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PubMed1991

The Bayesian approach to evaluation of diagnostic data.

Following review of the basic principles of Bayes' theorem, its application to diagnostic procedures is discussed. It is asserted that Bayes' theorem can be applied to clinical diagnostics, provided that disease prior probabilities can be calculated and it can be assumed that a particular patient and those included in the calculation of prior probabilities represent two samples of the same homogeneous population. Problems associated with both these requirements are briefly reviewed. With the aid of some clinical examples, the usefulness of Bayes' theorem is detailed in: (a) evaluating the information obtained through the results of diagnostic studies, (b) evaluating the level of diagnostic reliability achieved with obtained data and (c) a priori evaluation, i.e. before knowing the result, of what kind of information a test can supply. It is concluded that Bayes' theorem is a powerful tool in the rational control and improvement of diagnostic procedures, if not relevant in the formulation of the diagnosis of a single patient.

Bayes Theorem↗
PubMed1994

Bayesian-logit model for risk assessment in coronary artery bypass grafting.

Predictive models for the assessment of operative risk using patient risk factors have gained popularity in the medical community as an important tool for the adjustment of surgical outcome. The Bayes' theorem model is among the various models used to predict mortality among patients undergoing coronary artery bypass grafting procedures. Comparative studies of the various classic statistical techniques, such as logistic regression, cluster of variables followed by a logistic regression, a subjectively created sickness score, classification trees model, and the Bayes' theorem model, have shown that the Bayes' model is among those with the highest predictive power. In this study, the Bayes' theorem model is reformulated as a logistic equation and extended to include qualitative and quantitative risk factors. We show that the resulting model, the Bayesian-logit model, is a mixture of logistic regression and linear discriminant analysis. This new model can be created easily without complex computer programs. Using 12,712 patients undergoing coronary artery bypass grafting procedures at the Department of Veterans Affairs Continuous Improvement in Cardiac Surgery Study between April 1987 and March 1990, the predictive power of the Bayesian-logit model is compared with the Bayes' theorem model, logistic regression, and discriminant analysis. The ability of the Bayesian-logit model to discriminate between operative deaths and operative survivors is comparable with that of logistic regression and discriminant analysis.

Age Factors↗
PubMed1992

Development and validation of a computer program using Bayes's theorem to support diagnosis of rheumatic disorders.

A computer program has been developed to support the differential diagnosis of major rheumatic disease categories. Knowledge for the program was derived from the sensitivity and specificity of findings in a group of 1052 consecutive patients of a rheumatological outpatient clinic. Computer predictions based on two variations of Bayes's theorem were compared with 'gold standard' diagnoses in 570 test cases from the same clinic. The results demonstrate the feasibility of this approach, but also that refinements of both the method of calculation and the knowledge are required.

Adolescent↗
PubMed2003

Hypothesis testing and theory evaluation at the boundaries: surprising insights from Bayes's theorem.

Because the probability of obtaining an experimental finding given that the null hypothesis is true [p(F\H0)] is not the same as the probability that the null hypothesis is true given a finding [p(H0\F)], calculating the former probability does not justify conclusions about the latter one. As the standard null-hypothesis significance-testing procedure does just that, it is logically invalid (J. Cohen, 1994). Theoretically, Bayes's theorem yields p(H0\F), but in practice, researchers rarely know the correct values for 2 of the variables in the theorem. Nevertheless, by considering a wide range of possible values for the unknown variables, it is possible to calculate a range of theoretical values for p(H0\F) and to draw conclusions about both hypothesis testing and theory evaluation.

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↗
PubMed1990

Highly specific prediction of antineoplastic drug resistance with an in vitro assay using suprapharmacologic drug exposures.

Bayes' theorem has been used to describe the relationship between the accuracy of a predictive test (posttest probability) and the overall incidence of what is being tested (pretest probability). Bayes' theorem indicates that laboratory assays will be accurate in the prediction of clinical drug resistance in tumors with high overall response rates (e.g., previously untreated breast cancer) only when the assays are extremely (greater than 98%) specific for drug resistance. We developed a highly specific drug-resistance assay in which human tumor colonies were cultured in soft agar and drugs were tested at high concentrations for long exposure times. Coefficients for concentration x time exceeded those reported in contemporaneous studies by about 100-fold. We reviewed 450 correlations between assay results and clinical response over an 8-year period. Results were analyzed by subsets, including different tumor histologies, single agents, and drug combinations. Extreme drug resistance (an assay result greater than or equal to SD below the median) was identified with greater than 99% specificity. Only one of 127 patients with tumors showing extreme drug resistance responded to chemotherapy. This negligible posttest probability of response was independent of pretest (expected) probability of response. Once this population of patients with tumors showing extreme drug resistance had been identified, posttest response probabilities for the remaining cohorts of patients varied according to both assay results and pretest response probabilities, precisely according to predictions based on Bayes' theorem. This finding allowed the construction of a nomogram for determining assay-predicted probability of response.

