Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “PROBABILITY”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4Linked to original sources
PubMed2001

Effects of sequential and temporal probability of deviant occurrence on mismatch negativity.

The mismatch negativity (MMN) increases in amplitude as the probability of deviant occurrence decreases. It is unclear whether the determining variable is sequential probability (i.e. the probability of a deviant within a number of standards) or temporal probability (i.e. the probability of a deviant within a period of time). Eight subjects heard a train of frequently occurring 1000 Hz standard tones. The probability of a 1100 Hz pitch deviant was manipulated. In one condition the stimulus-onset-asynchrony (SOA) was 150 ms, with temporal probability of deviant occurrence being either 1/9.00, 1/4.50, 1/2.25, or 1/1.125 s (sequential probability being 1/60, 1/30, 1/15, or 1(deviant)/7.5(standards), respectively). In another condition the SOA was 600 ms, with temporal probability being either 1/9.00, 1/4.50, or 1/2.25 s (sequential probability being 1/15, 1/7.5, or 1/3.75, respectively). In a final condition, the SOA was 2400 ms with temporal probability being 1/9.00 s (sequential probability 1/3.75). Both sequential and temporal probabilities had a marked effect on the MMN. When a deviant occurred every 2.25, 4.50, or 9.00 s, the MMN increased as temporal probability decreased. When a deviant occurred once every 7.5 or 15 standards, the MMN was larger for lower sequential probability, but the effect was not significant. Nevertheless, when temporal probability was held constant at 1/9.00 s, the MMN increased as sequential probability decreased. At rapid rates of stimulus presentation, the MMN was largest. However, it was attenuated when the probability of deviant occurrence was very high perhaps due to the refractoriness of its generator. At the slowest rate, the MMN was diminished perhaps due to memory decay for the standard stimuli.

Acoustic Stimulation↗
PubMed1995

A reliable sequence alignment method based on probabilities of residue correspondences.

Probabilities of all possible correspondences of residues in aligning two proteins are evaluated by assuming that the statistical weight of each alignment is proportional to the exponent of its total similarity score. Based on such probabilities, a probability alignment that includes the most probable correspondences is proposed. In the case of highly similar sequence pairs, the probability alignments agree with the maximum similarity alignments that correspond to the alignments with the maximum similarity score. Significant correspondences in the probability alignments are those whose probabilities are > 0.5. The probability alignment method is applied to a few protein pairs, and results indicate that such highly probable correspondences in the probability alignments are probably correct correspondences that agree with the structural alignments and that incorrect correspondences in the maximum similarity alignments are usually insignificant correspondences in the probability alignments. The root mean square deviations in superimposition of corresponding residues tend to be smaller for significant correspondences in the probability alignments than for all correspondences in the maximum similarity alignments, indicating that incorrect correspondences in the maximum similarity alignments tend to be insignificant correspondences in probability alignments. This fact is also confirmed in 109 protein pairs that are similar to each other with sequence identities between 90 and 35%. In addition, the probability alignment method may better predict correct correspondences than the maximum similarity alignment method. Probability alignments do, of course, depend on a scoring scheme but are less sensitive to the value of parameters such as gap penalties. The present probability alignment method is useful for constructing reliable alignments based on the probabilities of correspondences and can be used with any scoring scheme.

Amino Acid Sequence↗
PubMed1996

Diagnostic value of echocardiography in suspected endocarditis. An evaluation based on the pretest probability of disease.

