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PubMed1994

Case-based explanation for medical diagnostic programs, with an example from gynaecology.

One of the most accountable methods of providing machine assistance in medical diagnosis is to retrieve and display similar previously diagnosed cases from a database. In practice, however, classifying cases according to the diagnoses of their nearest neighbours is often significantly less accurate than other statistical classifiers. In this paper the transparency of the nearest neighbours method is combined with the accuracy of another statistical method. This is achieved by using the other statistical method to define a measure of similarity between the presentations of two cases. The diagnosis of abdominal pain of suspected gynaecological origin is used as a case study to evaluate this method. Bayes' theorem, with the usual assumption of conditional independence, is used to define a metric on cases. This new metric was found to correspond as well as Hamming distance to the clinical notion of "similarity" between cases, while significantly increasing accuracy to that of the Bayes' method itself.

Abdomen, Acute↗

PubMed1996

[Introduction to quantitative semiology].

Clinicians regularly confront dilemmas when ordering and interpreting diagnostic tests. This paper presents the basic principles necessary for the critical appraisal of articles about diagnostic tests. Basic notions such as sensitivity and specificity are defined. The advantages of using the newer notion of likelihood ratios are underlined. Since all these quantities are estimates of unknown true values, the method for calculating confidence intervals are reported. Finally, the simplified expression of Bayes' theorem based on the use of likelihood ratios is described alongside with a simple nomogram making it possible to calculate posttest probabilities at the bedside.

Bayes Theorem↗

PubMed1989

Prediction of outcome from critical illness. A comparison of clinical judgment with a prediction rule.

Quantitative methods to enhance clinical judgment would be of tremendous benefit to physicians caring for the critically ill. The ability of physicians to predict outcome is a logical standard on which to base the prospective evaluation of a prediction rule intended for this clinical use. The APACHE (acute physiology and chronic health evaluation)-II score was compared with critical care physicians' prediction of outcome for a group of patients in a medical intensive care unit. Physicians were significantly better in predicting outcome in the critically ill. However, the APACHE-II score was still a good predictor of outcome in the intensive care unit and, according to analysis using Bayes' theorem, might still be a useful test to support physicians' judgment, especially in patients with a predicted mortality risk of less than 30%.

Bayes Theorem↗

PubMed1998

Predicting surgical outcome using Bayesian analysis.

Surgical outcome analysis is best performed using Bayesian statistics. The ability of this type of analysis to take into consideration multiple parameters affecting surgical outcome is a marked improvement over single-condition probabilities that ignore the many degrees of freedom in the dynamics of a surgical intervention. To illustrate the power of a Bayesian analysis a surgical population of 1017 patients undergoing cholecystectomy, colon resection, and appendectomy was developed. Each patient was assigned to a mutually exclusive outcome group (D1, survival; D2, survival with complications; D3, nonsurvival). A priori outcome probabilities for the population were D1 = 0.917, D2 = 0.066, and D3 = 0.017. A conditional probability matrix (CPM) was then developed for 59 patient parameters (Sj) that may have affected outcome. The CPM contained the conditional probability that a parameter was present given the known outcome P(Sj/Di). Once the CPM was matured Bayesian analysis allowed one to predict the surgical outcome given any set or combination of patient parameters P(Di/Sj). Posterior probabilities generated by the Bayes analysis allowed one to investigate the effect of a single parameter or any group of parameters on outcome. Criterion based validity testing based on comparison of Bayesian outcomes versus the surgeons perception of outcomes for computer simulated surgery on 15 artificial patients suggests that this type of analysis provides insightful and educational data to the operating surgeons (V-mortality = 0.547, SEE = 24.46; V-morbidity = 0.319, SEE = 25.86). Objective outcome analysis or surgical peer review cannot be fairly accomplished unless the statistical methodology takes into consideration all of the parameters affecting outcome. This study concludes that Bayes Theorem provides the ideal statistical framework for performing an outcome analysis that considers the many parameters affecting the results of a surgical intervention.

Adolescent↗

PubMed1996

Measurement of airborne 218Po--a Bayesian approach.

