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PubMed1978

Introduction to clinical decision making.

In the last few years there has been a remarkable increase in the amount of clinical data in the average hospital chart, and more and more problem-solving algorithms have been developed. We need better "thinking tools" to help us handle the flow of information. The term "clinical decision making" is used to describe a systematic way to handle data and algorithms to decide on a best course of action. This introductory article discusses some of the problems in establishing a decision criterion, both for a population and for an individual patient. Comparing the probabilities and utilities of various diagnostic outcomes (true positive, false positive, etc.) leads to a diagnostic strategy. The article also discusses conditional probability. Bayes' theorem, and likelihood ratios.

Bayes Theorem↗
PubMed2005

A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates.

BACKGROUND: Some people believe that likelihood ratios provide diagnostic information that is more useful than sensitivity and specificity estimates. OBJECTIVE: To assess how physicians' estimates about probability of illness are affected by the presentation of a diagnostic test's value as an estimate of sensitivity and specificity versus a likelihood ratio or an inexact numerical graphic. DESIGN: Random assignment of vignettes with different presentation formats of diagnostic test accuracy. SETTING: Auditorium at a continuing medical education conference. PARTICIPANTS: 183 physicians. INTERVENTION: After estimating probabilities of 6 common illnesses described in patient vignettes, physicians reviewed pertinent test results presented in 1 of 3 formats. MEASUREMENTS: Physicians' probability estimates of illness before and after receiving test information, and post-test probability estimates based on the Bayes theorem. RESULTS: Absolute percentage point differences between the physicians' estimated and the Bayes-based post-test probabilities varied from -7 to 31, from -7 to 28, and from 1 to 29 for the sensitivity and specificity, likelihood ratio, and graphical groups, respectively. Mean differences of probability estimates between the sensitivity and specificity and the likelihood ratio groups were small for all vignettes (-2 to 3 percentage points; summary mean z value across the 6 vignettes, 0.04 [95% CI, -0.14 to 0.21]). LIMITATIONS: The small pool of participants (who were potentially selected) and the limited number of vignettes prevented a more detailed analysis of relationships between the interpreted strength of diagnostic evidence and estimations of illness probability. CONCLUSIONS: These findings suggest that presenting diagnostic test accuracy with likelihood ratios does not affect some physicians' estimates of illness probability compared with presenting diagnostic test results as sensitivity and specificity.

Adult↗
PubMed2001

Introduction to Bayesian reasoning.

Interest in Bayesian analyses has increased recently, in part as a response to policy makers wanting sound scientific bases for health technology assessments, and associated healthcare funding decisions. This paper provides a brief and simplified description of Bayesian reasoning. Bayes is illustrated in a clinical setting of an expert helping a woman understand the potential risk of passing on an inheritable disease (hemophilia) to her next child, based on disease occurrence in two living children. The illustration describes fundamental concepts and derivations, such as Bayes theorem, likelihood functions, prior probability, and posterior probability. A second illustration shows the use of Bayes for interpreting clinical trial results. The uncertainty in the clinical effect before and after the trial analyses has been completed is characterized by the Bayes prior and posterior probabilities, respectively. Techniques are also shown for estimating the potential loss (e.g., in lives lost) for making the wrong decision with and without knowledge of the trial results, an estimation that cannot be carried out using techniques of hypotheses testing associated with the frequentist school of statistics. Information from Bayes analysis then may be used to help policy makers decide, or justify, whether the analyses provides a sufficient basis for making a treatment recommendation, or whether there remains a need to request more information. Subsequent papers in this volume offer additional examples and clarification of the use of Bayes in clinical practice and in interpretation of clinical studies.

Bayes Theorem↗
PubMed2002

Accuracy and power of bayes prediction of amino acid sites under positive selection.

Bayes prediction quantifies uncertainty by assigning posterior probabilities. It was used to identify amino acids in a protein under recurrent diversifying selection indicated by higher nonsynonymous (d(N)) than synonymous (d(S)) substitution rates or by omega = d(N)/d(S) > 1. Parameters were estimated by maximum likelihood under a codon substitution model that assumed several classes of sites with different omega ratios. The Bayes theorem was used to calculate the posterior probabilities of each site falling into these site classes. Here, we evaluate the performance of Bayes prediction of amino acids under positive selection by computer simulation. We measured the accuracy by the proportion of predicted sites that were truly under selection and the power by the proportion of true positively selected sites that were predicted by the method. The accuracy was slightly better for longer sequences, whereas the power was largely unaffected by the increase in sequence length. Both accuracy and power were higher for medium or highly diverged sequences than for similar sequences. We found that accuracy and power were unacceptably low when data contained only a few highly similar sequences. However, sampling a large number of lineages improved the performance substantially. Even for very similar sequences, accuracy and power can be high if over 100 taxa are used in the analysis. We make the following recommendations: (1) prediction of positive selection sites is not feasible for a few closely related sequences; (2) using a large number of lineages is the best way to improve the accuracy and power of the prediction; and (3) multiple models of heterogeneous selective pressures among sites should be applied in real data analysis.

