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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

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

Orthodontic probability tables for black patients of African descent: mixed dentition analysis.

Mixed dentition space analyses form an essential part of orthodontic diagnostic procedures to determine the amount of space available for the accommodation of permanent teeth. The Moyers' probability tables for computing the sizes of unerupted canines and premolars were formulated at the University of Michigan from a sample consisting of northern European white subjects and are currently used worldwide. Because tooth sizes vary significantly between different population groups, it was the purpose of this study to construct relevant probability tables that would be more applicable to black subjects. Data were collected from a series of 100 randomly selected study models of black patients. The sample was equally subdivided by gender and all subjects had Angle Class I molar relationships with only minor malocclusions such as minor crowding, rotations, or diastemas. Two investigators independently measured the teeth on the study casts with a Vernier gauge that had sharpened calliper tips. Intraexaminer and interexaminer reliability was determined at 0.2 mm. All teeth to and including the first molars were measured. These data were then utilized in regression equations for both maxillary and mandibular arches, to enable the prediction of the mesiodistal widths of the canines and two premolars. The equations and predicted values were compared with those of the Moyers' probability tables, and significant differences (p <0.05) were found (except for the prediction of maxillary canines and premolars in females at the 85 and 95 percentile probability level). New probability tables for black subjects were formulated. It is envisaged that the proposed probability tables would be more accurate for black patients of African ancestry.

Adolescent

Fixation probability in spatially changing environments.

The fixation probability of a mutant in a subdivided population with spatially varying environments is investigated using a finite island model. This probability is different from that in a panmictic population if selection is intermediate to strong and migration is weak. An approximation is used to compute the fixation probability when migration among subpopulations is very weak. By numerically solving the two-dimensional partial differential equation for the fixation probability in the two subpopulation case, the approximation was shown to give fairly accurate values. With this approximation, we show in the case of two subpopulations that the fixation probability in subdivided populations is greater than that in panmictic populations mostly. The increase is most pronounced when the mutant is selected for in one subpopulation and is selected against in the other subpopulation. Also it is shown that when there are two types of environments, further subdivision of subpopulations does not cause much change of the fixation probability in the no dominance case unless the product of the selection coefficient and the local population size is less than one. With dominance, the effect of subdivision becomes more complex.

Biological Evolution

Delineation of coding areas in DNA sequences through assignment of codon probabilities.

Codon usage tables have been produced for E. coli, yeast, human, and mouse. The nonrandom employment of codons allows assignment of probability values to trinucleotides in any DNA sequence. These values represent the probability that a given trinucleotide is used as a codon in the organism from which the table is derived. For the graphical delineation of coding areas in DNA sequences, a probability is assigned to each trinucleotide equal to its frequency in the codon table. Averaging and smoothing procedures then greatly enhance the detectability of areas of high average codon probability and better represent the mean codon probability. These manipulations increase graphical clarity without altering the overall magnitude of probabilities. Averaging introduces an error of less than 0.5% between "raw" and smoothed data. This graphical delineation of coding sequences does not depend on the presence of punctuation, ribosomal binding sites, etc: moreover the delineation of introns and exons is also possible.

Base Sequence

Mortality probability models for patients in the intensive care unit for 48 or 72 hours: a prospective, multicenter study.