BACKGROUND: We hypothesized that for the diagnosis of endocarditis, (1) transthoracic echocardiography (TTE) would be most valuable in patients with an intermediate clinical probability of the disease and (2) transesophageal echocardiography (TEE) would be most useful in patients with an intermediate probability when TTE either does not yield an adequate study or indicates an intermediate probability of endocarditis. We also sought to investigate the influence of echocardiographic results on antibiotic usage and its duration. METHODS AND RESULTS: TTE and TEE were performed in 105 consecutive patients with suspected endocarditis. Patients were classified as having either low, intermediate, or high probability of endocarditis on the basis of clinical criteria and separately on the basis of both TTE and TEE findings. TTE and TEE classified the majority (82% and 85%, respectively) of the 67 patients with a low clinical probability of endocarditis as having a low likelihood of the disease. Of the 14 patients with intermediate clinical probability, 12 had technically adequate TTE studies; 10 of these (83%) were classified as either high or low probability. All patients with intermediate clinical probability were classified as high or low probability by TEE. The majority of the 24 patients with high clinical probability were placed in the low-likelihood category by echocardiography (15 by TTE and 12 by TEE). There was concordance between TTE and TEE in 83% of all cases. TEE was useful for the diagnosis of endocarditis in patients with prosthetic valves and in those in whom TTE indicated an intermediate probability; these constituted < 20% of patients in our study. The course of antibiotic therapy was influenced only by the clinical profile and not by the echocardiographic results. CONCLUSIONS: Echocardiography should not be used to make a diagnosis of endocarditis in those with a low clinical probability of the disease. In those with an intermediate or high clinical probability, TTE should be the diagnostic procedure of choice. TEE for the diagnosis of endocarditis should be reserved only for patients who have prosthetic valves and in whom TTE is either technically inadequate or indicates an intermediate probability of endocarditis.

Adolescent↗
PubMed1979

Partial avoidance contingencies: Absolute omission and punishment probabilities.

Avoidance contingencies were defined by the absolute probability of the conjunction of responding or not responding with shock or no shock. The "omission" probability (rho(00)) is the probability of no response and no shock. The "punishment" probability (rho(11)) is the probability of both a response and a shock. The traditional avoidance contingency never omits shock on nonresponse trials (rho(00)=0) and never presents shock on response trials (rho(11)=0). Rats were trained on a discrete-trial paradigm with no intertrial interval. The first lever response changed an auditory stimulus for the remainder of the trial. Shocks were delivered only at the end of each trial cycle. After initial training under the traditional avoidance contingency, one group of rats experienced changes in omission probability (rho(00)>0), holding punishment probability at zero. The second group of rats were studied under different punishment probability values (rho(11)>0), holding omission probability at zero. Data from subjects in the omission group looked similar, showing graded decrements in responding with increasing probability of omission. These subjects approximately "matched" their nonresponse frequencies to the programmed probability of shock omission on nonresponse trials, producing a very low and approximately constant conditional probability of shock given no response. Subjects in the punishment group showed different sensitivity to increasing absolute punishment probability. Some subjects decreased responding to low values as punishment probability increased, while others continued to respond at substantial levels even when shock was inevitable on all trials (noncontingent shock schedule). These results confirm an asymmetry between two dimensions of partial avoidance contingencies. When the consequences of not responding included occasional omission of shock, all subjects showed graded sensitivity to changes in omission frequency. When the consequences of responding included occasional shock delivery, some subjects showed graded sensitivity to punishment frequency while others showed control by overall shock frequency as well.

Journal Article↗
PubMed2001

Assessing the clinical probability of pulmonary embolism.