The standard mathematical treatment of the buildup and decay of airborne radionuclides on a filter paper uses the solutions of the so-called Bateman equations adapted to the sampling process. These equations can be interpreted as differential equations for the expectation of an underlying stochastic process, which describes the random fluctuations in the accumulation and decay of the sampled radioactive atoms. The process for the buildup and decay of airborne 218Po can be characterized as an "immigration-death process" in the widely adopted, biologically based jargon. The probability distribution for the number of 218Po atoms, accumulated after sampling time t, is Poisson. We show that the distribution of the number of counts, registered by a detector with efficiency epsilon during a counting period T after the end of sampling, is also Poisson, with mean dependent on epsilon, t, T, the flowrate and N(o), the number of airborne 218Po atoms per unit volume. This Poisson distribution was used to construct the likelihood given the observed number of counts. After inversion with Bayes' Theorem we obtained the posterior density for N(o). This density characterizes the remaining uncertainty about the measured number of 218Po atoms per unit volume of air.

Air Pollution, Radioactive↗

PubMed2001

Student-centered distance learning in health and medical informatics.

Learning and teaching of health and medical Informatics is currently supported by web based material, which in the main has been derived from traditional texts. Aided by contributions from the expert community, the web site of the handbook of Medical Informatics has been developed to incorporate increased interactivity (with question and answers related to each section). This approach has proved beneficial to both student and teacher. To further increase the interactivity of the WWW we investigate the suitability of authoring tools for developing complex simulations and interactive tutorials, using an example from the area of quantitative decision support (Bayes Theorem). We propose that these tools provide a suitable platform for the preparation and delivery of collaboratively produced HMI courses, which address open and distance learning and pedagogic issues.

Bayes Theorem↗

PubMed2002

Diagnostic data in clinical toxicology--should we use a Bayesian approach?

A number of toxidromes (toxicology syndromes) have been described for various poisonings and are promoted as a means of reaching a diagnosis in patients presenting with unknown poisonings. Many are based entirely on deductive reasoning from the known pharmacological effects of these drugs rather than on documented clinical experience. In this paper, we used our database, where we have recorded clinical signs on presentation in unselected poisonings to explore how clinical signs actually alter the odds of ingestion of different poisons. Many signs substantially altered the list of drugs likely to have been ingested. We found that the most important factor determining whether an unconscious patient had ingested a particular drug was how frequently that drug was taken generally (i.e., the a priori probability), rather than the presence of any particular physical sign. It also follows that our (or anyone else's) intuitive or deductive approach to diagnosis, derived from experience, will not necessarily be very useful at another place where predominantly different drugs are involved in poisoning. Our data were used to derive odds ratios as a measure of the strength of association of physical signs or investigations with ingested poisons. These can be used to develop simple diagnostic algorithms orflow charts to identify the most likely drugs ingested, or using more complicated programming, could also be used to calculate the precise probability of different drug-ingestion using Bayes' Theorem. The usefulness (i.e., external validity) of clinical research from other centers can also be determined.

Adolescent↗

PubMed1980

Medical decisions.

In relation to the application of decision theory to medical problems, a description is given of the terms 'probability', 'utility' and 'coherence'. The use of utilities is illustrated by comparing the outcomes of various methods of palliating terminal renal failure. The use of Bayes' theorem in incorporating additional information is described. Reference is made to specific clinical applications of mathematical methods. Some general comments are made on the way in which clinical and other medical decisions are reached.

Bayes Theorem↗

PubMed1982

The cerebrospinal fluid immunoglobulin G index as a diagnostic aid in multiple sclerosis: a Bayesian approach.

Having determined immunoglobulin G (IgG) and albumin concentrations in 1100 cerebrospinal fluid and serum samples, we calculated the IgG index. Likelihood ratios for multiple sclerosis were calculated by using a training set consisting of 100 patients with definite multiple sclerosis and one consisting of 97 patients suffering from diseases from which multiple sclerosis must be differentiated. Predictive values for multiple sclerosis, given different values for the IgG index, are given in a graphical representation of Bayes' theorem. We conclude that this approach increases the diagnostic usefulness of the IgG index for the diagnosis of multiple sclerosis.