OBJECTIVE: To develop models in the Mortality Probability Model (MPM II) system to estimate the probability of hospital mortality at 48 and 72 hrs in the intensive care unit (ICU), and to test whether the 24-hr Mortality Probability Model (MPM24), developed for use at 24 hrs in the ICU, can be used on a daily basis beyond 24 hrs. DESIGN: A prospective, multicenter study to develop and validate models, using a cohort of consecutive admissions. SETTING: Six adult medical and surgical ICUs in Massachusetts and New York adjusted to reflect 137 ICUs in 12 countries. PATIENTS: Consecutive admissions (n = 6,290) to the Massachusetts/New York ICUs were studied. Of these patients, 3,023 and 2,233 patients remained in the ICU and had complete data at 48 and 72 hrs, respectively. Patients < 18 yrs of age, burn patients, coronary care patients, and cardiac surgical patients were excluded. OUTCOME MEASURE: Vital status at the time of hospital discharge. RESULTS: The models consist of five variables measured at the time of ICU admission and eight variables ascertained at 24-hr intervals. The 24-hr model demonstrated poor calibration and discrimination at 48 and 72 hrs. The newly developed 48- and 72-hr models--MPM48 and MPM72--contain the same 13 variables and coefficients as the MPM24. The models differ only in their constant terms, which increase in a manner that reflects the increasing probability of mortality with increasing length of stay in the ICU. These constant terms were adjusted by a factor determined from the relationship between the data from the six Massachusetts and New York ICUs and a more extensive data set, from which the ICU admission Mortality Probability Model (MPM0) and MPM24 were developed. This latter data set was assembled from ICUs in 12 countries. The MPM48 and MPM72 calibrated and discriminated well, based on goodness-of-fit tests and area under the receiver operating characteristic curve. CONCLUSIONS: Models developed for use among ICU patients at one time period are not transferable without modification to other time periods. The MPM48 and MPM72 calibrated well to their respective time periods, and they are intended for use at specific points in time. The increasing constant terms and associated increase in the probability of hospital mortality exemplify a common clinical adage that if a patient's clinical profile stays the same, he or she is actually getting worse.

Adult

Erythrocyte sodium transport and the probability of having hypertension.

BACKGROUND: A number of alterations of ion transport and concentrations have been reported in erythrocytes from patients with hypertension and their young normotensive offspring. Of these, only sodium-lithium countertransport appears to be capable of predicting the effects of genetic variation on interindividual differences in blood pressure. OBJECTIVE: As a first step toward identifying other erythrocyte traits capable of predicting the effects of genetic variation on interindividual differences in blood pressure, we evaluated whether furosemide-sensitive sodium or potassium cotransport, ouabain-sensitive sodium pump, passive permeability to sodium or potassium, or intracellular concentrations of sodium or potassium are predictors of the probability of having hypertension in a general Caucasian population; we also attempted to confirm our previous inference that sodium-lithium countertransport is a predictor of the probability of having hypertension in this population. METHODS: The sample for analyses consisted of 199 unrelated men, aged 56-91 years, and 216 unrelated, nonpregnant women, aged 53-87 years, from the population of Rochester, Minnesota. Logistic regression was used to assess the relationship between predictor traits and blood pressure diagnostic status (normotension or hypertension). We assessed whether each erythrocyte trait was a predictor of the probability of having hypertension when the trait was considered by itself and when it was considered after the effects of other identified predictors of the probability of hypertension were included in the logistic regression models. RESULTS: When each erythrocyte trait was considered by itself, the predictors of the probability of having hypertension were sodium-lithium countertransport in men and sodium-lithium countertransport, sodium and potassium cotransport, and intracellular sodium concentration in women. When each erythrocyte trait was considered after other predictors had been included in the logistic regression models, none of the erythrocyte traits made an additional contribution to prediction of the probability of having hypertension unless its interactions with other predictors were also included in the models. CONCLUSIONS: Multiple measures of erythrocyte ion transport are associated with hypertension in the general Caucasian population; however, most of these associations are context-dependent inasmuch as they are gender-specific and dependent on levels of other predictor traits.

Aged

The 1-month outcome of patients with a low probability Technegas ventilation/perfusion lung scan.

The objective was to study the 1-month outcome of patients who had a low probability ventilation/perfusion lung scan using Technegas radioaerosol as the inhalational agent and who did not receive anticoagulation. One hundred consecutive patients with suspected pulmonary embolism were studied retrospectively. Their Technegas lung scans were classified by two blinded and independent nuclear medicine physicians and the medical records of all patients with a low probability scan were reviewed. One hundred inpatients (42 males and 58 females) with a mean age of 63 years were studied. The three most common clinical presentations leading to lung scintigraphy were unexplained dyspnoea (30 cases), unexplained dyspnoea with pleuritic chest pain (26 cases) and pleuritic chest pain only (15 cases). Nine patients had been judged by their managing medical team to have a high clinical probability of true pulmonary embolism, 32 had an intermediate probability clinical presentation and 59 a low clinical probability of pulmonary embolism. None of the 100 patients experienced further episodes of suspected or proven pulmonary embolism during the follow-up period. Six patients died. In none of them was pulmonary embolism either the cause of or a major contributing factor to death. The finding of a low probability scan using Technegas as the ventilation scintigram agent of choice describes a group of patients who, even in the absence of therapeutic anticoagulation, have a favourable 1-month outcome free of either true or suspected clinical pulmonary embolism. Invasive, pulmonary angiography-based diagnostic strategies may not be needed in this group of patients.

