SEARCH · Search PubMed
Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Bayes' theorem, as applied to the interpretation of diagnostic tests, is reexpressed as a two-step transformation. This allows for the construction of graphic and tabular expressions of this important principle.
Bayes' theorem describes the effect of new information (e.g., a test result) on the probability of an outcome (e.g., a disease). Likelihood ratios for separate tests can be combined to assess the joint effect of their results on disease probability. This approach has been used to develop a test package for Alzheimer's disease that consists of some simple cognitive tests (Paired Associate Learning Test, Trailmaking Test, and Raven's Progressive Matrices) combined with age and family history of dementia. A total of 1,454 subjects who had been recruited into the Medical Research Council Elderly Hypertension Trial between 1983 and 1985 completed cognitive tests at entry to the trial (when they were without signs of dementia) and 1 month later. Their dementia status was ascertained in 1990-1991. The test package identified 52% of Alzheimer's disease cases with a 9% false-positive rate or 90% of Alzheimer's disease cases with a 29% false-positive rate. The author proposes the use of a similar test package in conjunction with a test for apolipoprotein E e4 status, which is a powerful risk factor for late-onset Alzheimer's disease, as a likelihood ratio approach to the prospective identification of Alzheimer's disease cases. This approach could be followed by ethically sound trials of new therapeutic agents for subjects who have a high probability of developing Alzheimer's disease.
Explore the source record for details and available documents.
The utility of Bayes' theorem in the noninvasive diagnosis of coronary artery disease (CAD) was analyzed in 147 patients who underwent electrocardiographic stress testing, thallium-201 perfusion imaging and coronary angiography. Eighty-nine patients had typical anginal chest discomfort and 58 had atypical chest pain. Sensitivity and specificity of the tests and prevalence of CAD at each level of testing were tabulated and compared with the results generated from Bayes' theorem. The sensitivity of electrocardiographic stress was higher in patients with multivessel CAD than in patients with 1-vessel CAD. Sensitivity, but not specificity, of each test was dependent, in part, on the result of the other test. However, the probabilities calculated from Bayes' theorem when used for sequential testing are remarkably close to the tabulated data. Thus, Bayes' theorem is useful clinically despite some evidence of test dependence. Sequential test analysis by Bayes' theorem is most useful in establishing or ruling out a diagnosis when the pretest prevalence is approximately 50% and when the 2 tests are concordant.
This article reintroduces a different form of Bayes' theorem that allows calculation of posttest probabilities by adding quantities known as "weights." A weight combines information found in both a test's sensitivity and specificity. A single value can describe how a given test result changes the posttest probability of disease. The use of weights and this form of Bayes' theorem should allow more widespread understanding and use of probability theory in clinical practice.
This report describes a method of using Bayes Theorem for determining the post-test likelihood for coronary disease from the exercise test. The pre-test likelihood is determined from the age, sex, and type of chest pain. Discriminant analysis of the amount of S-T depression, maximum pressure rate product and sex of the patient is then used to determine the sensitivity and specificity of the patient's exercise test for coronary artery disease. The post-test likelihood for coronary artery disease can then be calculated using Bayes Theorem. The discriminant function was estimated from a training set of 174 patients. This was then applied to 113 new patients who had both exercise tests and coronary arteriograms. In this new set, 47 patients had a post-test likelihood of 90% or greater for coronary disease. Only one of these patients had normal coronary arteriograms, a predictive accuracy of 98%. Of the 25 patients with a post-test likelihood of 10% or less for coronary disease, four had multivessel disease and four had single vessel disease. The predictive accuracy for the absence of coronary disease was 68%. The predictive accuracy for the exclusion of multivessel disease was 84%. Eight of 10 patients with left main disease had a post-test likelihood for coronary disease of greater than 90%.
Estimates of sensitivity and specificity can be biased by the preferential referral of patients with positive test responses or ancillary clinical abnormalities (the "concomitant information vector") for diagnostic verification. When these biased estimates are analyzed by Bayes' theorem, the resultant posterior disease probabilities (positive and negative predictive accuracies) are similarly biased. Accordingly, a series of computer simulations was performed to quantify the effects of various degrees of verification bias on the calculation of predictive accuracy using Bayes' theorem. The magnitudes of the errors in the observed true-positive rate (sensitivity) and false-positive rate (the complement of specificity) ranged from +11% and +23%, respectively (when the test response and the concomitant information vector were conditionally independent), to +16% and +48% (when they were conditionally non-independent). These errors produced absolute underestimations as high as 22% in positive predictive accuracy, and as high as 14% in negative predictive accuracy, when analyzed by Bayes' theorem at a base rate of 50%. Mathematical correction for biased verification based on the test response using a previously published algorithm significantly reduced these errors by as much as 20%. These data indicate 1) that selection bias significantly distorts the determination of predictive accuracies calculated by Bayes' theorem, and 2) that these distortions can be significantly offset by a correction algorithm.