Adolescent↗

PubMed1993

Diagnostic testing in obstetrics and gynecology: a clinician's guide.

As we enter a new era of health care in the United States with limited economic resources, there will be an increasing demand for thoughtful and critical evaluation of the diagnostic tests used in clinical medicine. To interpret the clinical utility of diagnostic tests, the physician must understand the fundamental concepts of sensitivity, specificity, and predictive values. The purpose of this paper is to define these terms, demonstrate the use of receiver operating characteristic curves and Bayes' theorem, and provide clinical examples in obstetrics and gynecology to illustrate their use. Practitioners must be able to interpret the results of diagnostic tests to provide accurate information to their patients.

Bayes Theorem↗

PubMed1993

[Diagnosis of lung embolism].

Although lung scanning has been performed for nearly 3 decades, the diagnosis of pulmonary embolism (PE) still remains problematic. Only about 20% of all autopsy proven cases of PE have been diagnosed during life time. Biello, and later authors of the PIOPED study defined 3 probability levels for perfusion/ventilation (inhalation) scan interpretation in comparison with pulmonary angiography: High probability (about 90% PE), indeterminate (27 to 50% PE) and low probability (about 5% PE). If the scan results are in the high and low probability group, the diagnostic procedure can be stopped. However, in the indeterminate group including 36 to 52% of all patients, diagnosis should be confirmed by pulmonary angiography. This diagnostic procedure is not well accepted by clinicians, only 0 to 15% of all patients suspected of PE undergo angiography. The diagnostic problem is more complicated due to the large amount of clinically silent PE (39 to 59% of all PE). The inclusion of the diagnosis of thrombosis ("thromboembolism") into the diagnosis of PE increases the pre-test probability for PE to 55 to 60% (= prevalence of PE in patients with deep vein thrombosis). According to Bayes' theorem, the post test probability then exceeds 95%. Without considering thrombosis, the pre-test probability is very low and therefore the post-test probability of a pathologic scan is markedly lower than 50%.

Bayes Theorem↗

PubMed1982

Blood group opinions. Their importance in court.

1. --Blood group opinions based on the gene systems and characteristics usual in the FRG are able to exclude about 93% of all non-fathers. With additional systems, including the HLA system, this can be increased to between 98 and 99%. 2. --Owing to repetition, additional systems hardly improve exclusion efficiency. But each and every system is useful for positive biostatistical proof. 3. --As a rule, a computer is necessary for the biostatistical evaluation of blood group findings in cases involving aliens, deficiency, brothers, and incest. The same holds for the evaluation of HLA findings, particularly if one wants to take account of the recombination rate between locus A and B. 4. --The W-value obtained on the basis of Essen-Möller's formula contains all the information necessary for a biostatistical evaluation of triplet cases. In all other cases the method of calculation must also be based on Bayes' Theorem, if necessary with the support of Bayes' Postulate, i.e. with a neutral a priori of 0.5 as a rule [5]. Decisions limited to probably values serve little purpose in court cases.

Blood Group Antigens↗

PubMed1996

A Bayesian approach to adult human age estimation from dental observations by Johanson's age changes.

Much of the data which appears in the forensic and archaeological literature is ordinal or categorical. This is particularly true of the age related indicators presented by Gustafson in his method of human adult age estimation using the structural changes in human teeth. This technique is still being modified and elaborated. However, the statistical methods of regression analysis employed by Gustafson and others are not particularly appropriate to this type of data, but are still employed because alternatives have not yet been explored. This paper presents a novel approach based upon the application of Bayes' theorem to ordinal and categorical data, which overcomes many of the problems associated with regression analysis.

Adolescent↗

PubMed2005

Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference.

We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.

Algorithms↗

PubMed2005

Statistical aspects in physical mapping application to the genome of O. oeni strain GM.

This work addresses issues around physical maps, in particular, for circular genomes. The overlapping relationship between two fragments obtained by applying two different restriction enzymes, separately, is classified as nonoverlapping, partial overlapping, and total overlapping. A double partial overlapping can also appear in a particular situation. Taking into account DNA fragment lengths and under the assumption that the left-hand endpoints of the two restriction fragments are independent random variables, each of which with a uniform distribution along a circular genome, we present expressions for prior probabilities of those events. This information is combined with hybridization data via Bayes' theorem, in order to evaluate corresponding posterior probabilities. Additionally, we explore a sensitivity analysis to quantify the effect of length variation in the results.

