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PubMed2002

Using Bayes' theorem to answer a practical heart valve question.

BACKGROUND AND AIM OF THE STUDY: The risk of thromboembolism (TE) risk in a heart valve patient who has lived perhaps for 15 years since implant without TE or thrombosis is unknown. As patients are heterogeneous with regard to embolic risk, these patients must have a lower than average risk; whether this risk reduction could be quantified was the aim of the present study. METHODS: If all patients had the same risk, the TE-free curve would be exponential, with a constant hazard (equal to the 'linearized' rate). With a mixture of risks in a population, the population hazard will be a decreasing function of time. By fitting a certain parametric function to the TE-free curve, the mixing distribution can be estimated. Subsequently, given an observation for a particular patient, e.g. zero emboli in 15 years, Bayes' theorem can be used to update the mixing distribution for these patients. RESULTS: Using observed TE-free curves for Starr-Edwards valves, the mixing distribution for TE-free periods from one to 25 years was estimated. Because the risk distributions were skewed, the mean value was higher than the median. The mean (median) risk (% per year) fell from 4.5 (1.8) at implant to 1.7 (0.7) at 15 years for the aortic position, and from 7.0 (3.4) to 2.4 (1.2) for the mitral position. Thus, the average risk after 15 years was approximately 35-40% of the risk at implant for both the aortic and mitral positions, using either the mean or median risk. CONCLUSION: The mean risk for patients after 15 TE-free years is approximately one-third of the risk of all patients at implant. However, there is a wide range, with some patients still having higher risks. Bayes' theorem is useful for deriving such answers. Linearized rates have limited value for describing TE risk in a heterogeneous population.

Aortic Valve↗
PubMed1983

The effect of assuming independence in applying Bayes' theorem to risk estimation and classification in diagnosis.

The effect of assuming independence in the use of Bayes' Theorem for classification and estimation of risk is examined. Analytic results are provided for two specific multivariate normal models and for a model involving binary variables. Monte Carlo results are presented for the former. In these specific cases and an example from medical research, the (false) independence assumption results in classification error rates comparable or better than rates obtained by using the correct model. For a number of covariance structures selected, the a posteriori distribution becomes more U-shaped as the number of variables increases, thus biasing the estimate of risk toward zero or one.

Bayes Theorem↗
PubMedDate not supplied

[Diagnosis of fever of unknown origin: use of Bayes theorem].

Sophisticated tests and time are needed to establish the diagnosis of fever of unknown origin (FUO). Bayes theorem can guide the clinician to early probabilistic diagnosis. The authors had estimated the a priori probabilities in a previous study yet. In this paper the diagnostic probabilities of four clinical signs (arthralgias, myalgias, splenomegaly, multiple micro-lymphoadenopathies) and the probabilities of abnormalities of some routine laboratory tests (neutrophils count, lymphocytes count, platelets count, hemoglobin, lactic-dehydrogenase, C3 and C4 complement subunits and fibrinogen plasma concentrations, erythrocyte sedimentation rate) and of the positive bacterial cultures, were estimated in the main groups of FUO disease (indefinite, aspecific bacteria infections, non-bacterial or specific bacteria infections, neoplasias, connective tissue diseases, miscellaneous group). The data suggest that the a priori probability is not affected by the clinical signs. Arthralgias increase the probability of connective tissue diseases. Normal erythrocyte sedimentation rate and plasma fibrinogen concentrations increase the probability of paraneoplastic and indefinite fever. Thrombocytosis increases the probability of paraneoplastic fever. Over 1200 U/l serum lactic-dehydrogenase serum concentrations guide to non-bacterial or specific bacteria infectious diseases and to malignancies. Neutrophilia decreases the probability of indefinite diagnosis, even though it is not specific. The heterogeneity of the miscellaneous group makes the interpretations of the data very hard.

Arthralgia↗
PubMed1988

An assessment of the use of Bayes' Theorem for forecasting in public health: the case of epidemic meningitis in China.

