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Two techniques for teaching the estimation of prior probabilities.

BACKGROUND: Studies indicate that practicing clinicians do not employ quantitative techniques in diagnosis. If evidence-based approaches to clinical care are to succeed, there is a need to develop pedagogical tools to introduce the relevant techniques in clinical medicine. DESCRIPTION: This article describes 2 heuristic techniques that can be used by clinical teachers to introduce residents and medical students to the practice of estimating prior probabilities in diagnostic reasoning. The techniques are the probability pie and the probability dollar. The techniques require learners to divide either a pie or a dollar according to the probability they assign in the differential diagnosis. The techniques also introduce related ideas such as likelihood ratios, posterior probabilities, diagnostic accuracy and intra- and interrater variability. EVALUATION: An example of a 60-year-old man presenting with chest pain is presented to illustrate the technique. CONCLUSION: This article presents a simple and clinically relevant method of introducing important concepts in quantitative reasoning. More systematic evaluation is required to assess its effectiveness.

Diagnosis, Differential↗

Calculation of radiation induced complication probabilities for brain, liver and kidney, and the use of a reliability model to estimate critical volume fractions.

Radiation induced normal tissue complication probability is calculated for three different organs: brain, liver and kidney. The model applied is a reliability model where the volume effect of the tissue is described by the structural parameter, k, which reflects the architecture of the functional subunits (p) and the irradiated volume fraction (n). For partial, homogeneous irradiation of the brain, a k-value close to unity was found, and the respective values for liver and kidney were 0.92 and 0.77. An extension of the reliability model to account for individual inactivation probability of the subunits allows calculation of complication probability for inhomogeneous dose distributions. For the brain, intercomparison of a three-field and a two-field technique demonstrated a small reduction in complication probability for the former at low total doses. At high total doses a minimum complication probability was achieved applying a three-field technique, being three times less than that associated with the two-field technique.

Brain↗

Blind chance? An investigation into the perceived probabilities of phrases used in oral radiology for expressing chance.

The necessity for numerical probabilities in oral radiographic diagnosis is increasing, due to recent developments in computer-aided diagnosis, decision analysis, informed consent and medical litigation. These numerical probabilities are only partly available from current texts on oral radiology, where they are often expressed by ill-defined, semiquantitative phrases. Therefore, in this study 30 phrases expressing the probability of a relationship between a diagnosis and its symptoms were taken from a selected textbook on oral radiology. Seven oral radiologists from the USA and the Netherlands scored each of these probabilistic phrases on a 20-cm visual analogue scale. Low intraradiologist and high interradiologist variation was found. Because the high variation among authors of texts on oral radiology in interpreting probability information could have a negative influence on their ability to transfer unambiguous information to their readers, it is recommended that the use of semiquantitative phrases in oral radiology is restricted to five probability groups.

Humans↗

Prevalence of acute pulmonary embolism in central and subsegmental pulmonary arteries and relation to probability interpretation of ventilation/perfusion lung scans.

PURPOSE: The purpose of this investigation is to determine the prevalence of acute pulmonary embolism (PE) limited to subsegmental pulmonary arteries. BACKGROUND: Contrast-enhanced helical (spiral) and electron-beam CT, in the hands of experienced radiologists who are skillful with this modality, are sensitive for the detection of acute PE in central pulmonary arteries, but have a low sensitivity for the detection of PE limited to subsegmental pulmonary arteries. The potential for CT to diagnose PE, therefore, is partially dependent on the prevalence of PE limited to subsegmental pulmonary arteries. METHODS: Data are from the Prospective Investigation of Pulmonary Embolism Diagnosis (PIOPED). The largest pulmonary arteries that showed PE, as interpreted by the PIOPED angiographic readers, were identified in 375 patients in PIOPED with angiographically diagnosed PE. RESULTS: Among all patients with PE, 6% (95% confidence interval [CI], 4 to 9%) had PE limited to subsegmental branches of the pulmonary artery. Patients with high-probability ventilation/ perfusion (V/Q) scans had PE limited to subsegmental branches in only 1% (95% CI, 0 to 4%). Among patients with low-probability V/Q lung scans, 17% (95% CI, 8 to 29%) had PE limited to the subsegmental branches. Patients with low-probability V/Q scans and no prior cardiopulmonary disease had PE limited to the subsegmental pulmonary arteries in 30% (95% CI, 13 to 53%), whereas patients with low-probability V/Q scans who had prior cardiopulmonary disease had PE limited to subsegmental pulmonary arteries in 8% (95% CI, 2 to 22%) (p < 0.05). CONCLUSION: Based on data from all patients with PE in PIOPED, the prevalence of PE limited to subsegmental pulmonary arteries is low, 6%. PE limited to subsegmental pulmonary arteries was most prevalent among patients with low-probability V/Q scans, particularly if they had no prior cardiopulmonary disease.