Probabilities or risks may change when new information is available. Common sense frequently fails in assessing this change. In such cases, Bayes' theorem may be applied. It is easy to derive and has abundant applications in biology and medicine. Some examples of the application of Bayes' theorem are presented here, such as carrier risk estimation in X-chromosomal disorders, maximal manifestation probability of a dominant trait with unknown penetrance, combination of genetic and non-genetic information, and linkage analysis. The presentation addresses the non-specialist who asks for valid and consistent explanations. The conclusion to be drawn is that Bayes' theorem is an accessible and helpful tool for probability calculations in genetics.
The utility of Bayes' theorem in paleopathological diagnoses is explored. Since this theorem has been used heavily by modern clinical medicine, its usefulness in that field is described first. Next, the mechanics of the theorem are discussed, along with methods for deriving the prior probabilities needed for its application. Following this, the sources of these prior probabilities and their accompanying problems in paleopathology are considered. Finally, an application using prehistoric rib lesions is presented to demonstrate the utility of this method to paleopathology.
Formal probability analysis based on Bayes' theorem greatly enhances the diagnostic capabilities of exercise testing in the detection of coronary artery disease. The pretest characteristics of a patient must be considered along with the test results in arriving at a post-test probability of disease. The essential concepts of probability analysis have broad applications in the entire field of medicine.
A model system is described which simulates the presenting features of cases of vaginal discharge. This system was used to examine the effects of removing individual clinical features on the overall efficiency of diagnosis by Bayes theorem. The diagnostic efficiency was significantly reduced by elimination of inflammation, of a frothy discharge, or of a curdy discharge. Elimination of more than one significant factor further reduced the number of correct diagnoses, but elimination of more than one non-significant factor made no obvious difference. The most significant clinical feature was presence of inflammation; elimination of this feature had a substantial effect on the diagnosis of gardnerella, viral, gonorrhoea and foreign body. Elimination of two of the variables (bloodstaining and odour) which did not influence overall diagnostic efficiency nevertheless had a substantial effect on the diagnosis of neoplasms and foreign bodies. It is proposed that a simulation of this type is of potential practical value in determining a minimum subset of clinical features for diagnostic systems involving Bayes theorem.
Computers are being investigated as diagnostic aids in many fields of medicine. Models employing Bayes' theorem, a statistical formula, commonly are used to supply valuable information on the likelihood of each disease in the differential diagnosis to help the clinician make the diagnosis. However, knowledge of elementary decision analysis is beneficial to help understand the current and potential uses of these models. We discussed Bayes' theorem as an introduction to decision analysis. Moreover, we described a Bayesian model for the differential diagnosis of leukocoria to illustrate the application of computers to ophthalmologic diagnosis.
Most radiological signs are of low specificity for predicting malignancy in patients with a solitary pulmonary nodule (SPN), making clinical management difficult. Only certain calcification patterns in SPN or the absence of growth over a period two years assures that the nodule is benign. The clinical and radiological characteristics of 31 patients with SPN were studied. Twenty-two were cases bronchopulmonary carcinoma and 9 were pulmonary tuberculoma. Accuracy in the prediction of malignancy was assessed using Bayes' theorem, which is based on degrees of likelihood of various radiological and clinical characteristics. Patients with carcinoma (mean age 65 +/- 9 years) were significantly older than those with tuberculoma (38 +/- 19 years) (p < 0.05). The proportion of smokers was significantly higher among patients with carcinoma (91%) than those with tuberculoma (44%) (p < 0.05). In 50% of the patients with SPN due to bronchopulmonary carcinoma (11 patients), the nodule was in the upper right lobe; in 55% of those with tuberculomas (5 patients) the nodule was found in the upper left lobe. There were no significant differences in the characteristics of the computerized tomography images for the two groups. Mean likelihood of malignancy for patients with carcinoma, by Bayes' theorem, was 83.7%, a rate that was significantly higher than that of tuberculoma patients (46%) (p < 0.05). The application of Bayes' probability theorem for a set of clinical and radiological characteristics can orient the physician as to whether an SPN is likely to be malignant or not, thereby providing guidance on the advisability of performing invasive diagnostic procedures to determine etiology.