Amino Acid Substitution↗
PubMed2004

Bayesian analysis and risk assessment in genetic counseling and testing.

Risk assessment is an essential component of genetic counseling and testing, and Bayesian analysis plays a central role in genetic risk assessment. Bayesian analysis allows calculation of the probability of a particular hypothesis, either disease or carrier status, based on family information and/or genetic test results. Genetic risk should be assessed as accurately as possible for family decision making. Additional information, from the pedigree and/or from genetic testing, can often dramatically improve the accuracy of genetic risk assessment. We illustrate herein the application of Bayes' theorem and describe important basic principles in genetic risk assessment.

Bayes Theorem↗
PubMedDate not supplied

Limits to diagnostic accuracy.

This paper explores the limits to computer-aided medical diagnosis. A specific application area (the diagnosis of abdominal pain of suspected gynaecological origin) is chosen, and the factors limiting the accuracy of computer programs are investigated by means of a simulation model which has been shown previously to generate realistic cases. The model is used to generate arbitrarily large training and test sets. The results suggest that, while statistical dependencies exist amongst symptoms and signs, there is little to be gained by taking interactions into account. However, failure to record all possible observations does limit diagnostic accuracy significantly. The results suggest that near-optimal diagnostic accuracy (75-80%) can be obtained with a training set size of 10(5) cases simply by applying Bayes' theorem with the usual assumption of conditional independence.

Abdominal Pain↗
PubMed2004

Pretest probability estimates: a pitfall to the clinical utility of evidence-based medicine?

OBJECTIVES: The Bayesian application of likelihood ratios has become incorporated into evidence-based medicine (EBM). This approach uses clinicians' pretest estimates of disease along with the results of diagnostic tests to generate individualized posttest disease probabilities for a given patient. To date, there is minimum scientific validation for the clinical application of this approach. This study is designed to evaluate variability in the initial step of this process, clinicians' estimates of pretest probability of disease, to assess whether this approach can be expected to yield consistent posttest disease estimates. METHODS: This cross-sectional cohort study was conducted at an urban county teaching hospital by using a sample of emergency and internal medicine residents and faculty, as well as emergency department (ED) midlevel practitioners. Participants read clinical vignettes designed to raise consideration for common ED disorders and were asked to estimate the likelihood of the suggested diagnosis based on the history and physical examination findings alone. No information about laboratory results or imaging studies was provided. RESULTS: Mean pretest probability estimates of disease ranged from 42% (95% confidence interval [95% CI] = 36.6% to 47.4%) to 77% (95% CI = 72.9% to 81.1%). The smallest difference in pretest probability magnitude for a single vignette was 70% (range 30-100%; interquartile range [IQR] 64-80%), whereas the largest was 95% (range 3-98%; IQR 30-60%). CONCLUSIONS: Wide variability in clinicians' pretest probability estimates of disease may present a possible concern about decision-making models based on Bayes' theorem, because it may ultimately yield inconsistent posttest disease estimates.

Bayes Theorem↗
PubMedDate not supplied

[Elements of probability calculation--II].

This is the second part of an introduction to probability calculation and covers basic concepts such as conditional and simple probabilities and independent events and also a definition of two fundamental laws, those of addition and multiplication, which permit a correct combination of probabilities. Explanation of probability concepts and ideas is illustrated with the aid of examples from the field of screening tests. Bayes theorem is derived by applying the addition and multiplication laws to conditional and simple probabilities.

Bayes Theorem↗
PubMed2003

A Bayesian analysis of pharmacoeconomic data from a clinical trial on schizophrenia.

Pharmacoeconomic studies are performed in a higher frequency to assess the economic interest of new drugs. However, a standard methodology does not still completely exist. We present here the principles and results of a cost-effectiveness Bayesian analysis on data from 146 patients (interim analysis) collected during a clinical trial. This trial was originally planned to enrol 245 patients with predominantly negative schizophrenia symptoms and involved four treatment groups (a new treatment given at low dose and high dose, a comparator and a placebo). First, some prior distributions of the cost-effectiveness ratio were numerically deduced from the effectiveness parameter clinical priors (based on investigators' opinions and questionnaires before going to blind breaking) and from cost function priors. The costs taken into account were hospitalizations, sick leave days, treatments, visits to the doctor, laboratory exams and suicide attempts. The effectiveness parameter was the change from baseline on SANS (scale for the assessment of negative symptoms). Posterior distributions were elaborated for the cost-effectiveness ratio by combining the cost-effectiveness ratio priors and likelihood together using the Bayes theorem. Results lead to a conclusion in favour of the new treatment given at high dose.

Antipsychotic Agents↗
PubMed1986

[Relation between the metastatic spread of stomach cancer and the factors characterizing the primary tumor].

The paper deals with the analysis of patterns of metastatic spread in 738 gastric cancer patients versus site, size, gross appearance and histologic pattern of tumor at presentation. The likelihood of organ involvement through dissemination or invasion by gastric tumor was determined by assessing unknown probabilities by Bayes' theorem. The probability of correct preoperative evaluation of dissemination pattern ranged 0-0.935.

