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PubMed1982

False positive stress tests due to undetected left ventricular hypertrophy.

Without large vessel coronary artery disease, clinically evident left ventricular hypertrophy (LVH) is an identified cause of ischemic ST segment changes during exercise. The contribution of subclinical LVH to false positive exercise stress test was evaluated from data of 31 patients without electrocardiographic evidence of LVH who underwent concurrent exercise stress testing, M-mode echocardiography and coronary arteriography at Temple University Hospital, Philadelphia, PA, between January, 1976, and December, 1979, and who met echocardiographic criteria for LVH. Using Bayes theorem, the authors found the probability was 0.59 that a patient with electrocardiogram-undetected LVH does not have significant coronary disease with a positive stress test. The probability of normal coronary arteries with a positive stress test in patients without LVH on echocardiogram was 0.24. Inapparent LVH detected by echocardiography increases the likelihood that a patient with a positive stress test does not have coronary disease. Thus, the positive exercise electrocardiogram should be cautiously interpreted in apparently normal patients who have LVH detectable only by echocardiography.

Angiocardiography↗

PubMed1987

[Factors contributing to the success of intracoronary thrombolytic therapy].

Intracoronary thrombolytic therapy (ICT) was used in 36 patients with acute transmural myocardial infarction. Recanalization of an infarction-dependent artery was achieved in 26 (72.2%) patients. Factors affecting the success of ICT were analysed, using Bayes' theorem. The ejection fraction (EF) is shown to have the highest predictive value as an indicator of left-ventricular pump function. The anticipated probability of ICT success is 84.9% in patients with acute myocardial infarction and a 35% EF baseline, and 25.7% in those with a 35% EF. In the absence of severe left-ventricular pumping and contractility disorders, the success of ICT is affected by patient's age, history of myocardial infarction and the site of thrombotic occlusion.

Adult↗

PubMed2006

Creating a web application that combines Framingham risk with Electron Beam CT Coronary Calcium Score to calculate a new event risk.

The Electron Beam CT (EBT) Coronary Calcium Score (CCS) is an independent predictor of coronary events and adds incremental information to standard risk factors. How to use this information was uncertain. To assist our referring physicians in utilizing this test, a web based calculator was created that combines the Framingham score risk with the EBT CCS risk to obtain a new risk for cardiac events. To create this calculator, CCS breakpoints of 0, 80, 400, and 600 were selected; and from these breakpoints, 5 ranges of calcium scores: 0, 1-80, 81-400, 401-600, and >600 were defined. Bayes theorem was used to derive equations for the combined Framingham score risk and calcium score range risk for each CCS range. The sensitivity and specificity of each of these CCS breakpoints for the prediction of events was derived from prospective studies. These equations were then translated into a JavaScript program that could be accessed from a web browser. This calculator can be easily used to restratify many individuals classified as low, intermediate, or even high risk according to the Framingham risk score system into a different risk group, allowing more appropriate matching of intervention intensity with absolute cardiovascular event risk.

Bayes Theorem↗

PubMed2002

The prosecutor's fallacy--a pitfall in interpreting probabilities in forensic evidence.

Forensic evidence is often given in terms of a mathematical probability. However, it is easy to make a particular type of error, 'the prosecutor's fallacy', in the interpretation of such probability. This paper highlights the source of this error and briefly introduces Bayes Theorem as the correct theoretical basis for interpreting such evidence. The first Californian legal case in which this error was committed is discussed, followed by all cases in the UK in which this error was highlighted and rectified by the Court of Appeal. It is important for all parties concerned--expert witnesses, lawyers and judges--to understand these principles correctly. Furthermore, the criminal courts face dilemmas when juries are involved. This paper concludes by discussing recent guidance from the Court of Appeal on how such evidence should be presented to the jury and the implications of this guidance.

Bayes Theorem↗

PubMedDate not supplied

The causal diagnosis of obstructive jaundice. A Bayesian approach.

