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Teaching medical students to estimate probability of coronary artery disease.

The authors conducted a randomized trial of two methods for teaching medical students how to estimate the probability of coronary artery disease in patients with chest pain. Eighty-two students were given a pre-test consisting of written protocols summarizing the histories of 25 patients who had undergone coronary arteriography. The students estimated the likelihood of coronary artery disease for each case and were then randomized to receive one of two short written clinical lessons: a cardiology textbook chapter on interpreting chest pain, or a lesson based on a prediction rule for estimating probability of coronary artery disease. All students were given a post-test similar to the pre-test. Students who were given the textbook lesson showed no change in the accuracy of their probability estimates. Students who were taught the prediction rule significantly improved their probability estimates, as measured by a statistical index of calibration. The authors conclude that traditional teaching methods do not provide students with guidance in estimating disease probability, and that better teaching methods are needed. In this study, a clinical prediction rule fulfilled the need for instruction in probability estimation.

Coronary Disease↗

PubMed2001

Ten year probabilities of osteoporotic fractures according to BMD and diagnostic thresholds.

The objectives of the present study were to estimate 10 year probabilities of osteoporotic fractures in men and women according to age and bone mineral density (BMD) at the femoral neck. Risks were computed from the incidence of a first hip, distal forearm, proximal humerus and symptomatic vertebral fracture from patient records in Malmö, Sweden and future mortality rates for each year of age from Poisson models using the Swedish patient register and statistical year book. Fracture probability was computed using the Swedish population and cut-off values for T-scores based on the NHANES III female population. We assumed that the risk of fracture increased with decreasing BMD as assessed by meta-analysis in independent studies. The 10-year probability of any fracture was determined from the proportion of individuals fracture-free from the age of 45 years. With the exception of forearm fractures in men, 10 year probabilities increased with age and T-score. In the case of hip and spine fractures, fracture probabilities for any age with low BMD were similar between men and women. The effect of age on risk independently of BMD suggests that intervention thresholds should not be at a fixed T-score but vary according to absolute probabilities. Intervention thresholds based on hip BMD T-scores are similar between sexes.

Age Factors↗

PubMed2004

Effects of ISI and stimulus probability on event-related go/nogo potentials after somatosensory stimulation.

The present study investigated the characteristics of the middle-latency negative potential of event-related potentials (ERPs) using somatosensory go/nogo tasks. We manipulated interstimulus interval (ISI) in Experiment 1 and stimulus probability in Experiment 2 and analyzed the subtracted difference waveform resulting from subtraction of the ERP evoked by the go stimulation from that evoked by the nogo stimulation. In Experiment 1, the peak latency of negativity became significantly longer as the ISI increased, but the peak amplitude was unchanged. The reaction time (RT) was longer with increasing ISI. In Experiment 2, manipulation of the stimulus probability yielded an increase in peak amplitude with decreasing probability of the nogo stimulus, but did not affect the latency. The RT increased as the probability of a nogo stimulus rose. Because manipulation of the ISI and stimulus probability elicited different brain activities, we hypothesized that manipulation of the ISI elicited a delay of the stimulus evaluation process including response inhibition, and that stimulus probability significantly affected the strength of the response inhibition process.

Adult↗

PubMed1998

Pulmonary embolism exclusion: a practical approach to low probability using the PIOPED data. Prospective Investigation of Pulmonary Embolism Diagnosis.

A recent trend among physicians is the categorisation of lung scans as normal [excludes pulmonary embolism (PE)], high probability (confirms PE) and non-diagnostic (no judgement on PE risk). The low probability scan is therefore being eliminated as a functional category. This occasional survey contends that such an approach is misguided. Correction of the original PIOPED data with certain assumptions provides a more reproducible, albeit restricted, low probability scan category which excludes PE in 97% of cases in the low pre-test clinical category. Patients with a low probability scan with risk factors for PE (i.e. medium clinical risk) will require further investigation. More important, the very low probability scan category excludes PE in 98% of patients with low and more than 92% of patients with medium pre-test clinical likelihood. The demise of "low probability" is premature.

Bayes Theorem↗

PubMed2005

The effects of the quality and probability of reinforcement on feeder selection by lobectomized dogs.