Female

The prior probability of autosomal linkage.

An expression is derived for the prior probability of linkage between a random trait locus and any one of m random marker loci, and this probability is computed form=1, 10, 20, 30, 50 and 100. A similar expression is derived for two trait loci, and computed for m=1, 10, 20 and 30. When one trait locus and 30 marker loci are being studied, a priori there is over a three-quarter probability that the trait locus should be syntenic with at least one of the markers, and about a one-half probability that there should be a linkage mappable from recombination frequencies. If two traits are studied, then the prior probability that at least one should be syntenic with one of the 30 markers is 0-94, and there is a three-quarter probability that such a linkage should be mappable.

Chromosome Mapping

On the effect of probability distributions of input variables in public health risk assessment.

A central part of probabilistic public health risk assessment is the selection of probability distributions for the uncertain input variables. In this paper, we apply the first-order reliability method (FORM) as a probabilistic tool to assess the effect of probability distributions of the input random variables on the probability that risk exceeds a threshold level (termed the probability of failure) and on the relevant probabilistic sensitivities. The analysis was applied to a case study given by Thompson et al. on cancer risk caused by the ingestion of benzene contaminated soil. Normal, lognormal, and uniform distributions were used in the analysis. The results show that the selection of a probability distribution function for the uncertain variables in this case study had a moderate impact on the probability that values would fall above a given threshold risk when the threshold risk is at the 50th percentile of the original distribution given by Thompson et al. The impact was much greater when the threshold risk level was at the 95th percentile. The impact on uncertainty sensitivity, however, showed a reversed trend, where the impact was more appreciable for the 50th percentile of the original distribution of risk given by Thompson et al. than for the 95th percentile. Nevertheless, the choice of distribution shape did not alter the order of probabilistic sensitivity of the basic uncertain variables.

Benzene

The probability of defibrillation success and the incidence of postshock arrhythmia as a function of shock strength.

The effects of high voltage defibrillation shocks given to six swine were studied to determine if there is a limit to the advantage gained from increasing the shock strength. An endocardial electrode was placed in the right ventricle, and a 114-cm2 cutaneous patch was placed on the left lateral thorax. Monophasic (10 msec) and single capacitor biphasic (5/5 msec) shocks with leading edge voltages of 200, 400, 600, 800, and 990 volts (approximately 2.3-59 J) were tested. For monophasic shocks, the probability of successful defibrillation ranged from 0% at 200 V to 90% at 990 V. The incidence of postshock arrhythmia increased from 0% for successful shocks at 600 V to 67% for successful shocks at 990 V. For biphasic shocks, the probability of success peaked at 97% for the 600-, 800-, and 990-V shocks. The incidence of postshock arrhythmia increased from 8% at 400 V to 55% at 990 V. Although more postshock arrhythmias occurred at lower strengths for biphasic than for monophasic shocks, an efficacy criterion, quantifying the probability of defibrillation success and the probability that a postshock arrhythmia will not occur, was always higher for biphasic shocks. The probability of success never reached 100% for either waveform while the incidence of postshock arrhythmia increased as the shock strength increased. In conclusion, for the catheter-patch electrode configuration, increasing the shock strength does not always improve the probability of success and may increase the incidence of postshock arrhythmia.

Animals

Application of conditional probability analysis to the clinical diagnosis of coronary artery disease.