To compare the contribution of clinical, laboratory and imaging data for the diagnostic accuracy in establishing the cause of obstructive jaundice, the records of 333 patients operated on for a presumed obstruction of the biliary ducts were analysed. The final diagnoses, after surgery, were divided into six groups: stones of the gallbladder and biliary tract, pancreatic cancer, biliary tract neoplasms, ampullary carcinoma, postoperative stenosis of the bile ducts, intrahepatic cholestasis (biliary cirrhosis, chronic cholangitis) and other causes of jaundice (liver tumours, cysts, extended cancer of the upper abdomen). Twenty-three parameters (9 clinical symptoms and signs, 10 biochemical alterations and 4 imaging methods) were examined. Not every case had all the investigations performed but the number of each group of data was large enough to allow a statistically significant conclusion. The contribution of each of the 23 parameters in increasing the probability of correct diagnosis was determined using a computer program based on Bayes' theorem. This analysis showed that for patients which presented suggestive clinical signs and symptoms for stones of the gallbladder and biliary tract and for pancreatic cancer, the diagnosis can be predicted with a probability of 90% only on the basis of clinical findings. The probability of a correct preoperative diagnosis was increased to 99% by imaging methods. On the contrary, for patients with a less clear diagnostic probability (with ampullary carcinoma, intrahepatic cholestasis and other causes) only ultrasonography and computed tomography could increase the probability of correct diagnosis.(ABSTRACT TRUNCATED AT 250 WORDS)

Bayes Theorem↗

PubMedDate not supplied

[Predictive value of 99m-Tc-Sn(II) methylene diphosphonate in the study of acute myocardial infarction].

Myocardial scintigraphy with 99mTc-Sn (II)-Methylenediphosphonate (MDP) was performed in 90 patients with proven acute myocardial infarction (AMI), and in 37 subjects with acute chest pain of a different etiology, during the first five days after the onset of their illness. The procedure was 82.2% sensitive, 86.5% specific, and 83.5 accurate for the diagnosis of AMI. Based on the usual clinical, electrocardiographic and biochemical criteria, the likelihood of AMI in this population was of 70.9% before the scintigraphic test. Application of Bayes' Theorem showed an increase in the likelihood of AMI, from 70.9% to 93.7%, when myocardial scintigraphy was positive, an incremental ruling-in-gain of 22.8%. A normal scintigraphy, on the other hand, reduced the likelihood of AMI, from 70.9% to 33.4%, an incremental ruling-out gain of 37.5%. It is concluded that myocardial scintigraphy with MDP is an important clinical procedure for the study of patients with acute chest pain: a positive test tends to confirm AMI, while a normal image, although it reduces the likelihood of this disease, is not particularly helpful in ruling it out.

Bayes Theorem↗

PubMed1995

Probability and characteristics of human immunodeficiency virus infection in male Greek military personnel with tuberculosis.

The probability of an AIDS patient being infected with tuberculosis (TB) has been studied in different populations and found to be increased by as much as 500 times, but the reverse, i.e. the probability of a patient with TB being infected with HIV, has not been studied. The aim of this study was to investigate the hypothesis of greater HIV seropositivity and altered immune status, as indicated by CD4+ T-lymphocyte counts, in TB patients. We prospectively studied 162 males, aged 18-30 years, hospitalized for active, proven TB. Serum for HIV antibodies was tested twice by ELISA and confirmed by the Western blot technique. The control group consisted of 145,000 blood donor volunteers serving in the army, aged 18-30 years. The number of CD4+ T lymphocytes was also measured in the patients and the control group. We found that the rate of HIV seropositivity in TB patients was 2.4% (4 of 162), while it was 0.214% in the control group (p < 0.0001). Using the Bayes' theorem we found that the probability of a TB patient being infected with HIV was 9.1%, approximately 150 times higher than the expected rate in the matched control group (p < 0.0001). The number of CD4+ T lymphocytes was significantly lower in pulmonary and extrapulmonary TB patients than in the control group, taking into account the HIV status (p < 0.001). Our results suggest that there is a 150 times greater probability of a TB patient being infected with HIV. CD4+ T lymphocytes are significantly lower in all groups of TB patients.

AIDS-Related Opportunistic Infections↗

PubMed1982

'Pseudodiagnosticity' in an idealized medical problem-solving environment.