The role of the prefrontal cortex was studied in an active selection situation in which dogs had to choose one of two feeders, with changes in the quality and probability of the reinforcement provided in one of the feeders. The study was performed in two stages. Before surgery, animals were trained to place themselves on a start area during the interstimulus interval. Dogs were presented with a conditioned stimulus for investigation of the sequence of selection of feeders with identical reinforcements. After bilateral extirpation of the prefrontal areas (the proreal gyrus), dogs continuously ran from one feeder to the other during the interstimulus period. In response to the conditioned stimulus, the animals repeated the reaction of selecting the same feeder on many occasions during the first few (7-9) days. When there was a conflict between the probability and quality of reinforcement, the dogs came to prefer the feeder with the greater reinforcement quality despite its lower probability of presentation. In our experiments, operated animals presented with food at probabilities of 30% and 100% performed feeder selections with different probabilities. One of the functions of the prefrontal cortex in intact animals would appear to be to support the reaction of selecting the greater probability of reinforcement.

Animals↗

PubMed1982

Diagnostic accuracy of cardiologists compared with probability calculations using Bayes' rule.

Probability analysis has provided insights into the use of diagnostic tests in coronary artery disease, and recent developments may permit clinical application of individual patients. To validate independently two available methods of probability calculation, their diagnostic accuracy was compared with that of cardiologists. Ninety-one cardiologists participated in the study; each evaluated the clinical summaries of eight randomly selected patients. For each patient, the cardiologist assessed the probability of coronary artery disease after reviewing the clinical history, physical examination and laboratory data, including complete results from a treadmill exercise test. The probability of coronary artery disease was also obtained for each patient, using the identical information, from two methods employing Bayes' rule: (1) from a published table of data based on the patient's age, sex, symptoms and degree of S-T segment change during exercise; and (2) from a computer program using the age, sex, risk factors, resting electrocardiogram and multiple exercise measurements. Diagnostic accuracy was assessed on a scale from 0 to 100 with the coronary angiogram as the diagnostic standard. The average diagnostic accuracy on this scale was: 80.2 for the cardiologists' estimates, 78.0 for the estimates based on tables (difference from cardiologists' estimates p less than 0.05) and 83.1 for the estimates based on computer calculations (p less than 0.01). Thus probability analysis incorporating sufficient detail can achieve a diagnostic accuracy comparable with that of cardiologists. Studies of the efficacy of probability analysis in patient care are warranted.

Bayes Theorem↗

PubMed1983

Revising ranked probabilities: a Bayesian approach to incomplete knowledge.

Incomplete knowledge refers to situations in which a decision maker can rank the probabilities of occurrence for events of interest, but cannot specify these probabilities exactly. In this paper a Monte Carlo approach is used to investigate how physicians can arrive at revised or posterior rankings of disease probability given only rank order information about both the patient's prior probabilities of disease and the conditional probabilities of specific clinical findings for each disease. Computer-generated estimates of the expected frequencies of the posterior rankings are presented for the cases of 2, 3, and 4 disease states. The application of probability revision under conditions of incomplete knowledge to therapeutic decision making is discussed.

Bayes Theorem↗

PubMed1990

Amplitude variations in P300 component due to unpredictable stepwise change of stimulus probability.

The present study investigates whether the amplitude of the P300 in 'normal' subjects adapts to unexpected changes in global stimulus probability. The adaptation level (AL) metrics (in terms of Helson's [1964] theory) was applied to explain the variations in the P300 amplitude. In an oddball paradigm the probability of the deviant tone (target 1000 Hz, 80 dB, 50 ms) occurring randomly in a train of standard ones (non-target 1100 Hz, 80 dB, 50 ms) was changed in a stepwise way from 0.5 to 0.3 and then to 0.1 in 3 blocks without interruption of the stimulus presentation. Two experiments were performed. In the first one the subjects did not receive any prior information about the changes in the stimulus probability, whereas in the second experiment they were aware of such changes. The task always required the subject to silently count the deviants. EEG was recorded monopolarly from Fz, Cz and Pz in a total of 15 subjects. The block averaged P300 increased monotonically with probability, the increase being larger in Expt. II. In contrast to the block averaged P300, the variations in the P300 amplitude following the abrupt change in probability showed a non-linear dependency. On the basis of the AL a simulation of the time course of the P300 variations with probability was performed and a clear similarity between the simulated P300 and the experimental data was found. Some properties of the AL model are discussed.

Acoustic Stimulation↗

PubMed1994

Analysis of the probability and risk of cause-specific failure.