Adenocarcinoma↗
PubMed1999

An evaluation of the significance of transfers of debris: criteria for association and exclusion.

Several criteria are proposed for making decisions about comparing sets of debris involving the transfer of non-component particles and fibers--those produced from something other than the item itself--using a model based upon rudimentary set theory. Decisions about the significance of an association or an exclusion based upon trace evidence require an evaluation of debris in its context; reference points for such evaluation are presented. Samples of debris from the sites relevant to the event under investigation must be available, as well as debris standards from the usual environments of the people involved, and must be adequate to permit a determination of normal versus foreign debris. Criteria are proposed for establishing contact based upon corresponding sets of particles and fibers, for excluding contact in the absence of corresponding particles or fibers, and for refraining from making either an association or an exclusion. Conditions for reaching qualified conclusions or other types of associations when these criteria are only partially met are also discussed; conclusions may sometimes be reached if potential sources for debris particles and fibers can be found. Decisions about the strength of an association or an exclusion based upon comparisons of non-component debris particles and fibers can be made by reference to the criteria for reaching a conclusion. The criteria can be tested via Bayes' Theorem. The analysis itself is based primarily upon light microscopy, although other methods may be used as well. Case examples are presented.

Adult↗
PubMed2002

[Errors in methodology (conclusion). XXXIX. The ultimate truth].

Studies that have methodological shortcomings may still lead to the right conclusion. Sometimes, the bias is small, or the shortcoming is not relevant for the issue being studied. It is also possible that a perfectly designed and executed study does not yield the 'right' answer. For example, chance circumstances might lead to the incomparability of groups. Bayes' theorem clarifies why different experts may come to opposite conclusions based on the same studies. The ultimate truth remains elusive.

Bayes Theorem↗
PubMed1997

Regional assignment of genetic markers using a somatic cell hybrid panel: a WWW interactive program available for the pig genome.

MOTIVATION: Quick and easy gene mapping by the use of a panel of cytogenetically characterized somatic cell hybrids is possible, even if some discordant experimental results arise. RESULTS: An interactive program is proposed and is made available on a WWW site to users of a somatic cell hybrid panel. Assignments to chromosomes and subchromosomal regions are based on likelihood calculations and Bayes' theorem, and a confidence level is provided. The method is illustrated in the case of the pig genome.

Animals↗
PubMed1990

Application of DNA fingerprinting to parentage and extended family relationship testing.

For the purpose of applying DNA fingerprinting to parentage or other extended blood relationship testing, we have developed a general system for estimating blood relationship between a set of individuals. This system can be used for any blood relationship testing, even if critical family members are unavailable. A general formula for calculating the probability of such relationships based on Bayes' theorem has been devised and the ability of DNA fingerprinting produced by Jeffrey's polycore probe to determine the relationships has been evaluated.

Bayes Theorem↗
PubMed1993

An epidemiological approach to quality assurance in the hospital.

This article discusses epidemiological methodology: comparing rates, confounding, the use of confidence intervals, Bayes' theorem, and occurrence screening. An appreciation of the limits of epidemiological methods will provide the manager with realistic expectations of the quality assurance process.

Bayes Theorem↗
PubMed1997

Principles of an adaptive method for measuring the slope of the psychometric function.

Recent developments in the efficient estimation of threshold are here extended to the problem of how best to estimate the slope of the psychometric function. An adaptive method is described for selecting stimulus intensities that are optimal for slope estimation. A two-dimensional array of probabilities of different thresholds and slopes is used to calculate the stimulus intensity for the next trial; this array is updated after the trial, using Bayes' theorem to incorporate information from the subject's response. The practical implementation and efficiency of the method are demonstrated and discussed.

Bayes Theorem↗
PubMed2005

Introduction to Bayesian methods I: measuring the strength of evidence.

Bayesian inference is a formal method to combine evidence external to a study, represented by a prior probability curve, with the evidence generated by the study, represented by a likelihood function. Because Bayes theorem provides a proper way to measure and to combine study evidence, Bayesian methods can be viewed as a calculus of evidence, not just belief. In this introduction, we explore the properties and consequences of using the Bayesian measure of evidence, the Bayes factor (in its simplest form, the likelihood ratio). The Bayes factor compares the relative support given to two hypotheses by the data, in contrast to the P-value, which is calculated with reference only to the null hypothesis. This comparative property of the Bayes factor, combined with the need to explicitly predefine the alternative hypothesis, produces a different assessment of the strength of evidence against the null hypothesis than does the P-value, and it gives Bayesian procedures attractive frequency properties. However, the most important contribution of Bayesian methods is the way in which they affect both who participates in a scientific dialogue, and what is discussed. With the emphasis moved from "error rates" to evidence, content experts have an opportunity for their input to be meaningfully incorporated, making it easier for regulatory decisions to be made correctly.

Bayes Theorem↗