Antineoplastic Agents↗
PubMed1981

Probabilities of success and failure in endodontic treatment: a Bayesian approach.

Bayes' theorem provides a mathematical rule for changing a (prior) probability into a new (posterior) probability incorporating additional information. Application of the theorem is a way to overcome some limitations that the human mind has in processing information. A Bayesian approach is useful for the processing of data and as a tool for decision making. Bayes' theorem is expounded, and examples are given of the use of the theorem for computing the odds on success or failure of endodontic treatment of a tooth, given a particular preoperative status and given also the results of the preparation and filling of the root canal of the tooth in question. Application of Bayes' theorem using data collected provides an insight based upon probabilities and odds in the way preoperative conditions and operative results affect the ultimate treatment result.

Bayes Theorem↗
PubMed2004

Policy relevance of Bayesian statistics overestimated?

OBJECTIVES: The observed posterior probability distributions regarding the benefits of surgery for otitis media with effusion (OME) with expected probability distributions, using Bayes' theorem are compared. METHODS: Postal questionnaires were used to assess prior and posterior probability distributions among ear-nose-throat (ENT) surgeons in the Netherlands. RESULTS: In their prior probability estimates, ENT surgeons were quite optimistic with respect to the effectiveness of tube insertion in the treatment of OME. The trial showed no meaningful benefit of tubes on hearing and language development. Posterior probabilities calculated on the basis of prior probability estimates and trial results differed widely from those, elicited empirically 1 year after completion of the trial and dissemination of the results. CONCLUSIONS: ENT surgeons did not adjust their opinion about the benefits of surgical treatment of glue ears to the extent that they should have done according to Bayes' theorem. Users of the results of Bayesian analyses, notably policy-makers, should realize that Bayes' theorem is prescriptive and not necessarily descriptively correct. Health policy decisions should not be based on the untested assumption that health-care professionals use new evidence to adjust their subjective beliefs in a Bayesian manner.

Attitude of Health Personnel↗
PubMed1979

Application of Bayes's theorem to results of quantitative clinical chemical determinations.

The diagnostic implication of a certain test result with regard to a certain condition can be expressed as a single number, L, the likelihood ratio of this result. This ratio allows Bayes's theorem to be written in a convenient form. We show that the practice of calculating predictive values for the results of quantitative tests by use of discrimination limits leads to incorrect predictive values. Including L values in laboratory reports seems a more logical approach to optimum interpretation of laboratory results than the use of discrimination values.

Blood Glucose↗
PubMedDate not supplied

Value of Doppler ultrasonography in management of patients with follicular thyroid biopsy specimens.

OBJECTIVE: To perform a statistical evaluation with use of Bayes' theorem, evaluating the prognostic value of Doppler flow analysis, to determine the probability of cancer in thyroid nodules with a prior follicular biopsy specimen. METHODS: The medical literature was reviewed to identify studies in which ultrasonographic Doppler flow analysis was performed on thyroid nodules with a prior fine-needle aspiration biopsy sample showing follicular cytologic features. For inclusion in the study, all nodules must have had pathologic confirmation of the final diagnosis. The pretest probability of cancer was considered to be the incidence of carcinoma within the population studied. The posttest or conditional probability was calculated by using Bayes' theorem. RESULTS: Two well-designed prospective studies met the criteria for inclusion. The sensitivity of demonstration of intranodular flow by Doppler analysis for detection of thyroid carcinoma ranged from 80% to 86%. The specificity of intranodular flow indicating cancer ranged from 85% to 89%. The incidence of thyroid cancer (pretest probability) ranged from 12% to 14%. Application of Bayes' theorem indicated that the posttest probability of thyroid cancer declined to 3% when no central intranodular flow was present and increased to nearly 50% in the presence of intranodular flow. CONCLUSION: Doppler flow analysis, when performed on thyroid nodules with follicular cytologic findings on fine-needle aspiration biopsy, can provide extremely useful information regarding the probability of malignant involvement. This information can be used in the decision-making process about the need for, and the extent of, surgical resection of follicular lesions.

Bayes Theorem↗
PubMed2002

The inverse fallacy: an account of deviations from Bayes's theorem and the additivity principle.