PURPOSE: Kaplan-Meier curves are frequently misused in the analysis of nonsurvival endpoints, such as time to local failure or time to late complications. More appropriate analyses are available and described. METHODS AND MATERIALS: Cumulative incidence is an unbiased estimate of probability of cause-specific failure. Cumulative conditional probability of cause-specific failure reflects risk to patients remaining at risk. Hazard rates also measure risk. RESULTS: Kaplan-Meier curves overestimate the probability of late complications when there is a high mortality rate. Cumulative incidence and cumulative conditional probability accurately give the probability and risk of cause-specific failure. CONCLUSION: Kaplan-Meier analysis of cause-specific failure should be avoided because of its misinterpretation as an estimate of probability, in favor of appropriate methods.

Colorectal Neoplasms↗

PubMed2006

Prospective multicenter study of quantitative pretest probability assessment to exclude acute coronary syndrome for patients evaluated in emergency department chest pain units.

STUDY OBJECTIVE: We compare the diagnostic accuracy of 3 methods--attribute matching, physician's written unstructured estimate, and a logistic regression formula (Acute Coronary Insufficiency-Time Insensitive Predictive Instrument, ACI-TIPI)--of estimating a very low pretest probability (< or = 2%) for acute coronary syndromes in emergency department (ED) patients evaluated in chest pain units. METHODS: We prospectively studied 1,114 consecutive patients from 3 academic EDs, evaluated for acute coronary syndrome. Physicians collected data required for pretest probability assessment before protocol-driven chest pain unit testing. A pretest probability greater than 2% was considered "test positive." The criterion standard was the outcome of acute coronary syndrome (death, myocardial infarction, revascularization, or > 60% stenosis prompting new treatment) within 45 days, adjudicated by 3 independent reviewers. RESULTS: Fifty-one of 1,114 enrolled patients (4.5%; 95% confidence interval [CI] 3.4% to 6.0%) developed acute coronary syndrome within 45 days, including 4 of 991 (0.4%; 95% CI 0.1% to 1.0%) patients, discharged after a negative chest pain unit evaluation result, who developed acute coronary syndrome. Unstructured estimate identified 293 patients with pretest probability less than or equal to 2%, 2 had acute coronary syndrome, yielding sensitivity of 96.1% (95% CI 86.5% to 99.5%) and specificity of 27.4% (95% CI 24.7% to 30.2%). Attribute matching identified 304 patients with pretest probability less than or equal to 2%; 1 had acute coronary syndrome, yielding a sensitivity of 98.0% (95% CI 89.6% to 99.9%) and a specificity of 26.1% (95% CI 23.6% to 28.7%). ACI-TIPI identified 56 patients; none had acute coronary syndrome, yielding sensitivity of 100% (95% CI 93.0% to 100%) and specificity of 6.1% (95% CI 4.7% to 7.9%). CONCLUSION: In a low-risk ED population with symptoms suggestive of acute coronary syndrome, patients with a quantitative pretest probability less than or equal to 2%, determined by attribute matching, unstructured estimate, or logistic regression, may not require additional diagnostic testing.

Acute Disease↗

PubMed2005

Probability theory for number of mixture components resolved by n independent columns.

A general theory is proposed for the probability of different outcomes of success and failure of component resolution, when complex mixtures are partially separated by n independent columns. Such a separation is called an n-column separation. An outcome of particular interest is component resolution by at least one column. Its probability is identified with the probability of component resolution by a single column, thereby defining the effective saturation of the n-column separation. Several trends are deduced from limiting expressions of the effective saturation. In particular, at low saturation the probability that components cluster together as unresolved peaks decreases exponentially with the number of columns, and the probability that components cluster together on addition of another column decreases by a factor equal to twice the column saturation. The probabilities of component resolution by n-column and two-dimensional separations also are compared. The theory is applied by interpreting three sets of previously reported retention indices of the 209 polychlorinated biphenyls (PCBs), as determined by GC. The origin of column independence is investigated from two perspectives. First, it is suggested that independence exists when the difference between indices of the same compound on two columns is much larger than the interval between indices required for separation. Second, it is suggested that independence exists when the smaller of the two intervals between a compound and its adjacent neighbors is not correlated with its counterpart on another column.

Chromatography↗

PubMed2006

The probability of causal conditionals.

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.