Sixty-five senior medical students chose symptom information that would allow them to assess which of two diagnoses was more appropriate for hypothetical patients. Although Bayes' theorem should have governed their data selection, 83 percent of the subjects did not choose the symptom information required for Bayesian computation. Instead, they showed an overwhelming tendency to seek data relevant to a single disease, while ignoring information related to an equally plausible alternative diagnosis. The tendency for subjects to select diagnostically irrelevant information in such tasks has been labeled "pseudodiagnosticity." The effect result from the difficulty of simultaneously evaluating the relevance of a single symptoms in relation to single diagnosis. Medical educators might incorporate classroom demonstrations of the pseudodiagnosticity effect in order to increase students' accuracy in differential diagnosis.

Bayes Theorem↗

PubMed2006

Diagnosis of deep vein thrombosis.

Deep vein thrombosis (DVT) requires a prompt and accurate diagnosis to avoid the potentially fatal consequences of a delay in adequate treatment. The diagnostic strategy of suspected venous thromboembolism is an example of the application of Bayes' theorem. As a result, the available diagnostic tools, both noninvasive (such as ultrasonography, D-dimer, and computed tomography) and invasive (such as venography), are usually integrated in diagnostic strategies that require the evaluation of the a priori clinical probability of disease (pretest probability). These strategies also vary according to the patient characteristics that allow the definition of five different categories: symptomatic outpatients, symptomatic inpatients, high-risk asymptomatic subjects, patients with suspected recurrence, and pregnant women. Some areas are still a matter of debate, such as the clinical relevance of isolated distal DVT and the diagnosis of suspected ipsilateral recurrence.

Bayes Theorem↗

PubMed1990

Precipitins in bird breeder's disease: how useful are they?

Precipitating antibodies to avian antigens play a controversial role in the diagnosis of bird breeder's disease (BBD). In order to establish the sensitivity, specificity and accuracy of precipitins in our laboratory, we conducted a prospective study including 128 sera received in 1988 for determination, by immunoelectrophoresis, of avian precipitins. Accurate information was obtained for 90 patients; definitive clinical diagnosis was given by the patient's own physician. We found a high sensitivity (86%), specificity (93%) and accuracy (92%) of avian precipitins in the diagnosis of BBD. Bayes' theorem was applied to determine the predictive value of the test with varying disease prevalence, and established that precipitins were particularly valuable for low or medium a priori probability. Using the receiver operating characteristic (ROC) curve we evaluated the effects of varying the positivity threshold of precipitins. The threshold used in this study appeared to offer the best compromise between sensitivity and specificity. These results suggest that the diagnostic value of avian precipitins in the work-up of BBD should be reconsidered, also because they represent a simple, cheap and non-invasive diagnostic test.

Adolescent↗

PubMed1995

[Predictive analysis of the response to treatment with diuretics of patients with liver cirrhosis and ascites].

Our aim was to develop and validate a prognostic model to predict the evolution of cirrhotic patients admitted to the hospital because of ascites and treated with diuretics. Two hundred and two patients were evaluated. After collection of clinical and laboratory data, a prognosis of the response to diuretics was given by one of us. After univariate analysis, 37 parameters were used to construct a database. A new prognosis was obtained for each patient comparing his/her data with the database, with the help of a computer and using Bayes' theorem. Gender: female, poor general status, disturbed consciousness, increased serum glucose, increased BUN, low prothrombin time, increased bilirubin, leucocytosis, thrombopenia and low urine sodium were associated with a poor response to diuretics. Sensitivity and specificity of clinical and computer prognosis were similar. Computer prognosis allowed the classification of patients in groups of risk which showed a different evolution and improved the accuracy of the clinical prognosis. We conclude that the objective analysis of clinical and laboratory data is useful to improve the accuracy of the prediction of the evolution in cirrhotic patients with ascites treated with diuretics.

Ascites↗

PubMed1985

Bronchoalveolar lavage cell differential in the diagnosis of sarcoid interstitial lung disease. Likelihood ratios based on computerized data base.