Acute Disease↗

Application of probability analysis in the diagnosis of coronary artery disease.

The accuracy and applicability of probability analysis to the diagnosis of coronary artery disease is still an open question. Although earlier criticisms are well taken, much of the resistance to the application of probability analysis is based on tradition, rather than logic. Probabilistic algorithms, like any new technology, must be researched and developed and then withstand the test of time. They should not be dismissed simply because they are not traditional. On the other hand, probability analysis in the diagnosis of coronary artery disease must not be accepted just because it is attractive or because it appears to simplify clinical decisions. Application of probabilistic approaches should depend on their accuracy. There is evidence that results of tests and clinical data are not statistically independent. There is also evidence that sensitivities and specificities derived from pooled literature cannot be appropriately applied to just any patient in a particular institution. This is due to variability in the population of patients, a lack of standardization of testing methods, and methodologic problems in reporting results of sensitivities and specificities. In a large institution, where probabilistic formulae can be derived with some degree of confidence, probability analysis has an application today. Discriminant functions will be more accurate than Bayesian formulas, but whatever method one chooses, one must be certain that the parameters used are appropriate. Where the institution is not large enough to generate such a data base, there is presently no accurate approach to the estimation of the probability of coronary disease.

Algorithms↗

Probability of coincident vaccination in the 24 or 48 hours preceding sudden infant death syndrome death in Australia.

OBJECTIVE: Vaccination does not cause sudden infant death syndrome (SIDS). However, SIDS peaks at 2 months of age, when vaccination encounters are frequent. There are no published estimates using population data on age of death and immunization coverage to indicate to practitioners how often coincident vaccination may occur by chance. This study aimed to determine the probability that an Australian infant who has died of SIDS was vaccinated in the days before death. METHODS: An analytical study of population death data and immunization coverage was conducted for Australian children who were born between April 1, 2002, and March 31, 2003. Also evaluated were Australian children who were registered as dying of SIDS between 1997 and 2001. The main outcomes measured were distribution of SIDS deaths by age and distribution of immunization coverage by age. RESULTS: The probability of recent vaccination and SIDS coinciding varied by age and day of the week of death. The overall estimated probability of vaccination within the last 24 hours for a child who has died of SIDS in Australia is estimated as 1.3%. In the last 48 hours, it is 2.6%. With the average number of SIDS deaths for the period 1997-2001 equal to 130 cases per year, we estimated that a case of SIDS will occur when vaccination was given in the last 24 hours in 1.7 cases per year and within 48 hours in 3.5 cases. CONCLUSIONS: Although coincident vaccination and SIDS should not be a frequent problem, it can be expected to occur at least annually in Australia by chance alone. The probabilities of vaccination by age estimated in this study can also be applied to estimate the probability of a vaccination encounter for children who have experienced any unusual medical condition or death, when these occurrences are known to be unrelated to vaccination.

Age Factors↗

A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme.

The purpose of this study was to determine the treatment protocol, in terms of dose fractions and interfraction intervals, which minimizes normal tissue complication probability in the spinal cord for a given total treatment dose and treatment time. We generalize the concept of incomplete repair in the linear-quadratic model, allowing for arbitrary dose fractions and interfraction intervals. This is incorporated into a previously presented model of normal tissue complication probability for the spinal cord. Equations are derived for both mono-exponential and bi-exponential repair schemes, regarding each dose fraction and interfraction interval as an independent parameter, subject to the constraints of fixed total treatment dose and treatment time. When the interfraction intervals are fixed and equal, an exact analytical solution is found. The general problem is nonlinear and is solved numerically using simulated annealing. For constant interfraction intervals and varying dose fractions, we find that optimal normal tissue complication probability is obtained by two large and equal doses at the start and conclusion of the treatment, with the rest of the doses equal to one another and smaller than the two dose spikes. A similar result is obtained for bi-exponential repair. For the general case where the interfraction intervals are discrete and also vary, the pattern of two large dose spikes is maintained, while the interfraction intervals oscillate between the smallest two values. As the minimum interfraction interval is reduced, the normal tissue complication probability decreases, indicating that the global minimum is achieved in the continuum limit, where the dose delivered by the "middle" fractions is given continuously at a low dose rate. Furthermore, for bi-exponential repair, it is seen that as the slow component of repair becomes increasingly dominant as the magnitude of the dose spikes decreases. Continuous low-dose-rate irradiation with dose spikes at the start and end of treatment yields the lowest normal tissue complication probability in the spinal cord, given a fixed total dose and total treatment time, for both mono-exponential and bi-exponential repair. The magnitudes of the dose spikes can be calculated analytically, and are in close agreement with the numerical results.