A mathematical model based upon Bayes' Theorem (BT) was used to forecast the occurrence of epidemic cerebrospinal meningitis (ECM) in ten communities in North China. Reports of ECM from each ten-day period during the meningitis season and records of special population movement during 1960-82 were analysed to establish forecast models. Calibration, split-sample, random-sample selection, as well as actual forecast tests, were used to check the efficiency of the models. For all the tests, the theoretical occurrence of ECM forecast by the BT method was compared with the observational data. Since the BT method offers efficiency and convenience, it is recommended for use in planning for the prevention and control of ECM in China.

Bayes Theorem↗
PubMed2000

The meaning of malingering data: further applications of Bayes' theorem.

A previous Behavioral Sciences and the Law article (Mossman & Hart, 1996) asserted that information from malingering tests is best conceptualized using Bayes' theorem, and that courts therefore deserve Bayesian interpretations when mental health professionals present evidence about malingering. Mossman and Hart gave several examples of estimated Bayesian posterior probabilities, but they did not systematically address how one constructs confidence intervals for these estimates. This article explains how the usually imperfect nature of humanly created diagnostic tests mandates Bayesian interpretations of test results, and describes methods for generating confidence intervals for posterior probabilities. Sample calculations show that Bayesian reasoning is quite feasible and would not require investigators to expend unusual efforts when constructing and validating malingering instruments. Bayesian interpretations most accurately capture what malingering tests do: provide information that alters one's beliefs about the likelihood of malingering.

Attitude to Health↗
PubMed1994

Foundations of medical diagnosis: what actually are the parameters involved in Bayes' theorem?

Three decades ago, the thesis was adduced that setting diagnostic probabilities requires, by the inherent nature of diagnosis-pertinent medical knowledge, the use of Bayes' theorem. That paper was both vague and inconsistent in its delineation of the nature of the parameters involved in this formulation, and subsequent authors have only added to the confusion. Nevertheless, that thesis has been, and continues to be, enthusiastically embraced by clinical scholars. We here posit what those parameters must be taken to represent in principle; and this explication reveals that their quantification poses generally unsurmountable epistemologic challenges. The implication of this is not that informed setting of diagnostic probabilities is generally infeasible. Our conclusion is, instead, that the seminal thesis was founded on an untenable pair of premises about the nature of scientifically attainable knowledge pertinent to diagnosis.

Bayes Theorem↗
PubMed1984

Bayes' theorem and X-linked ophthalmic disorders.

Many X-linked disorders are confined to the eye or have ocular manifestations. The provision of genetic counseling for potential carriers requires accurate risk assessment. An application of Bayes' theorem to risk assessment for the daughter of an obligate carrier, and her daughter, is given.

Adult↗
PubMed1984

Differentiation between diseases using a programmable hand-held calculator and Bayes' theorem: application to lower gastrointestinal tract disorders.

A program is presented for the Hewlett-Packard HP-41C programmable pocket calculator that computes posterior probabilities of more than 200 diseases on the basis of Bayes' theorem. Data for specific applications are stored in ASCII files. The program and data are retained in the non-volatile memory of the calculator. An example of the application of the program to six lower gastrointestinal tract disorders is given using data from the literature.

Bayes Theorem↗
PubMed1990

[The use of Bayes' theorem in controlling the coming epidemic peak of epidemic meningitis in the 1980s].

To control the coming epidemic peak of epidemic cerebrospinal meningitis (ECM) in the 1980s in the regions with 100 million population in China, the mathematical models based upon Bayes' theorem (BT) were established and used respectively in provincial, regional and county's level. Reports of ECM from each ten-day's period or each month during the meningitis season were analysed to create forecast models. Records of ECM vaccinating rate in previous years were fully taken into account to modify the theoretical values. Calibration, split-sample, random-sample selection, as well as actual forecast tests, were used to check the efficiency of the models. The distribution of meningitis vaccine was planned according to the final predictive results. The incidence rates of ECM of above regions decreased obviously faster than other areas in China. Attributing the application of BT forecast research, it was estimated only in Henan province 79795 ECM cases; 4388 deaths and 21 million Yuan economic damage were avoided during the 4 years period, from 1985 to 1988.