Analysis of Variance↗

PubMed2006

Impact of target point deviations on control and complication probabilities in stereotactic radiosurgery of AVMs and metastases.

OBJECTIVE: Determination of the impact of inaccuracies in the determination and setup of the target point in stereotactic radiosurgery (SRS) on the expectable complication and control probabilities. METHODS: Two randomized samples of patients with arteriovenous malformation (AVM) (n=20) and with brain metastases (n=20) treated with SRS were formed, and the probability for complete obliteration (COP) or complete remission (CRP), the size of the 10 Gy-volume in the brain tissue (VOI10), and the probability for radiation necrosis (NTCP) were calculated. The dose-effect relations for COP and CRP were fitted to clinical data. Target point deviations were simulated through random vectors and the resulting probabilities and volumes were calculated and compared with the values of the treatment plan. RESULTS: The decrease of the relative value of the control probabilities at 1mm target point deviation was up to 4% for AVMs and up to 10% for metastases. At 2 mm the median decrease was 5% for AVMs and 9% for metastases. The value for the target point deviation, at which COP and CRP decreased about 0.05 in 90% of the cases, was 1.3 mm. The increase of NTCP was maximally 0.0025 per mm target point deviation for AVMs and 0.0035/mm for metastases. The maximal increase of VOI10 was 0.7 cm(3)/mm target point deviation in both patient groups. CONCLUSIONS: The upper limit for tolerable target point deviations is at 1.3mm. If this value cannot be achieved during the system test, a supplementary safety margin should be applied for the definition of the target volume. A better accuracy level is desirable, in order to ensure optimal chances for the success of the treatment. The target point precision is less important for the minimization of the probability of radiation necroses.

Brain↗

PubMed2006

Assessment of pretest probability of pulmonary embolism in the emergency department by physicians in training using the Wells model.

INTRODUCTION: Assessment of pretest probability should be the initial step in investigation of patients with suspected pulmonary embolism (PE). In teaching hospitals physicians in training are often the first physicians to evaluate patients. OBJECTIVE: To evaluate the accuracy of pretest probability assessment of PE by physicians in training using the Wells clinical model and to assess the safety of a diagnostic strategy including pretest probability assessment. PATIENTS AND METHODS: 291 consecutive outpatients with clinical suspicion of PE were categorized as having a low, moderate or high pretest probability of PE by physicians in training who could take supervising physicians' advice when they deemed necessary. Then, patients were managed according to a sequential diagnostic algorithm including D-dimer testing, lung scan, leg compression ultrasonography and helical computed tomography. Patients in whom PE was deemed absent were followed up for 3 months. RESULTS: 34 patients (18%) had PE. Prevalence of PE in the low, moderate and high pretest probability groups categorized by physicians in training alone was 3% (95% confidence interval (CI): 1% to 9%), 31% (95% CI: 22% to 42%) and 100% (95% CI: 61% to 100%) respectively. One of the 152 untreated patients (0.7%, 95% CI: 0.1% to 3.6%) developed a thromboembolic event during the 3-month follow-up period. CONCLUSION: Physicians in training can use the Wells clinical model to determine pretest probability of PE. A diagnostic strategy including the use of this model by physicians in training with access to supervising physicians' advice appears to be safe.

Adolescent↗

PubMed1997

Development and validation of a clinical score to estimate the probability of coronary artery disease in men and women presenting with suspected coronary disease.

PURPOSE: Guidelines for the management of patients with suspected coronary disease have emphasized stratification into groups with low, intermediate, and high probability of significant coronary disease. Previously derived clinical prediction rules have been difficult to apply in clinical settings. The purpose of this study was to develop and validate a clinical score that facilitates this stratification process. PATIENTS AND METHODS: We performed a retrospective analysis of prospectively acquired data from 915 patients with suspected coronary disease and normal resting electrocardiograms who presented for exercise testing at a university hospital. All patients subsequently underwent coronary angiography. Analysis included logistic regression with significant coronary disease (> or = 1 vessel with a > or = 50% lesion) presence as the dependent variable and clinical variables as independent variables. From this analysis, a coronary disease score was developed to estimate prevalence of coronary disease from clinical variables. Validation of this score was performed in a separate prospectively acquired cohort of 348 patients. RESULTS: For the entire validation group, the prevalence of significant coronary disease was 16% (10/63) in the low probability group, 44% (86/195) in the intermediate probability group, and 69% (62/90) in the high probability group. Both men and women were stratified equally well into the 3 probability groups. CONCLUSION: The clinical score is an easily memorized and accurate method for categorizing patients with suspected but not proven coronary disease and normal resting electrocardiograms into clinically meaningful probability groups upon which decisions concerning appropriate diagnostic test selection could potentially be based.