With the use of a microcomputer, the authors prospectively stored the bronchoalveolar lavage (BAL) cell differential counts from 208 patients undergoing initial evaluation for chronic interstitial lung disease. Sarcoidosis subsequently was diagnosed in 46% of these patients; the remainder had several other etiologies of their lung disease. The BAL lymphocyte count did not allow for clear separation between these two groups. To facilitate the interpretation of the BAL percent lymphocyte data, the authors applied a modification of Bayes' theorem to calculate likelihood ratios for the differential diagnosis of sarcoidosis versus other interstitial lung disease. These values ranged from 0.15 for patients with less than 6% lymphocytes to 3.5 when more than 40% lymphocytes were found. Similar results were obtained with a subsequent, independently analyzed group of 46 patients. To provide a more meaningful interpretation of the BAL fluid lymphocyte count, the authors designed a reporting scheme that includes both a written description and a graphic representation of the likelihood ratio. Prospective collection of data using microcomputers should extend this useful form of reporting to additional laboratory studies.

Bayes Theorem↗

PubMed2005

Evaluation of phenytoin dosage regimens based on genotyping of CYP2C subfamily in routinely treated Japanese patients.

Two research groups have reported the effect of genetic polymorphisms of CYP2C9 and CYP2C19 on the pharmacokinetic parameters of phenytoin in Japanese epileptic patients. We measured the plasma phenytoin concentrations at steady-state in 20 routinely treated Japanese patients, and evaluated the usefulness of genotyping the CYP2C subfamily in predicting plasma concentrations and determining the dosage regimens of phenytoin. The plasma phenytoin concentrations predicted by genotypes of the CYP2C subfamily were well correlated with the observed concentrations in some patients, but not in some patients. The pharmacokinetic parameters (Vmax and Km) in individual patients, which were obtained from population estimates according to Bayes' theorem, showed considerable interindividual variability even among patients with the same genotype. In addition, we assessed the effect of plasma protein binding on the residual interindividual variability in the clearance of phenytoin; however, there was no significant correlation between the unbound fraction and the intrinsic metabolic activity (Vmax/Km). These findings suggested that the mechanism responsible for the large variability in the clearance of phenytoin is not completely resolved, and that we should not overestimate the usefulness of genotyping the CYP2C subfamily in determining the dosage regimens of the drug.

Adolescent↗

PubMed1989

Screening for possible human carcinogens and mutagens. False positives, false negatives: statistical implications.

A screening method aimed at identifying potential human carcinogens using either animal cancer bioassays or short-term genotoxic assays has 4 possible results: true positive, true negative, false positive and false negative. Such a categorisation is superficially similar to the results of hypothesis testing in a statistical analysis. In this latter case the false positive rate is determined by the significance level of the test and the false negative rate by the statistical power of the test. Although the two types of categorisation appear somewhat similar, different statistical issues are involved in their interpretation. Statistical methods appropriate for the analysis of the results of a series of assays include the use of Bayes' theorem and multivariate methods such as clustering techniques for the selection of batteries of short-term test capable of a better prediction of potential carcinogens. The conclusions drawn from such studies are dependent upon the estimates of values of sensitivity and specificity used, the choice of statistical method and the nature of the data set. The statistical issues resulting from the analysis of specific genotoxicity experiments involve the choice of suitable experimental designs and appropriate analyses together with the relationship of statistical significance to biological importance. The purpose of statistical analysis should increasingly be to estimate and explore effects rather than for formal hypothesis testing.

Bayes Theorem↗

PubMed1987

Value of visual evoked response and oligoclonal bands in cerebrospinal fluid in diagnosis of spinal multiple sclerosis.

To assess the predictive value of prolongation of visual evoked response (VER) plus the presence of oligoclonal bands in the cerebrospinal fluid (CSF) in the diagnosis of multiple sclerosis (MS) in patients with isolated cord lesions, the false-positive rate for the two tests combined was determined by a prospective analysis of 42 patients with a structural spinal cord lesion. The false-positive rate for the combination of VER and CSF abnormalities was zero, but the individual false-positive rates were 10% for VER and 12% for CSF protein oligoclonal bands. According to Bayes' theorem, and taking into account the false-positive rates of the tests in the population studied and the prevalence of MS and the true-positive rates for the tests as derived from published reports, abnormalities of VER and CSF protein together gave a probability of MS of 100%. However, if only either the VER or the CSF were abnormal, the probability of MS was 44% or 49%, respectively. An abnormal result for both tests thus indicates a sufficiently high probability of MS to exclude myelography, but a positive result in only one test warrants the procedure.