Bayes Theorem↗
PubMed2002

Restoration of movement using functional electrical stimulation and Bayes' theorem.

Various computational approaches have been applied to predict aspects of animal behavior from the recorded activity of populations of neurons. Here we invert this process to predict the requisite neuromuscular activity associated with specified motor behaviors. A probabilistic method based on Bayes' theorem was used to predict the patterns of muscular activity needed to produce various types of desired finger movements. The profiles of predicted activity were then used to drive frequency-modulated muscle stimulators to evoke multijoint finger movements. Comparison of movements generated by electrical stimulation with desired movements yielded root mean squared errors between approximately 18 and 26%. This reasonable correspondence between desired and evoked movements suggests that this approach might serve as a useful strategy to control neuroprosthetic systems that aim to restore movement to paralyzed individuals.

Algorithms↗
PubMed2000

[Evaluation of medical diagnostic tests: application of Bayes theorem, ROC-curve and Kappa-test] .

With the technical improvement of the sensitivity and specificity of the medical diagnostic tests the principles and methods of statistical analysis of the tests are in developing too. The technical development of the diagnostic tests and the exact statistical evaluation of the data will improve the reliability and effectiveness of the decisions for medical interventions. Application, statistical evaluation and interpretation of the Bayes theorem, ROC curve and Kappa test are presented.

Bayes Theorem↗
PubMed1983

Interactive microcomputer-based graphical tools for physician decision support. Aids to test selection and interpretation and use of Bayes' theorem.

Three microcomputer programs have been developed to give the practicing physician graphic aid in assessing the usefulness of obtaining a diagnostic test, to assist in interpreting the result after a test has been obtained, and to facilitate exploration of, and familiarity with, the use of Bayes' theorem in clinical practice. Each program uses a different representation for depicting the transformation of pretest to post-test probability produced by the various results of the test. Choice of representation depends on whether multiple tests or results are evaluated concurrently, on the probability range of interest, and on which model the user finds most intuitively appealing. A library of data on sensitivities and specificities of various tests and procedures can be used to select tests of interest from a menu, or data may be entered by the user.

Bayes Theorem↗
PubMed1990

Two-locus linkage analysis using recombinant inbred strains and Bayes' theorem.

Recombinant inbred (RI) strains are useful in linkage analysis and gene mapping. The currently available statistical tests of linkage using data derived from the study of RI strains, including a previous Bayesian analysis, have not been stringent enough guides for conclusions about linkage. In this paper, the probability of linkage was estimated using Bayes' theorem. Tables are presented that give the probability of linkage in sets of up to 30 RI strains and the critical values of i (the number of recombinants) in sets of up to 100 RI strains. Several means of increasing the power of RI strains in linkage analysis are discussed.

Animals↗
PubMed1999

Clinical experience with a decision support computer program using Bayes' theorem to diagnose chest pain patients.

A decision support computer program (DSP) was used by the emergency room physician as a diagnostic tool on patients admitted with acute chest pain to guide the referral of these patients either to the Coronary Care Unit (CCU) or general ward. The DSP used Bayes' theorem on 38 anamnestic and clinical variables to classify patients into one of nine diagnoses. During a six months trial period 32 physicians used the DSP to diagnose 493 patients admitted with acute chest pain. The physicians referred the patients to CCU or general ward based on their clinical judgements, the ECG findings and the diagnostic estimates given by the DSP. The program correctly diagnosed 150 (84%) of 178 patients with acute myocardial infarction and 63 of 112 patients with unstable angina. However, acute ischemic heart disease (acute myocardial infarction or unstable angina) was correctly classified by the DSP for 259 (89%) of 290 patients. By using the DSP, the number of patients unnecessarily referred to CCU was reduced from 35% to 19% and the number of patients in need of CCU observation misallocated to general ward was reduced from 13% to 10%. Thus, use of the DSP in the emergency room on easily available anamnestic and clinical variables may improve referrals to the CCU, optimize therapy and resource use.

Adult↗