Clinical assessment is a cornerstone of the recently validated diagnostic strategies for pulmonary embolism (PE). Although the diagnostic yield of individual symptoms, signs, and common laboratory tests is limited, the combination of these variables, either by empirical assessment or by a prediction rule, can be used to express a clinical probability of PE. The latter may serve as pretest probability to predict the probability of PE after further objective testing (posterior or post-test probability). Over the last few years, attempts have been made to develop structured prediction models for PE. In a Canadian multicenter prospective study, the clinical probability of PE was rated as low, intermediate, or high according to a model which included assessment of presenting symptoms and signs, risk factors, and presence or absence of an alternative diagnosis at least as likely as PE. The prevalence of PE in the low, intermediate, and high pretest probability categories was 3, 28, and 78%, respectively. This model relies heavily on the clinician's subjective judgement as to whether an alternative diagnosis is as likely as or more likely than PE, and, as such, it can be hardly standardized. Furthermore, the inherent complexity of the model may limit its applicability in daily clinical practice. Recently, a simple clinical score was developed to stratify outpatients with suspected PE into groups with low, intermediate, or high clinical probability. Logistic regression was used to predict parameters associated with PE. A score =/<4 identified patients with low probability of whom 10% had PE. The prevalence of PE in patients with intermediate (score 5-8) and high probability (score > or = 9) was 38 and 81%, respectively. As opposed to the Canadian model, this clinical score is standardized. The predictor variables identified in the model, however, were derived from a data base of emergency ward patients. This model may, therefore, not be valid in assessing the clinical probability of PE in inpatients. In the PISA-PED study, a clinical diagnostic algorithm was developed which rests on the identification of three relevant clinical symptoms and on their association with electrocardiographic and/or radiographic abnormalities specific for PE. Among patients who, according to the model, had been rated as having a high clinical probability, the prevalence of proven PE was 97%, while it was 3% in those with low probability. The prevalence of PE in patients with intermediate clinical probability was 41%. These results underscore the importance of incorporating the standardized reading of the electrocardiogram and of the chest radiograph into the clinical evaluation of patients with suspected PE. The interpretation of these laboratory data, however, requires experience. Future research is needed to develop standardized models, of varying degree of complexity, which may find application in different clinical settings to predict the probability of PE.

Algorithms↗
PubMed1999

Comparison of the Diamond-Forrester method and a new score to estimate the pretest probability of coronary disease before exercise testing.

OBJECTIVE: We compared the Diamond-Forrester (DF) tabular method to assess pretest probability of coronary artery disease to a new scoring method (NS). METHODS: We evaluated 544 patients with suspected coronary disease who underwent both exercise electrocardiography and coronary angiography. The prevalence of any coronary artery disease (CAD) (>/=1 vessel with a >/=50% stenosis) within low, intermediate, and high pretest probability groups defined by the 2 methods was compared. The DF method used age, sex, and symptoms. The NS used those 3 factors plus 7 other risk factors. RESULTS: Overall prevalence of CAD was 41%. We compared the respective prevalence of CAD within pretest probability groups. Low probability: DF 27% versus NS 17% (P <.03); intermediate probability: DF 42% versus NS 47%; high probability: DF 70% versus NS 72%. We evaluated results separately in men and women. In women, no significant differences were found. However, in men, a significant difference in the low probability group was found (DF 47% versus NS 22%; P <.03). When the 47 asymptomatic patients were removed from the analysis, there were no differences between the 2 methods. Men: low probability, DF 17% versus NS 21%; intermediate probability, DF 45% versus NS 49%; high probability, DF 67% versus NS 72%. Women: low probability, DF 17% versus NS 15%; intermediate probability, DF 38% versus NS 27%; high probability, DF 83% versus NS 70%. CONCLUSION: In symptomatic patients, the accuracy of the 2 methods was the same. In asymptomatic patients, further evaluation in larger populations will be needed.

Coronary Angiography↗
PubMed2002

Adjusting the outputs of a classifier to new a priori probabilities: a simple procedure.

It sometimes happens (for instance in case control studies) that a classifier is trained on a data set that does not reflect the true a priori probabilities of the target classes on real-world data. This may have a negative effect on the classification accuracy obtained on the real-world data set, especially when the classifier's decisions are based on the a posteriori probabilities of class membership. Indeed, in this case, the trained classifier provides estimates of the a posteriori probabilities that are not valid for this real-world data set (they rely on the a priori probabilities of the training set). Applying the classifier as is (without correcting its outputs with respect to these new conditions) on this new data set may thus be suboptimal. In this note, we present a simple iterative procedure for adjusting the outputs of the trained classifier with respect to these new a priori probabilities without having to refit the model, even when these probabilities are not known in advance. As a by-product, estimates of the new a priori probabilities are also obtained. This iterative algorithm is a straightforward instance of the expectation-maximization (EM) algorithm and is shown to maximize the likelihood of the new data. Thereafter, we discuss a statistical test that can be applied to decide if the a priori class probabilities have changed from the training set to the real-world data. The procedure is illustrated on different classification problems involving a multilayer neural network, and comparisons with a standard procedure for a priori probability estimation are provided. Our original method, based on the EM algorithm, is shown to be superior to the standard one for a priori probability estimation. Experimental results also indicate that the classifier with adjusted outputs always performs better than the original one in terms of classification accuracy, when the a priori probability conditions differ from the training set to the real-world data. The gain in classification accuracy can be significant.