Aged↗

PubMed2003

The influence of hierarchy on probability judgment.

Consider the task of predicting which soccer team will win the next World Cup. The bookmakers may judge Brazil to be the team most likely to win, but also judge it most likely that a European rather than a Latin American team will win. This is an example of a non-aligned hierarchy structure: the most probable event at the subordinate level (Brazil wins) appears to be inconsistent with the most probable event at the superordinate level (a European team wins). In this paper we exploit such structures to investigate how people make predictions based on uncertain hierarchical knowledge. We distinguish between aligned and non-aligned environments, and conjecture that people assume alignment. Participants were exposed to a non-aligned training set in which the most probable superordinate category predicted one outcome, whereas the most probable subordinate category predicted a different outcome. In the test phase participants allowed their initial probability judgments about category membership to shift their final ratings of the probability of the outcome, even though all judgments were made on the basis of the same statistical data. In effect people were primed to focus on the most likely path in an inference tree, and neglect alternative paths. These results highlight the importance of the level at which statistical data are represented, and suggest that when faced with hierarchical inference problems people adopt a simplifying heuristic that assumes alignment.

Adult↗

PubMed2001

Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-1-discordant couples in Rakai, Uganda.

BACKGROUND: The probability of HIV-1 transmission per coital act in representative African populations is unknown. We aimed to calculate this probability overall, and to estimate how it is affected by various factors thought to influence infectivity. METHODS: 174 monogamous couples, in which one partner was HIV-1 positive, were retrospectively identified from a population cohort in Rakai, Uganda. Frequency of intercourse and reliability of reporting within couples was assessed prospectively. HIV-1 seroconversion was determined in the uninfected partners, and HIV-1 viral load was measured in the infected partners. Adjusted rate ratios of transmission per coital act were estimated by Poisson regression. Probabilities of transmission per act were estimated by log-log binomial regression for quartiles of age and HIV-1 viral load, and for symptoms or diagnoses of sexually transmitted diseases (STDs) in the HIV-1-infected partners. RESULTS: The mean frequency of intercourse was 8.9 per month, which declined with age and HIV-1 viral load. Members of couples reported similar frequencies of intercourse. The overall unadjusted probability of HIV-1 transmission per coital act was 0.0011 (95% CI 0.0008-0.0015). Transmission probabilities increased from 0.0001 per act at viral loads of less than 1700 copies/mL to 0.0023 per act at 38 500 copies/mL or more (p=0.002), and were 0.0041 with genital ulceration versus 0.0011 without (p=0.02). Transmission probabilities per act did not differ significantly by HIV-1 subtypes A and D, sex, STDs, or symptoms of discharge or dysuria in the HIV-1-positive partner. INTERPRETATION: Higher viral load and genital ulceration are the main determinants of HIV-1 transmission per coital act in this Ugandan population.

Adolescent↗

PubMed1999

Can the probability for obliteration after radiosurgery for arteriovenous malformations be accurately predicted?

PURPOSE: To investigate how accurate different models predict the probability for obliteration following radiosurgery for an arteriovenous malformation (AVM). METHODS AND MATERIALS: The probability for obliteration was calculated for all 838 AVMs with a known treatment outcome and treated at the Karolinska Hospital with Gamma Knife surgery 1970-1993. Four different models were used for the calculation, resulting in four different values of the probability for obliteration. The calculated prediction values were added for each model, and the total number of predicted obliteration compared to that observed in the whole patient material as well as in different subgroups. RESULTS: Three of the four models predicted the total number of obliterations accurately. In two of those three models, the accuracy of the prediction was dependent on AVM volume and treatment dose. In one model only, the prediction was accurate and independent of all investigated parameters. CONCLUSIONS: The probability for obliteration was accurately predicted by one of the models analyzed. In this model, the probability for obliteration was related to the dose to the AVM periphery only. The AVM volume had no independent impact on the probability for obliteration. There was a trend that AVMs with a central location had a better obliteration rate than predicted.

Adult↗