In judging posterior probabilities, people often answer with the inverse conditional probability--a tendency named the inverse fallacy. Participants (N = 45) were given a series of probability problems that entailed estimating both p(H / D) and p(approximately H / D). The findings revealed that deviations of participants' estimates from Bayesian calculations and from the additivity principle could be predicted by the corresponding deviations of the inverse probabilities from these relevant normative benchmarks. Methodological and theoretical implications of the distinction between inverse fallacy and base-rate neglect and the generalization of the study of additivity to conditional probabilities are discussed.

Bayes Theorem↗
PubMed1986

Probability theory in the use of diagnostic tests. An introduction to critical study of the literature.

The purpose of this article is to provide an understanding of methods that are useful in formulating advice about when to use diagnostic tests. If the clinician expresses diagnostic uncertainty as the probability of a disease in a patient, Bayes' theorem may be used to predict the effect of doing various tests and their impact on patient management. To use Bayes' theorem wisely, one must be aware of pitfalls in estimating probability and must understand the limitations of most studies of the sensitivity and specificity of diagnostic tests.

Bayes Theorem↗
PubMed1999

Heuristics and biases: selected errors in clinical reasoning.

Many clinical decisions are made in uncertainty. When the diagnosis is uncertain, the goal is to establish a diagnosis or to treat even if the diagnosis remains unknown. If the diagnosis is known (e.g., breast cancer or prostate cancer) but the treatment is risky and its outcome uncertain, still a choice must be made. In researching the psychology of clinical judgment and decision making, the major strategy is to compare observed clinical judgments and decisions with the normative model established by statistical decision theory. In this framework, the process of diagnosing is conceptualized as using imperfect information to revise opinions; Bayes' theorem is the formal rule for updating a diagnosis as new data are available. Treatment decisions should be made so as to maximize expected value. This essay uses Bayes' theorem and concepts from decision theory to describe and explain some well-documented errors in clinical reasoning. Heuristics and biases are the cognitive factors that produce these errors.

Bayes Theorem↗
PubMed2005

An automatic warning system for epileptic seizures recorded on intracerebral EEGs.

OBJECTIVE: A new clinical seizure waning system for intracerebral EEG is proposed. It is aimed at a better performance than existing systems and at user tuneability. METHODS: The system employs data filtering in multiple bands, spectral feature extraction, Bayes' theorem, and spatio-temporal analysis. The a priori information in Bayes' theorem was provided by 407 h of EEG from 19 patients having 152 seizures. RESULTS: The testing data (19 patients, 389 h, 100 seizures, independent of the training data) yielded a sensitivity of 89.4%, a false detection rate of 0.22/h, and median delay time of 17.1 s when tuning was used, and 86%, 0.47/h and 16.2 s without tuning. Missed seizures were of short duration or had subtle seizure activity. False detections were caused by technical artefacts, non-epileptic large amplitude rhythmic bursts or very low amplitude activity. It was established that performance could easily be tuned. Results were also compared to the clinical system of . CONCLUSIONS: The system offers a performance that is acceptable for clinical use. User tuneability allows for reduction in false detection with minimal loss to sensitivity. SIGNIFICANCE: Epilepsy monitoring generates large amounts of recordings and requires intense observation. Automatic seizure detection and warning systems reduce review time and facilitate observation. We propose a method with high sensitivity and few false alarms.

Acute Disease↗
PubMed1993

Overestimation of test effects in clinical judgment.

The purpose of this study was to assess the ability of health care professionals to evaluate the effect of test results on disease risk. Fifty health care professionals, including 29 physicians and 21 nonphysicians, associated with a university hospital were studied. Subjects were presented with two hypothetical scenarios involving a common clinical situation to assess the effect of test results on the estimation of disease risk. Estimates of the pretest and posttest probability of breast cancer and mammography sensitivity and specificity were elicited for hypothetical 30- and 70-year-old patients presenting with a breast lump. There was no significant difference between physician and nonphysician probability and sensitivity estimates, although physicians provided higher specificity estimates which were more consistent with literature-derived values. Both physicians and nonphysicians consistently overestimated the risk associated with a positive test result compared to probabilities derived from Bayes' theorem based on the subject's pretest probability and sensitivity and specificity estimates, as well as standard test performance estimates. There was no significant difference between posttest probability estimates for negative test results and those derived from Bayes' theorem utilizing the subject's pretest probability and sensitivity and specificity estimates. Physicians and nonphysicians both estimate test performance characteristics accurately but consistently overestimate the effect of positive test results on the probability of disease. In addition to experience with specific clinical problems, decision making by clinicians could be enhanced by training in the formal methods of decision analysis.

Adult↗