Classification↗
PubMed1998

A test of the claim that plan rankings are determined by relative complication and tumor-control probabilities.

PURPOSE: This study tests an accepted claim regarding tumor control (TCP) and normal tissue complication (NTCP) probability functions. The claim is that treatment plans can be ranked using relative probabilities, even when the absolute probabilities are unknown. The assumption supports the use of probability models for plan optimization and the comparison of treatment techniques. METHODS: The claim was tested using a hypothetical model consisting of two tissues, and illustrated with clinical data. Plans were scored using the probability of uncomplicated tumor control. The scores of different plans were compared by fixing their relative risks for an individual tissue complication, but adjusting the absolute probability levels up or down. The tested claim is that the plan rankings should not change. RESULTS: In the two-tissue model, the rankings of competing plans were reversed by doubling all the probabilities. The preference ordering of lung cancer plans changed after the risk of pulmonary complication was reduced by 3-fold. In another site, the ranking of plans by overall complication-free probability was disturbed by errors that preserved the ordering of plans with respect to any individual complication. An adjustment of +/- 2.5% in the initial NTCP values for two tissues changed the direction in which a plan score moved in response to a fixed tradeoff in complication risk in an optimization search. CONCLUSIONS: Contrary to claims, plan rankings are not determined by the relative probabilities of adverse events. The effect on plan scores of trading one complication for another depends on the absolute levels of risk. Absolute errors in NTCP and TCP functions result in the wrong ranking of plans, even when relative probabilities are correct. An optimization routine based on TCP and NTCP calculations may be forced in the wrong direction by small errors in the probability estimates.

Humans↗
PubMed1997

Need probability affects retention: a direct demonstration.

Recent memory theory has emphasized the concept of need probability--that is, the probability that a given piece of learned information will be tested at some point in the future. It has been proposed that, in real-world situations, need probability declines over time and that the memory-loss rate is calibrated to match the progressive reduction in need probability (J.R. Anderson & Schooler, 1991). The present experiments were designed to examine the influence of the slope of the need-probability curve on the slope of the retention curve. On each of several trials, subjects memorized a list of digits, then retained the digits in memory for 1, 2, 4, 8, or 16 sec. Some trials ended with a recall test; other trials ended with the message, "no test." In Experiment 1, the likelihood of encountering a memory test (i.e., the need probability) was made to either increase or decrease as the retention interval increased; in Experiment 2, need probability either was flat (invariant across retention intervals) or decreased as the retention interval increased. The results indicated that the shape of the need-probability curve influenced the slope of the retention curve (Experiment 1) and that the effect became larger as the experimental session progressed (Experiment 2). The findings support the notion that memory adapts to need probabilities and that the rate of forgetting is influenced by the slope of the need-probability curve. In addition, all of the forgetting curves approximated a power function, suggesting that need probability influences the slope but not the form of forgetting.

Educational Measurement↗
PubMed2005

[The clinical relationship between symptoms and the final diagnosis in general practice, determined by means of posterior probabilities calculated on the basis of the Transition Project].