Adult↗

PubMed1992

Predictive value of the P wave at implantation for atrial fibrillation after VVI pacemaker implantation.

This study assesses the value of P wave measurements on the surface ECG at implantation, in the prediction of atrial fibrillation in VVI paced patients. From a consecutive series of 320 pacemaker implantations 172 VVI paced patients for symptomatic atrioventricular block (AVB) (n = 126; mean age 69 +/- 14) or sick sinus syndrome (SSS) (n = 56; mean age 68.6 +/- 12) and in sinus rhythm at implantation were used in this study. P wave duration in V1 is correlated with the incidence of atrial fibrillation during 5 years of follow-up. V1 at implantation was significantly longer (114.6 +/- 2.7 msec) in the patients who developed atrial fibrillation than in those who did not (91.9 +/- 2.7 msec) (P < 0.001). Although positive predictive accuracy increases progressively for higher V1 values for AVB and SSS, the negative predictive and diagnostic accuracy of V1 criteria were less in SSS. Application of the Bayes' theorem showed that in SSS the probability to develop atrial fibrillation is 33% for V1 < 110 msec and is for V1 < 90 msec still higher than that reported in DDD paced patients. In the AVB group the probability to develop atrial fibrillation is 8% for V1 < 110 msec and 6% for V1 < 100 msec. It seems, therefore, that atrial stimulation (AAI or DDD) is always indicated in SSS. In AVB with V1 < 100 msec, DDD pacing, if not needed for other indications, apparently does not offer much benefit in the prophylaxis of atrial fibrillation.

Aged↗

PubMed2005

New patient-oriented diagnostic test characteristics analogous to the likelihood ratios conveyed information on trustworthiness.

OBJECTIVE: Suggesting patient-oriented ratio measures of diagnostic tests analogous to the likelihood ratios. STUDY DESIGN AND SETTING: Algebraic equation based on Bayes' theorem. RESULTS: Two new measures are suggested: the positive predictive ratio (PPR), relating the positive predictive value (PPV) to the false negative rate in the patient population, and the negative predictive ratio (NPR), relating the negative predictive value (NPV) to the false positive rate in the patient population. The new measures are analogous to likelihood ratios. These measures are calculable from the familiar 2x2 table in a selected study population or in a target (general) population. Examples are given, using published data. CONCLUSION: PPR adds to the information given by the PPV, and NPR adds to the information given by the NPV. PPR and NPR may be more appropriate in the clinical setting than likelihood ratios.

Bayes Theorem↗

PubMed2000

The meaning of diagnostic test results: a spreadsheet for swift data analysis.

AIMS: To design a spreadsheet program to: (a) analyse rapidly diagnostic test result data produced in local research or reported in the literature; (b) correct reported predictive values for disease prevalence in any population; (c) estimate the post-test probability of disease in individual patients. MATERIALS AND METHODS: Microsoft Excel(TM)was used. Section A: a contingency (2 x 2) table was incorporated into the spreadsheet. Formulae for standard calculations [sample size, disease prevalence, sensitivity and specificity with 95% confidence intervals, predictive values and likelihood ratios (LRs)] were linked to this table. The results change automatically when the data in the true or false negative and positive cells are changed. Section B: this estimates predictive values in any population, compensating for altered disease prevalence. Sections C-F: Bayes' theorem was incorporated to generate individual post-test probabilities. The spreadsheet generates 95% confidence intervals, LRs and a table and graph of conditional probabilities once the sensitivity and specificity of the test are entered. The latter shows the expected post-test probability of disease for any pre-test probability when a test of known sensitivity and specificity is positive or negative. RESULTS: This spreadsheet can be used on desktop and palmtop computers. The MS Excel(TM)version can be downloaded via the Internet from the URL ftp://radiography.com/pub/Rad-data99.xls CONCLUSION: A spreadsheet is useful for contingency table data analysis and assessment of the clinical meaning of diagnostic test results.

Bayes Theorem↗