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Bayesian analysis and inference from QSAR predictive model results.

QSAR models have been under development for decades but acceptance and utilization of model results have been slow, in part, because there is no widely accepted metric for assessing their reliability. We reapply a method commonly used in quantitative epidemiology and medical decision-making for evaluating the results of screening tests to assess reliability of a QSAR model. It quantifies the accuracy (expressed as sensitivity and specificity) of QSAR models as conditional probabilities of correct and incorrect classification of chemical characteristic, given a true characteristic. Using Bayes formula, these conditional probabilities are combined with prior information to generate a posterior distribution to determine the probability a specific chemical has a particular characteristic, given a model prediction. As an example, we apply this approach to evaluate the predictive reliability of a CATABOL model and base on it a "ready" and "not ready" biodegradability classification. Finally, we show how predictive capability of the model can be improved by sequential use of two models, the first one with high sensitivity and the second with high specificity.

Bayes Theorem↗

Bayesian analysis of hierarchical pattern-mixture models for clinical trials data with attrition and comparisons to commonly used ad-hoc and model-based approaches.

This article addresses the problem of making scientifically sound inferences from clinical trials data with attrition, when reasons of attrition seem related to the outcomes of interest. The problem is particularly difficult when the effect of a covariate is to be estimated and if the dropout mechanism appears to operate differently at different levels of the covariate. In this context, multiple imputation under a multilevel pattern-mixture model that allows random variation across dropout groups is presented. Using simulated data generated around an alcoholic hepatitis trial, we compare the performance of this model and commonly used ad-hoc and model-based approaches.

Algorithms↗

Bayesian analysis of stress thallium scintigraphy for the detection of multivessel coronary disease.

This study was performed in 224 men to determine the respective contribution of history and thallium-201 stress myocardial scintigraphic imaging in the non-invasive prediction of the severity of coronary disease. Myocardial scintigraphic imaging had the better diagnostic accuracy (80%) for the detection of multivessel disease but the results emphasize the importance of the history in predicting the extent of coronary artery disease. In patients with myocardial infarction, the diagnostic accuracy of the history (80%) was similar to the diagnostic accuracy of myocardial scintigraphic imaging (79%); in the subgroup of patients with residual angina pectoris after infarction, the accuracy of the history was even greater (87%) than that of myocardial scintigraphic imaging (78%). Thus, after myocardial infarction, scintigraphy was useful only in the small subgroup of patients without residual angina pectoris when it had a diagnostic accuracy of 79%, slightly but insignificantly superior to that of the history (62%). In patients without previous myocardial infarction, but with typical angina, myocardial scintigraphy was clearly superior to the simple history (diagnostic accuracy of 78% versus 53%; P less than 0.001). In patients without myocardial infarction and with atypical angina the prevalence of multivessel disease was low (17%) and the diagnostic accuracy of history (83%) was barely different from the diagnostic accuracy of myocardial scintigraphic imaging (90%). Thus, when the likelihood of multivessel disease is very high (angina pectoris post myocardial infarction), or very low (atypical angina), the contribution of exercise testing is very limited. Important additional information is provided by maximal exercise testing and myocardial scintigraphic imaging only in the groups with an intermediate prevalence of multivessel disease, namely in the asymptomatic patients after myocardial infarction and in the patients with typical angina but no previous myocardial infarction.

Angiography↗

Bayesian analysis of data: reconstruction of track structure at 100% detection efficiency for a track-nanodosimetric counter.

An algorithmic reconstruction of the probability distribution of ionisation cluster-size formation from measurements performed with detectors having a non-uniform sensitive volume is presented. From such a data analysis, ionisation spectra, which correspond to a detection efficiency of 100% are extracted for the track-nanodosimetric counter at L.N.L.-I.N.F.N.

Algorithms↗

Estimating the posterior probability of LTP failure by sequential Bayesian analysis of an imperfect Bernoulli trial model.

A tetanically stimulated (TS) neuron is said to have failed to fire if its voltage-clamped excitatory postsynaptic current (EPSC) measurement is devoid of a long-term potentiation (LTP) response. This paper provides a method for evaluating the posterior probability of "failure" for TS neurons. A sequential Bayes algorithm is employed on an imperfect Bernoulli trial model to refine the posterior with each EPSC data record processed. The method is applied to both real and simulated LTP data and is shown to be consistent with the theoretical Beta-distributed posterior and the reported in vitro voltage-clamped EPSC failure rates.