OBJECTIVE: To determine how, with the aid of the database of the Transition Project (www.transitionproject.nl), one can calculate posterior probabilities for general practice that provide insight into the clinical significance of the simultaneous occurrence of two events (a symptom and a diagnosis, or two diseases) in general practice. DESIGN: Descriptive. METHOD: The use of the 'International classification of primary care' (ICPC) to code both the patient's reason for encounter and the diagnosis of the general practitioner in the Transition Project has resulted in a database for the period 1985-2002 with a total of 201,127 patient-years, in which the posterior probability of a diagnosis in the presence of a complaint or symptom is available in the form of an odds ratio. Also in the case of the simultaneous occurrence of 2 episodes of care (comorbidity) in a patient it is now possible to determine whether the ratio between the prior and the posterior probability indicates a clinically relevant relationship or that it is a chance finding. Such posterior probabilities have been calculated for the conditions otitis media, hypertension in diabetes mellitus, shortness of breath and heart failure. In the calculation ofthe prior and posterior probabilities, only 'certain' diagnoses were used. RESULTS: For the diagnosis 'otitis media' in the age group 0-4 years, otalgia had the highest posterior probability (odds ratio: 15.77), with discharge from the ear taking second place (odds ratio: 8.59). 'Fever' contributed almost nothing. The odds ratio for hypertension in 45-74-year-old women with diabetes mellitus was 3.42. When the symptom was 'shortness of breath', the prior probability of heart failure in the age group 45-64 years was relatively low (2.0) but the posterior probability was relatively high (24.2). In this way, the combination of prior and posterior probabilities can provide support for the clinical work of the general practitioner. As a predictive variable for heart failure in the age group 65-74 years, 'ankle oedema' played an important role while 'fatigue' contributed nothing to the diagnosis. It was apparent from the database that the care for patients with heart failure often coincided with that for chronic diseases such as diabetes mellitus, hypertension, ischaemic heart disease, chronic obstructive pulmonary disease and atrial fibrillation. But the question whether there is a clinically relevant relationship could only be answered on the basis of the posterior probabilities: the highest odds ratio's were found for 'atrial fibrillation/atrial flutter' (32.5), 'chronic obstructive pulmonary disease' (22.5) and 'chronic skin ulcer' (20.2). CONCLUSION: The calculation of prior and posterior probabilities on the basis of the database of the Transition Project makes it possible for general practitioners to determine the clinical relevance of their observations.

Adolescent↗
PubMed2026

RR-interval-based atrial fibrillation detection and burden estimation: cross-dataset validation and calibration-aware probability analysis.

Objective.Atrial fibrillation (AF) burden has become an increasingly important endpoint in long-duration rhythm monitoring, but reliable burden estimation requires more than accurate AF detection alone. In particular, when burden is derived by aggregating predicted AF probabilities over time, probability calibration may directly affect burden validity under external dataset shift.Approach.This study developed an interpretable-interval feature model for AF detection and evaluated it using record-wise cross-validation on a development cohort and independent cross-dataset external validation on public Holter electrocardiographic databases. Window-level performance was assessed using the area under the receiver operating characteristic curve (ROC-AUC), area under the precision-recall curve (PR-AUC), Brier score, expected calibration error (ECE), and calibration intercept and calibration slope. Recording-level AF burden was estimated using both probability-based and hard-label aggregation and evaluated using mean absolute error (MAE) and agreement analyses.Main results.The model showed high discrimination in both development and external evaluation, with external ROC-AUC ofand PR-AUC of. However, external calibration deteriorated despite preserved ranking performance, with Brier score of, ECE(15) of, calibration intercept of, and calibration slope of. In the external cohort, probability-based burden estimation preserved strong association with reference burden but showed weaker raw agreement than hard-label aggregation, with MAE ofversus, consistent with systematic probability underprediction. Repeated external recalibration across record-level splits substantially improved probability quality and probability-based burden estimation. Median probability-burden MAE decreased fromwithout recalibration toafter Platt recalibration andafter isotonic recalibration, while median ECE(15) decreased fromtoand, respectively.Significance.These findings indicate that-interval-based AF detection maintained strong ranking performance in the tested external cohort, but probability calibration should be evaluated explicitly when predicted probabilities are aggregated into AF-burden estimates.