Analysis of multiple noninvasive tests offers the promise of more accurate diagnosis of coronary artery disease, but discordant test responses can occur frequently and, when observed, result in diagnostic uncertainty. Accordingly, 43 patients undergoing diagnostic coronary angiography were evaluated by noninvasive testing and the results subjected to analysis using Bayes' theorem of conditional probability. The procedures used included electrocardiographic stress testing for detection of exercise-induced ST segment depression, cardiokymographic stress testing for detection of exercise-induced precordial dyskinesis, myocardial perfusion scintigraphy for detection of exercise-induced relative regional hypoperfusion, and cardiac fluoroscopy for detection of coronary artery calcification. The probability for coronary artery disease was estimated by Bayes' theorem from each patient's age, sex, and symptom classification, and from the observed test responses. This analysis revealed a significant linear correlation between the predicted probability for coronary artery disease and the observed prevalence of angiographic disease over the entire range of probability from 0 to 100% (P less than 0.001 by linear regression). The 12 patients without angiographic disease had a mean posttest likelihood of only 7.0 +/- 2.6% despite the fact that 13 of the 60 historical and test responses were falsely "positive." In contrast, the mean posttest likelihood was 94.1 +/- 2.8% in the 31 patients with angiographic coronary artery disease, although 45 of the 155 historical and test responses were falsely "negative." In 8 of the 12 normal patients, the final posttest likelihood was under 10% and in 26 of the 31 coronary artery disease patients, it was over 90%. These estimates also correlated well with the pooled clinical judgment of five experienced cardiologists (P less than 0.001 by linear regression). The observed change in probability for disease for each of the 15 different test combinations correlated with their information content predicted according to Shannon's theorem (P less than 0.001 by linear regression). These results support the use of probability analysis in the clinical diagnosis of coronary artery disease and provide a formal basis for comparing the relative diagnostic effectiveness and cost-effectiveness of different test combinations.

Adult

The reliability of probability analysis in the prediction of coronary artery disease in two hospitals.

To assess the accuracy of the Bayesian computer program CADENZA for the prediction of coronary artery disease, the authors examined the probabilities generated by the application of this program to the clinical and noninvasive test results of 303 patients in a private referral center and 199 patients in a veterans' hospital. These probabilities were compared with those produced by applying a six-variable discriminant function derived by logistic regression at the private referral center. Two statistical approaches were employed in evaluating the relative performances of the Bayesian program and the discriminant function. The first of these involved the sorting of patients in both test groups into ascending deciles of probability and comparing expected probability with observed angiographic disease prevalence in each decile. The second involved the calculation and comparison of a standardized reliability measure. The latter was significantly lower for the discriminant function both at the private hospital (0.200 for the discriminant function versus -17.5 +/- 1.96 for the Bayesian program) and at the veterans' hospital (-0.8 +/- 1.96 for the discriminant function versus -11.3 for Bayesian program). This suggests that the discriminant function is significantly superior to the Bayesian algorithm CADENZA for predicting coronary artery disease probabilities in subjects who have relatively high pretest disease probabilities.

Bayes Theorem

Clinical assessment of the probability of coronary artery disease: judgmental bias from personal knowledge.

Probability estimates of angiographic coronary artery disease made by experienced, board-certified staff cardiologists were compared with those of cardiologists in training (fellows). In addition, estimates made before coronary angiography were compared with those made several months later based on written clinical summaries of 15 items of objective clinical and test data. Cardiologists were asked to estimate the probabilities of coronary artery disease, multivessel disease, and triple-vessel or left main disease. The study population consisted of 510 consecutive patients without valvular disease referred for the first time for coronary angiography to three hospitals. Both staff and fellows consistently overestimated the pre-angiographic probability of coronary artery disease. The probabilities estimated from patient summaries were always significantly lower than the pre-angiographic assessments. Only staff cardiologists reliably assessed the probabilities of coronary artery disease during the second assessment (p less than 0.05). Thus, estimates of disease probability based on clinical judgment vary according to the source of information, and these estimates are more accurate when physicians have objective data on hand and do not know the identities of the patients.

Coronary Angiography

Developmental change in subjective probability during adolescence.

The developmental change in subjective probability during adolescence, an important period for establishing the probability concept, was investigated. 75 Japanese adolescents, from 12 to 23 yr. of age, were asked to make probability judgments for a lottery under 15 conditions. Analysis showed that with increase in age their subjective probability came closer to the objective probability. Discussion of these results took into consideration recent studies on the development of the concept of probability.

Adolescent

[The initial clinical probability in the diagnosis of the hospitalized pediatric patient].