A computer simulation is described which generates 'cases' of vaginal discharge. This simulation was used to evaluate the potential effects of dependence between clinical features on the diagnostic performance of Bayes' theorem. The following observations were made: (1) dependence between some but not all pairs of features reduced the overall diagnostic efficiency (judged by the number of true positive diagnoses); (2) the overall reduction in efficiency was never substantial; (3) the largest effects on the diagnosis of individual conditions was observed with rarer diseases, and with combinations of features which were inherently unlikely to be dependent. It is concluded that the diagnostic efficiency of Bayes' theorem will not be greatly influenced by dependence if a reasonable amount of commonsense is applied to the selection of the knowledge base.
Most obstetricians share the belief that an estimate of gestational age based on several clinical measures that agree with one another is more accurate than an estimate based on a single measurement. This paper presents a formal justification for this belief by applying Bayes' theorem to calculate the probability of a fetus being a certain gestational age by using information from several clinically established single predictors. The application of Bayes' theorem justifies the use of multiple measures of gestational age in individual ultrasound examinations and the use of serial ultrasound studies in the third trimester to more accurately estimate gestational age. The same technique could be applied to obstetric research studies that need to establish accurate gestational dating.
The objective of this study was to examine the incidence of aminoglycoside-associated nephrotoxicity related to extended-interval dosing, individualized pharmacokinetic monitoring, and multiple-daily dosing by applying Bayes theorem. An electronic literature search of MEDLINE (1966-2003) and a manual search of references from published meta-analyses and review articles were performed. Studies using extended-interval dosing, individualized pharmacokinetic monitoring, or multiple-daily dosing and reported aminoglycoside-associated nephrotoxicity for patients > or = 16 years of age were included. Quality scores were assigned based on the rigor of definition of aminoglycoside-associated nephrotoxicity, duration of therapy, and length of follow-up of renal function after completion of therapy. Inclusion criteria were then based on these quality scores. Quantitative data on the incidence of aminoglycoside-associated nephrotoxicity were abstracted. Twelve extended-interval dosing studies (n = 916), 10 individualized pharmacokinetic monitoring studies (n = 2066), and 27 multiple-daily dosing studies (n = 4251) met the inclusion criteria. Prior probabilities of aminoglycoside-associated nephrotoxicity were derived from a combination of a review of published studies and expert judgment. The maximum densities for the final posterior probabilities of aminoglycoside-associated nephrotoxicity for extended-interval dosing, individualized pharmacokinetic monitoring, and multiple-daily dosing were located at 12% to 13%, 10% to 11%, and 13% to 14%, respectively. Application of Bayes theorem demonstrates that aminoglycoside dosing by individualized pharmacokinetic monitoring results in less aminoglycoside-associated nephrotoxicity than extended-interval dosing or multiple-daily dosing.
To assess the immediate impact of the proposed CD4-based expansion of the AIDS case definition, we determined two key proportions from a subsample of men from the San Francisco City Clinic Cohort (SFCCC). We then used Bayes theorem to project the number of persons fitting the proposed definition in the entire SFCCC and in the city of San Francisco. Among those men meeting the 1987 AIDS case definition, the proportion with a CD4 cell count < 200 cells (within 6 months of their AIDS diagnosis) is 0.70 (16 of 23). Among those with a CD4 count ever < 200 cells, the proportion with AIDS is 0.40 (29 of 73). Our estimates show that 446 persons in the SFCCC and 3,603 persons in San Francisco would fit only the expanded definition. Thus, the proposed definition would likely more than double the number of persons who could be diagnosed with AIDS. Bayes theorem offers a simple method for estimating the immediate impact of the proposed CD4-based expansion of the AIDS case definition.
Bayesian inference presupposes that practitioners' belief in the effectiveness of medical intervention is the product of prior belief and recent evidence from studies. Although increasingly used, up to now the posterior belief calculated according to the theorem has not been compared with an empirically measured posterior belief. We conducted a RCT, which was preceded by elicitation of prior beliefs among ENT-surgeons, and which was followed by elicitation of posterior beliefs among ENT-surgeons, 1 year after completion of the trial. We compared the posterior beliefs of ENT-surgeons about the effect of grommets in children with glue ears, as predicted by Bayes' theorem with actual measured posterior beliefs. The distribution of the measured posterior beliefs was not in line with the calculated posterior, but almost identical to the distribution of the measured prior beliefs. The results showed that our trial had little or no impact on the beliefs of the ENT-surgeons, i.e. they did not adjust their belief to the extent that was expected according to Bayes' theorem.