Algorithms↗

PubMed1992

Clusters galore: insights about environmental clusters from probability theory.

The posterior probability of a causal explanation given that an environmental cancer cluster is statistically significant depends on the prior probability of an environmentally caused cluster, the sensitivity of the statistical test and its specificity. The prior probability is low, because it is rare to have enough carcinogen in the general environment to cause a relative risk of cancer high enough to achieve statistical significance in a small geographic area. The sensitivity and specificity are not great. The likelihood that a census tract escapes statistically significant elevations in all 80 types of cancer can be calculated. Many of the thousands of census tracts will, by chance alone, have at least one type of cancer whose elevation is statistically significant. Actual observation from a large cancer registry confirms this probabilistic prediction. Applying the principles of Bayes' Theorem would suggest that most statistically significant environmental cancer clusters are not due to environmental carcinogens. One would have to investigate hundreds of environmental cancer clusters to find one with a true environmental cause.

Bayes Theorem↗

PubMed1981

[Dynamic ECG, exercise stress testing and coronary arteriography for the diagnosis of ischaemic heart disease. A Bayesian analysis of probability (author's transl)].

In spite of great technological improvement in Ambulatory ECG Monitoring (AEM), there is still debate about its reliability in detecting ECG signs of myocardial ischemia and about the utility of AEM and Exercise Stress Testing (ET)--apart and/or in association--to predict Coronary Artery Disease (CAD). 50 consecutive male patients (pts) (mean age 51 +/- 69 years, 37 to 64 years) were studied for precordial chest pain. 17 had evidence of previous myocardial infarction. Resting ECG was normal in 21 pts and abnormal in 29; no pt received therapy during the examination period. ECG recordings were considered positive for ischemic ECG changes if there was greater than or equal to 1 mm of horizontal or down sloping ST-segment depression or ST-segment elevation of the same degree for greater than or equal to 0.08 sec in at least 15 consecutive beats; coronary arteriography was considered positive for significant CAD if any major vessel had greater than or equal to 75% luminal diameter narrowing. The percentage of false negative results was similar in AEM and ET (22.7% vs 22.2%); the false positives were few with both tests: 2 pts and 1 pt respectively; Bayesian probability (post-test likelihood for disease) calculated using the prevalence of CAD estimated from 2124 male pts who underwent coronary angiography in our Laboratory, for a given test result was very high: 97.1% +/- 1.3% (AEM), 98.6% +/- 1.1% (ET) and 98.1% +/- 1.1% (AEM & ET if concordant); post-test likelihood for CAD in a patient who did not show the given test result decreased to 67.8% +/- 1.3% (AEM), 60.9% +/- 1.1% (ET) and 52.1% +/- 1.1% (AEM & ET if concordant). The application of Bayes' theorem to these two non invasive tests improves the evaluation of patients with suspected CAD; the association of AEM and ET enhances the diagnostic accuracy.

Adult↗

PubMed1990

Cardiovascular screening in Army personnel over age 40 in the State of Hawaii.

A cardiovascular screening protocol was applied prospectively to 1,900 soldiers over 40 years of age to identify individuals with latent coronary artery disease. Primary screening included a cardiovascular history, physical examination, electrocardiogram, serum cholesterol and serum glucose determinations, and calculated Framingham risk index. Seven hundred ninety-six individuals required secondary screening, consisting of stress testing and cardiac fluoroscopy. The screening process led to coronary angiography in 43 individuals; of these, 17 had obstructive coronary artery disease, ten had nonobstructive coronary artery disease, and 16 had normal coronary arteries. Application of primary screening before exercise testing increased the posttest probability of obstructive coronary artery disease to 50% in the individuals with a positive treadmill test. This is four times the expected value of 11% calculated using Bayes' theorem. The combination of a positive treadmill test and the finding of coronary artery calcification on fluoroscopy was an excellent predictor of obstructive coronary artery disease.

Adult↗