be determined. Bayesian analysis of experiments with one substance has been treated in GRIEVE (1988). In the present article the mathematically interested reader is shown how to compare two substances. The probability of higher ED50 in the one substance as well as estimates of the ratio of the ED50's are obtained. The methods are easily extended to the effective dose for any other reasonable percentage of animals, e.g. ED90 or ED25. Experiments concerning lethal doses can be analysed by these methods as well. Both types of analysis are applied in two examples which compare new batches of vaccines with an established standard. In the first example both substances are nearly equivalent, while in the second example the new batch is considerably more efficient. An interactive FORTRAN program for a personal computer is available (cf. last section of 5.). It computes the maximum likelihood and the Bayesian solution, using approximate formulas in the latter case. Due to these approximations it was possible to develop a Bayesian program which is fast enough to run on a PC. Validation procedures have been performed. The output consists of a print file and, optionally, an ASCII file containing the coordinates of the posterior probability density and distribution functions.

Animals↗