Atrial Fibrillation↗
PubMed2003

Probabilities of encounters between objects in biological systems 2: cognizer view.

The same event may not necessarily occur against a given cognition (action) upon repetition. The degree of certainty in which a particular event actually occurs following a current cognition is the probability of the event viewed (experienced) by the focal cognizer. This is the internal concept of probability, which is contrasted with the external probability concept, the probability viewed by the meta-observer located outside the system, expressed as the relative frequencies of events. The internal probability may be a measure of the adaptive cognitions or actions of a cognizer by which it generates or maintains a particular relation to its surroundings. In this paper, the quantitative description of encounter probabilities based on the internal concept is explored in the framework of the cognizers system model. The internal analysis derives the same formulation as that derived by the meta-observer concept of probability reported in a previous paper (Nakajima, 2001a), indicating the theoretical consistency of encounter probabilities between the analyses by the two contrasting probability concepts. The formulation suggests that a cognizer can raise (or reduce) the encounter probability with targets by a discriminative and selective response to a given situation, which describes a quantitative aspect of biological adaptation to the environment.

Adaptation, Physiological↗
PubMed1989

Comparison of three Bayesian methods to estimate posttest probability in patients undergoing exercise stress testing.

To determine whether recent refinements in Bayesian methods have led to improved diagnostic ability, 3 methods using Bayes' theorem and the independence assumption for estimating posttest probability after exercise stress testing were compared. Each method differed in the number of variables considered in the posttest probability estimate (method A = 5, method B = 6 and method C = 15). Method C is better known as CADENZA. There were 436 patients (250 men and 186 women) who underwent stress testing (135 had concurrent thallium scintigraphy) followed within 2 months by coronary arteriography. Coronary artery disease ([CAD], at least 1 vessel with greater than or equal to 50% diameter narrowing) was seen in 169 (38%). Mean pretest probabilities using each method were not different. However, the mean posttest probabilities for CADENZA were significantly greater than those for method A or B (p less than 0.0001). Each decile of posttest probability was compared to the actual prevalence of CAD in that decile. At posttest probabilities less than or equal to 20%, there was underestimation of CAD. However, at posttest probabilities greater than or equal to 60%, there was overestimation of CAD by all methods, especially CADENZA. Comparison of sensitivity and specificity at every fifth percentile of posttest probability revealed that CADENZA was significantly more sensitive and less specific than methods A and B. Therefore, at lower probability thresholds, CADENZA was a better screening method. However, methods A or B still had merit as a means to confirm higher probabilities generated by CADENZA (especially greater than or equal to 60%).(ABSTRACT TRUNCATED AT 250 WORDS)

Algorithms↗
PubMedDate not supplied

Value of assessment of pretest probability of deep-vein thrombosis in clinical management.

BACKGROUND: When ultrasonography is used to investigate deep-vein thrombosis, serial testing is recommended for those who test negative initially. Serial testing is inconvenient for patients and costly. We aimed to assess whether the calculation of pretest probability of deep-vein thrombosis, with a simple clinical model, could be used to improve the management of patients who present with suspected deep-vein thrombosis. METHODS: Consecutive outpatients with suspected deep-vein thrombosis had their pretest probability calculated with a clinical model. They then underwent compression ultrasound imaging of proximal veins of the legs. Patients at low pretest probability underwent a single ultrasound test. A negative ultrasound excluded the diagnosis of deep-vein thrombosis whereas a positive ultrasound was confirmed by venography. Patients at moderate pretest probability with a positive ultrasound were treated for deep-vein thrombosis whereas patients with an initial negative ultrasound underwent a single follow-up ultrasound 1 week later. Patients at high pretest probability with a positive ultrasound were treated whereas those with negative ultrasound underwent venography. All patients were followed up for 3 months for thromboembolic complications. FINDINGS: 95 (16.0%) of all 593 patients had deep-vein thrombosis; 3%, 17%, and 75% of the patients with low, moderate, and high pretest probability, respectively, had deep-vein thrombosis. Ten of 329 patients with low pretest probability had the diagnosis confirmed, nine at initial testing and one at follow-up. 32 of 193 patients with moderate pretest probability had deep-vein thrombosis, three diagnosed by the serial (1 week) test, and two during follow-up. 53 of 71 patients with high pretest probability had deep-vein thrombosis (49 by the initial ultrasound and four by venography). Only three (0.6%) of all 501 (95% CI 0.1-1.8) patients diagnosed as not having deep-vein thrombosis had events during the 3-month follow-up. Overall only 33 (5.6%) of 593 patients required venography and serial testing was limited to 166 (28%) of 593 patients. INTERPRETATION: Management of patients with suspected deep-vein thrombosis based on clinical probability and ultrasound of the proximal deep veins is safe and feasible. Our strategy reduced the need for serial ultrasound testing and reduced the rate of false-negative or false-positive ultrasound studies.