Algorithms↗

Geometric probability distribution for modeling of error risk during prescription dispensing.

PURPOSE: The relationship between the number of prescriptions dispensed by individual pharmacy staff during a single workday and the probability of committing at least one dispensing error during that same workday period was evaluated using a geometric probability distribution. SUMMARY: A cross-sectional descriptive study involving 50 pharmacies located in six cities across the United States was conducted. A pharmacist trained to detect dispensing errors recorded the number of prescriptions filled by each pharmacy staff member and noted which prescription represented the staff member's first dispensing error (defined as any deviation from the prescriber's order) made during the observation period. The Kolmogorov-Smirnov tests for discrete distributions revealed that the observed cumulative distribution of dispensing errors could have come from a geometric probability distribution that assumed dispensing error rates of 2-3%. In terms of risk analysis, this study's findings suggest that there can be a quantifiable statistical relationship between a measure of workload and the risk of committing at least one dispensing error. The ability to model dispensing errors using a geometric probability distribution enables the safety and health care practitioner to directly assess dispensing error risk as a function of a pharmacy's accuracy rate and the number of prescriptions a pharmacy staff member should dispense during a work shift. CONCLUSION: A geometric probability distribution effectively modeled the relationship between the number of prescriptions filled and the occurrence of the first dispensing errors.

Drug Prescriptions↗

Importance of pretest probability score and D-dimer assay before sonography for lower limb deep venous thrombosis.

OBJECTIVE: The purpose of our study was to develop and validate a clinical score (the Hamilton score) for the assessment of lower limb deep venous thrombosis (DVT) and to determine the usefulness of this score and a D-dimer assay before a complete lower limb sonographic examination. SUBJECTS AND METHODS: Five hundred forty-two consecutive ambulatory patients presenting to the emergency department were prospectively recruited, of whom 16 patients were excluded from the study. Eighteen history and examination variables were collected by the emergency department physicians. The Simplify D-dimer assay and a complete, single lower limb sonographic examination were performed in all patients. All patients with a negative sonographic examination for DVT were followed up for 3 months, and all those with a positive sonographic examination were given anticoagulation therapy. The Hamilton score was developed using the data from the first 214 patients and was prospectively validated in the next 312 patients. RESULTS: The most significant factors associated with a diagnosis of DVT were immobilization of the lower limb, active malignancy, and a strong clinical suspicion of DVT without other diagnostic possibilities by the emergency department physicians. Other factors were bed rest or recent surgery, male sex, calf circumference difference greater than 3 cm, and erythema. The Hamilton score was developed with the following weights: immobilization of the lower limb (2 points), active malignancy (2 points), strong clinical suspicion of DVT without other diagnostic possibilities by the emergency physicians (2 points), bed rest or recent surgery (1 point), male sex (1 point), calf circumference difference greater than 3 cm (1 point), and erythema (1 point). A score of 3 or greater indicates a likely probability for DVT, and a score of 2 or less represents an unlikely probability for DVT. Of the 103 patients with an unlikely probability Hamilton score and a negative D-dimer assay, only one patient had isolated calf DVT. A combined diagnostic strategy of unlikely-probability Hamilton score and a negative D-dimer would have a negative predictive value of 99% (95% confidence interval, 94.7-100%). CONCLUSION: An unlikely-probability Hamilton score and a negative Simplify D-dimer assay effectively exclude lower limb DVT, and a sonographic examination is unnecessary in this group of ambulatory emergency department patients.

Adolescent↗

[The probability of finding HLA identical or partially matched unrelated donors in the population of Vojvodina].

INTRODUCTION: Allogeneic bone marrow transplantation and hematopoietic stem cell transplantation from unrelated donors are treatments of choice for patients lacking HLA identical siblings or family matched donors. MATERIAL AND METHODS: Class I HLA typing was performed by using a standard microlymphocytotoxicity test in 434 unrelated persons from Vojvodina, while, class II HLA typing was performed using a modified immunofluorescent technique. The estimated gene frequencies for the populations of Crete, Korea, China, Scotland, Romania, and North America, were used to calculate phenotype frequencies, the probability of finding HLA identical or partially (in 5/6 HLA antigens) matched unrelated donors, the number of donors necessary for research, as well as genetic distances between populations. RESULTS: The probability of finding HLA identical or partially matched unrelated donors for patients from Vojvodina is higher in closely related populations with low genetic distances, such as populations of Crete, Romania and Scotland. DISCUSSION: The probability of finding HLA identical or partially matched unrelated donors is in inverse proportion with the number of unrelated donors necessary for research with aim of finding at least one HLA compatible donor. CONCLUSION: The probability of finding compatible unrelated donors depends on the degree of HLA matching between the donor and recipient, HLA phenotype frequencies and the donor pool size. These methodology may have a wider usage, because it can be applied in calculating the probability of finding suitable genotypically matched donors, by using HLA allele frequencies defined by molecular techniques.