Algorithms↗

Bayesian analysis.

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Bayes Theorem↗

Determining the likelihood of malignancy in solitary pulmonary nodules with Bayesian analysis. Part I. Theory.

Only two radiographic findings allow reliable distinction of benign from malignant solitary pulmonary nodules. Intuitively, it is clear that other radiographic and clinical findings should also be important in making this distinction. Subjectively incorporating these other findings into the decision of whether a nodule is benign or malignant is difficult. Likelihood ratios, which indicate the degree of malignancy or benignity represented by a test result or clinical finding, can be combined by means of the Bayes theorem to quantitate the probability of malignancy of a given nodule. From a literature survey, likelihood ratios were derived for six radiographic and four clinical characteristics associated with solitary pulmonary nodules. There were a total of 15 malignant and 19 benign findings, the most important of which were radiographic characteristics. For malignant nodules, the most important radiographic characteristics were thickness of the cavity wall spicular edge, and diameter of over 3 cm. For benign nodules, the most important radiographic characteristics were benign growth rate and a benign pattern of calcification.

Adult↗

Bayesian analysis of diastolic blood pressure measurement.

A mathematical model is presented for measurements that include substantial fluctuation and error. Under the assumptions that the fluctuation-error variance is the same for all subjects, and that the distributions of fluctuation-error variance within subjects and "true" values of the measurements in the population are normal, Bayes' theorem produces a simple estimate of the "true" value of a measurement, and a standard error, conditional on a single observation. The model is easily extended to several observations. Methods for estimating the parameters of the model from a data set are presented, and applied to diastolic blood pressures of patients in the authors' primary care clinic. The test-retest reliability of a single blood pressure measurement for this population is 0.41. Because continuous measurements are often dichotomized into "normal" and "abnormal" ranges by a threshold criterion, the authors present formulas for the positive predictive value when a decision rule based on a given number of observations is used in a population with respect to a threshold criterion for the "true" values. For example, classifying their patients as hypertensive on the basis of the average of two readings exceeding 90 mm Hg diastolic pressure would have a positive predictive value of 52% for the "gold standard" of average diastolic pressure exceeding 90 mm Hg. Formulas to calculate the frequency with which patients will be classified "abnormal" by one decision rule but will be classified "normal" by later application of another rule are provided and used to "predict" the frequency with which this crossover phenomenon should have occurred in the enrollment phase of the Hypertension Detection and Follow-up Programs.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

The single-cutoff trap: implications for Bayesian analysis of stress electrocardiograms.

Quantitative analysis of exercise electrocardiograms has been emphasized by many investigators. Specific problems have been found when a single cutoff is used to define a positive or a negative test: a single cutoff does not distinguish stress electrocardiography results that are slightly positive from those that are markedly positive. This may lead clinicians to underweigh strong evidence for or against coronary artery disease. This study evaluated clinicians' quantitative analysis of stress electrocardiograms. Two hundred and thirty-five physicians interpreted the results of mildly positive (1.2 mm ST-segment depression) and strongly positive (2.2 mm ST-segment depression) stress electrocardiograms. Their posttest probability estimates were too high for a mildly positive test (0.62 +/- 0.02 versus actual of 0.38; p less than 0.001) and too low for a strongly positive test (0.77 +/- 0.01 versus actual of 0.98; p less than 0.001). Physicians should understand decision aids and should use multiple rather than single cutoffs to interpret the results of stress electrocardiography.

Bayes Theorem↗

A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits.

Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear.

Animals↗

Diagnosing liver metastases: a Bayesian analysis.

Clinicians frequently perform tests to determine whether patients have liver metastases. Optimal use of a laboratory test requires that the clinician know the test's operating characteristics (its sensitivity and specificity) and have an estimate of the pretest probability that disease is present. We have surveyed studies that examined the value of four biochemical and three imaging tests in establishing a diagnosis of hepatic metastases in patients who underwent an invasive procedure to establish the presence or absence of disease. We have pooled the data from these studies to arrive at values for the sensitivity and specificity of each of these tests, and calculated the predictive values for these tests over a wide range of pretest probabilities of disease. Several examples illustrate how this information may be used clinically. We provide a framework for the optimal interpretation of these commonly ordered tests and indicate the data needed for their complete analysis.

Bayes Theorem↗