Algorithms↗
PubMed2004

Probabilities of death from breast cancer and other causes among female breast cancer patients.

BACKGROUND: Among cancer patients, probabilities of death from that cancer and other causes in the presence of competing risks are optimal measures of prognosis and of mortality across demographic groups. We used data on breast cancer patients from the Surveillance, Epidemiology, and End Results (SEER) Program in a competing-risk analysis. METHODS: We determined vital status and cause of death for 395,251 white and 35,259 black female patients with breast cancer diagnosed from January 1, 1973, through December 31, 2000, by use of SEER data. We calculated probabilities of death from breast cancer and other causes according to stage, race, and age at diagnosis; for cases diagnosed from January 1, 1990, to December 31, 2000, we also calculated some such probabilities according to tumor size and estrogen receptor (ER) status. All statistical tests were two-sided. RESULTS: The probability of death from breast cancer after nearly 28 years of follow-up ranged from 0.03 to 0.10 for patients with in situ disease to 0.70 to 0.85 for patients with distant disease, depending on race and age. The probability of death from breast cancer at the end of the follow-up period generally declined with age at diagnosis; the probability among the oldest (> or =70 years) compared with the youngest (<50 years) patients was 33% lower for white and 46% lower for black patients with localized disease and 14% lower for white patients and 13% lower for black patients with distant disease. The probability of death from breast cancer exceeded that from all other causes for patients diagnosed with localized disease before age 50 years, with regional disease before age 60 years, and with distant disease at any age. The probability of death from breast cancer for patients diagnosed with localized or regional disease was statistically significantly greater in black patients than in white patients (all six P values < or =.01 for age groups 30-49 to 60-69 years; two P values < or =.04 for ages > or =70 years). Among patients with localized or regional disease and known ER status, the probability of death from breast cancer after nearly 11 years of follow-up ranged from 0.04 to 0.11 for patients with localized ER-positive tumors of 2 cm or less to 0.37 to 0.53 for patients with regional ER-negative tumors. CONCLUSIONS: The probability of death from breast cancer versus other causes varied substantially according to stage, tumor size, ER status, and age at diagnosis in both white and black patients.

Adult↗
PubMed2003

Probabilistic reasoning and clinical decision-making: do doctors overestimate diagnostic probabilities?

BACKGROUND: The "threshold approach" is based on a physician's assessment of the likelihood of a disease expressed as a probability. The use of Bayes' theorem to calculate disease probability in patients with and without a particular characteristic, may be hampered by the presence of subadditivity (i.e. the sum of probabilities concerning a single case scenario exceeding 100%). AIM: To assess the presence of subadditivity in physicians' estimations of probabilities and the degree of concordance among doctors in their probability assessments. DESIGN: Prospective questionnaire. METHODS: Residents and trained physicians in Family Medicine, Internal Medicine and Cardiology (n = 84) were asked to estimate the probability of each component of the differential diagnosis in a case scenario describing a patient with chest pain. RESULTS: Subadditivity was exhibited in 65% of the participants. The total sum of probabilities given by each participant ranged from 44% to 290% (mean 137%). There was wide variability in the assignment of probabilities for each diagnostic possibility (SD 16-21%). DISCUSSION: The finding of substantial subadditivity, coupled with the marked discordance in probability estimates, questions the applicability of the threshold approach. Physicians need guidance, explicit tools and formal training in probability estimation to optimize the use of this approach in clinical practice.