Bone Marrow Transplantation↗

Genetic evaluation of the probability of pregnancy at 14 months for Nellore heifers.

To estimate the heritability for the probability that yearling heifers would become pregnant, we analyzed the records of 11,487 Nellore animals that participated in breeding seasons at three farms in the Brazilian states of São Paulo and Mato Grosso do Sul. All heifers were exposed to a bull at the age of about 14 mo. The probability of pregnancy was analyzed as a categorical trait, with a value of 1 (success) assigned to heifers that were diagnosed pregnant by rectal palpation about 60 d after the end of the breeding season of 90 d and a value of 0 (failure) assigned to those that were not pregnant at that time. The estimate of heritability, obtained by Method R, was 0.57 with standard error of 0.01. The EPD was predicted using a maximum a posteriori threshold method and was expressed as deviations from 50% probability. The range in EPD was -24.50 to 24.55%, with a mean of 0.78% and a SD of 7.46%. We conclude that EPD for probability of pregnancy can be used to select heifers with a higher probability of being fertile. However, it is mainly recommended for the selection of bulls for the production of precocious daughters because the accuracy of prediction is higher for bulls, depending on their number of daughters.

Age Factors↗

Probability and interstimulus interval effects on the N140 and the P300 components of somatosensory erps.

Event-related potentials (ERPs) evoked by somatosensory stimuli were studied in two experiments with manipulation of the interstimulus interval (ISI) in the range from 1 to 4 seconds and the stimulus probability from 10 to 50% in fine steps. All the stimuli were presented randomly on both index fingers as odd-ball paradigm, and the stimulus intensities on both sides were equally set at 2.5 times the subjective sensory threshold at which the stimuli could easily be ignored when delivered as nontarget stimuli. During the course of two experiments, the N140 was evoked by the target and nontarget stimuli, otherwise the P300 was evoked by the target stimuli alone. In the experiment on the effects of ISIs change, the N140 amplitude showed a tendency to increase with increasing ISI and the P300 amplitude increased with increasing ISI. In the other experiment on the effects of change in stimulus probability, the amplitudes of both the N140 and the P300 decreased with increasing stimulus probability. From the results across two experiments. it is argued that the effects of both probability and ISI changes on the amplitudes of both the N140 and the P300 do not directly reflect the recovery time of psychological functions but may also involve the complicated effects derived from the habituation of the individual generators and the difficulty for performing the task. Moreover, it is indicated that the stimulus intensity used is one of major factors to be considered for comparing results to discuss the effects of ISI and probability on the ERPs.

Adult↗

Estimation of extinction probabilities of five german cattle breeds by population viability analysis.

The estimation of the expected loss of genetic diversity and marginal diversities in a set of breeds within a defined future time horizon requires initial estimates of breed extinction probabilities. In this study, the extinction probabilities of 5 German dual-purpose cattle breeds were estimated by population viability analysis. Regression was used to estimate the infinitesimal mean and variance of the population growth and this was based on the diffusion approximation of the density independent population growth (also known as the Dennis regression model). The annual number of milk-recorded cows in each breed was used as census data. Based on the regression results, the extinction probabilities and their confidence intervals were estimated for a wide variety of future time horizons using Monte Carlo time series simulations. The estimates of extinction probabilities were sensible, but in 2 cases they depended heavily on the time horizon considered. Additionally, the confidence intervals became very wide with an increased time horizon. We recommend the estimation of extinction probabilities for a set of future time horizons rather than for a single future time and the selection of an upper bound for this set that is not too large to be meaningful. The validity of the use of the number of milk-recorded cows as census data and of the model assumptions is discussed in detail.

Animals↗

Why is p = .90 better than p = .70? Preference for definitive predictions by lay consumers of probability judgements.