OBJECTIVES: 1. To determine the degree of correlation among different physicians concerning their initial diagnosis and 2. identify the degree of correlation between the probability that physicians assing an initial diagnosis and the number of days the patient is hospitalized, laboratory test and X-rays taken of the patient. DESIGN: A comparative questionnaire. STUDY SITE: Pediatric hospitalization Unit of a third level medical care ward of the Mexican Social Security Institute. STUDY UNITS: All new admissions or non-programmed readmitted patients to the hospital during the months of November and December 1990. MAIN MEASUREMENTS: The treating physicians (Staff pediatricians (MB) and third (R3) and second (R2) year residents) were each asked to independently assign a probability (0 to 100) to each of the diagnosis emitted on the day the patient was admitted. When the patient was discharged, the number of days hospitalized as well as the number of laboratory tests and X-rays taken of the patient were added. RESULTS: 106 patients were evaluated, a correlation was gathered between MBs and R3s of 0.79 (P less than 0.001) and among MBs and R2s of 0.83 (P less than 0.001). The correlation between resident physicians was discretely less 0.60 (P less than 0.01). When relating the probability assigned by the physicians and the number of days the patients were hospitalized, associations were observed of 0.31 (P less than 0.05), 0.15 (P less than 0.05) and 0.19 (P = 0.04) for the MB, R3 and R2s respectively. In the case of laboratory test a correlation of 0.38, 0.06 and 0.04 (MB, R3, R2 respectively) was found. None of these correlations were statistically significant. The X-rays showed a significant correlation in cases of the MBs (0.50, P less than 0.05). CONCLUSIONS: The probabilities assigned by the staff physician as well as the resident doctors are closely related and a lesser grade of association is seen when comparing the residents among each other. No tendencies were identified in the correlation of the probability assigned by the residents and the variables analyzed. A consistent relation was seen between the staff physician and high probabilities, longer stays, and greater number of laboratory tests and X-rays.

Adult

An application of probability theory to a group of breath-alcohol and blood-alcohol data.

Many jurisdictions have "per se" driving-while-intoxicated (DWI) status expressed in terms of a blood-alcohol concentration (BAC) standard (in grams per 100 mL or the equivalent). Since breath-alcohol (BrAC) analysis is typically employed to determine BAC, there is often challenge to the use of an assumed 2100:1 conversion ratio. This concern may be relevant in light of considerable data that show a low percentage of cases in which BrAC greater than BAC, and this concern increases when the BrAC is used to predict BAC in the context of "per se" legislation. Probability theory provides a basis for estimating the likelihood of an individual having a BrAC greater than or equal to g/210 L with a corresponding BAC less than 0.10 g/100 mL. Actual field data from the state of Wisconsin (n = 404) were evaluated to determine the probability of this occurrence. The probability for this occurrence involves the multiplication law for independent events. The computed probability from the data was 0.018. The actual number of occurrences where BrAC greater than or equal to 0.10 g/210 L and BAC less than 0.10 g/100 mL was 5, resulting in a probability of 0.012. The concern of having BrAC greater than BAC at the critical "per se" level has a very low probability of occurrence, which thus supports the reasonableness of "per se" DWI legislation based upon a blood-alcohol standard determined by breath-alcohol analysis.

Alcoholic Intoxication

[Variable cycle avoidance program: systematic variation of the probability of a programmed noxious stimulus].

Six albino rats were exposed in three groups to different values of T (a repetitive time cycle at the end of which an electric shock occurs with a specified probability in absence of a first response), (V.g.: P(E-/R) = .75 and .10) on different weeks. When occurs at least one response on each T cycle it has a probability to delete the shock equal to P(E-/R) that changed on different weeks from .50 to .10. In this way, as the Bayesian probability system indicate for exclusive events, Pk = P(E-/R) - [P(E-/R) x P(E-/R)] was the effective probability of shocks when at least one response occur on each T cycle and Pm = P(E-/R) - [P(E-/R) x P(E-/R) x P(1rst Response)] is the modulated probability of shocks when a first response occur on some T cycles. The results indicated that T/Pk (the mean interval between shocks before the experimental session) nor T/Pm (The mean interval between shocks after the experimental session when the subject responds), or its inverse, are reductional continua that explains monotonically ordered changes of the response rate or the mean total number of responses. As a consequence T and P must be dissociated. On the other hand, corrected response rate (Total responses minus Total first responses/minute) is a direct and monotonically increased function of Pk and of 1/T. In this sense is the increased probability with which noxious stimuli impinge on the behavior stream and the time reduction between stimuli, that separated, sustain responding.

Animals