Bayes Theorem↗
PubMed1971

Fitting discrete probability distributions to evolutionary events.

The assumptions underlying the use of the Poisson distribution are essentially that the probability of an event is small but nearly identical for all occurrences and that the occurrence of an event does not alter the probability of recurrence of such events. These assumptions do not seem to be met for evolutionary events since (i) the probability of fixing nucleotide codon substitutions is not equal for all substitutions at a codon, and probably varies for the same substitution in different lineages; (ii) the probability of fixing codon substitutions varies among positions of a cistron; and (iii) the fixation of a nucleotide codon substitution at one position in a cistron modifies, and may even promote, the fixation of a codon substitution elsewhere along the cistron. Natural selection presumably is the causative factor that acts to modify the probability of a nucleotide codon substitution's being fixed in a population. The use of the negative binomial distribution is consistent with the evidence that selective pressure on amino acid or nucleotide codon positions varies both among codon positions of a cistron and at a particular position during evolutionary time. If the number of fixations of nucleotide codon substitutions per position of cistrons encoding cytochromes c are phyletically inferred (phylogeny based on a paleontological record) rather than phenetically inferred (based on paired comparisons of extant species' differences in the absence of a phylogeny) the distribution of these fixation data cannot be described adequately by a single Poisson distribution. The fit of these same data to a negative binomial distribution is very satisfactory. It has been argued that the fit of phenetically inferred fixation data, which do not take account of parallel or reverse fixations, to the Poisson distribution was supportive evidence for the hypothesis that protein evolution results from the fixation of selectively neutral codon substitutions. This argument now appears to be undercut by the evidence that data on nucleotide codon fixation are more probably distributed according to the negative binomial distribution. The fact that fixation data can be described by a particular discrete probability distribution does not of itself provide insight into the mechanisms of the evolutionary process. However, the facts-(i) that the assumptions underlying the use of the negative binomial distribution adequately deal with the varying probability of fixing amino acid or nucleotide codon substitutions at and among the positions of a cistron and (ii) that the negative binomial distribution provides an excellent fit for the phyletically inferred fixation data-suggest that the negative binomial is a very appropriate discrete probability distribution for describing evolutionary events. Amino acids or their nucleotide codon substitutions may be fixed at a position of a cistron as though selectively neutral relative to the codon being replaced, even though the codon position will not be selectively neutral, since many amino acids cannot function there. The negative binomial distribution treats this situation well whereas a single Poisson distribution could only be satisfactory if all codon positions that could vary were selectively neutral.

Amino Acid Sequence↗
PubMed2005

Spatial probability as an attentional cue in visual search.

We investigated the role of spatial probabilities in target location during participants' performance of a visual search task. Experiments 1 and 2 demonstrated that spatial probabilities could serve as a powerful attentional bias that produced faster detection of targets in high-probability locations than of those in low- or random-probability locations. The effect could not be explained by repetition priming alone. Moreover, responses to targets in low-probability locations were slowed only when a distractor was present in the high-probability location. In Experiments 3-5, we compared the effects of spatial probability with an explicit endogenous cue and a salient exogenous cue. Facilitation due to spatial probability was independent of any benefit afforded by the explicit endogenous cue but interacted with the salient exogenous cue, such that the exogenous cue validity effect was compressed for targets in the high-probability location. Together, these results suggest that the spatial probabilities governing target location constitute a potent bias of visual processing and, as such, can be considered an attentional cue that differs from both typical explicit endogenous and salient exogenous cues.

Adolescent↗