What do people regard as an informative and valuable probability statement? This article reports four experiments that show participants to have a clear preference for more extreme and higher probabilities over less extreme and lower ones. This pattern emerged in Experiment 1, in which no context was provided, and was further explored in Experiment 2 within a positive and a negative context. The findings were further confirmed in Experiment 3, which employed a Bayesian framework with revisions of opinions. Finally, Experiment 4 showed how preference for high probabilities can lead people to prefer an overconfident to a more well-calibrated (accurate) forecaster. The results are interpreted as manifestations of a search for definitive predictions principle, which asserts that high probabilities are preferred to medium ones and often favored over the corresponding complementary low probabilities on the basis of their capacity to predict the occurrence of single outcomes.

Adult↗

[Effects of goals and perceived probabilities of goal attainment on self-assessment].

This study examined effects of explicitness of achievement goals and perceived probabilities of goal attainment on self-assessment. Subjects were 251 undergraduate students. They were first asked, as measure of explicitness of goals, if they hope to acquire good capability in scientific research, and second how they perceived their probabilities of goal attainment. Self-assessment behavior was measured by task choice and task preference for four tasks which differ in diagnosticity. The main results were as follows. (a) The most diagnostic task was chosen more often by the subjects who both had an explicit goal and perceived the probability of goal attainment high, and those who didn't have an explicit goal and perceived the probability low. (b) On task preference, the effects of goal explicitness and perceived probability were not found. These results suggest that self-assessment be done for future self-enhancement.

Achievement↗

[Explanation and estimation of subjective probability by generalized model of Support Theory].

The purpose of this paper is to develop a new model for describing the cognitive process of decision making. Being of a generalization of Tversky and Koehler's Support Theory, the proposed model firstly defines the choice probability among several alternatives in terms of degree of "support." Secondly the model defines the degree of support in terms of objective probability and representativeness. Thirdly, this model specifies the integration process by which one reaches the probability of an event utilizing the already assessed subevents. This model was applied to and tasted by, real experimental data. In the experiment, subjects were asked to evaluate the proportions (a kind of probability) and the degrees of representativeness of two objects. Compared to the estimates derived by a Bayesian approach, the subjective probabilities estimated by the proposed model were shown to be closer to those reported by the subjects.

Adult↗

Probabilities of transversions and transitions.

The values of the mean relative probabilities of transversions and transitions have been refined on the basis of the data collected by Jukes and found to be equal to 0.34 and 0.66, respectively. Evolutionary factors increase the probability of transversions to 0.44. The relative probabilities of individual substitutions have been determined, and a detailed classification of the nonsense mutations has been given. Such mutations are especially probable in the UGG (Trp) codon. The highest probability of AG, GA transitions correlates with the lowest mean change in the hydrophobic nature of the amino acids coded.

Amino Acids↗

[The usefulness of the association of clinical probability, rapid plasma measurement of D-dimer, compression echography of the lower limbs and echocardiography in the diagnosis of acute pulmonary embolism].

BACKGROUND: The aim of this study was to investigate the diagnostic utility of clinical probability, rapid plasma D-dimer assay, compression ultrasonography (CUS) and transthoracic echocardiography (TTE) in patients with suspected pulmonary embolism. METHODS: One hundred forty consecutive outpatients with suspected pulmonary embolism were enrolled in a prospective trial. We evaluated sensitivity, specificity, positive and negative predictive value of a combination of clinical probability, D-dimer, CUS and TTE using perfusion lung scan and pulmonary angiography as a combined gold standard for determining the presence or absence of pulmonary embolism. Clinical probability was assessed in accordance with the PIOPED criteria. The D-dimer (Nycocard) level was considered as abnormal > 0.3 mg/l, the CUS if incompressibility of the leg veins was showed, and the TTE if right ventricular dilation was present, in the absence of chronic pulmonary disease. The combination of these tests was considered consistent with the presence of pulmonary embolism if D-dimer plus CUS and/or TTE showed abnormal results. A pulmonary embolism was excluded if D-dimer and CUS showed normal findings or a low clinical probability was associated with normal findings of CUS and TTE. RESULTS: One hundred eleven patients were evaluated. Pulmonary embolism was present in 45/111 (40%) patients. The combination of tests showed positive findings in 39/39 patients with pulmonary embolism, negative findings in 47/50 without pulmonary embolism and non-diagnostic results in 22/111 (20%) patients (95% confidence interval--CI 12-28%). There were three false positive and no false negative results. Sensitivity and specificity were 100 and 94% respectively (95% CI 92-100% and 87-100%); positive and negative predictive values were 93 and 100% (95% CI 85-100% and 93-100%). None of these tests, separately, showed enough sensitivity and specificity. CONCLUSIONS: The combination of clinical probability, D-dimer, CUS and TTE was highly accurate to confirm or rule out pulmonary embolism.

Acute Disease↗