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PubMed1995

Posterior probability of linkage and maximal lod score.

To detect linkage between a trait and a marker, Morton (1955) proposed to calculate the lod score z(theta 1) at a given value theta 1 of the recombination fraction. If z(theta 1) reaches +3 then linkage is concluded. However, in practice, lod scores are calculated for different values of the recombination fraction between 0 and 0.5 and the test is based on the maximum value of the lod score Zmax. The impact of this deviation of the test on the probability that in fact linkage does not exist, when linkage was concluded, is documented here. This posterior probability of no linkage can be derived by using Bayes' theorem. It is less than 5% when the lod score at a predetermined theta 1 is used for the test. But, for a Zmax of +3, we showed that it can reach 16.4%. Thus, considering a composite alternative hypothesis instead of a single one decreases the reliability of the test. The reliability decreases rapidly when Zmax is less than +3. Given a Zmax of +2.5, there is a 33% chance that linkage does not exist. Moreover, the posterior probability depends not only on the value of Zmax but also jointly on the family structures and on the genetic model. For a given Zmax, the chance that linkage exists may then vary.

Genetic Markers↗

PubMed2006

Cost and probability of flowering at the shoot level in relation to variability in shoot size within the crown of Vaccinium hirtum (Ericaceae).

Size-related variation in the cost and probability of flowering among shoots within a crown of Vaccinium hirtum was investigated to clarify patterns and regulation of flowering at the shoot-module level, below the level of the individual. The apices of previous-year shoots differentiated into current-year shoots vegetatively (vegetative branches) or became reproductive by developing inflorescences (reproductive branches). Length growth and fate of current-year shoots were determined, and the future potential for reproduction was estimated using a matrix model of shoot dynamics. Reproductive branches had fewer current-year shoots and shorter total shoot lengths and thus had a reduced potential for reproduction compared with vegetative branches, indicating the cost of flowering at the shoot level. This cost of flowering was higher in longer shoots. The probability of the initiation of flowering in a shoot increased with increasing shoot length in shorter shoots, reached a maximum in medium-sized shoots, and decreased in longer shoots. The size-related changes in the probability of flowering at the shoot level can be largely explained by the size-dependent changes in shoot-level resource availability and cost of flowering.

Flowers↗

PubMed1987

Probability of neurodevelopmental disorders estimated from ultrasound appearance of brains of very preterm infants.

The neurodevelopmental status of 342 very preterm infants who had undergone prospective ultrasound brainscans was assessed at a median corrected age of 52 weeks. The probabilities for neurodevelopmental disorders were calculated according to the ultrasound findings. The results showed that the probability of a major or minor disorder was low for infants whose scans did not show periventricular haemorrhage or markedly increased parenchymal echodensities in the first week of life, and for those whose scans at discharge gave no evidence of ventricular dilatation, hydrocephalus or cerebral atrophy. By contrast, the probability of a disorder was very high for infants with markedly increased parenchymal echodensities in the first week, and for infants with evidence of cerebral atrophy at discharge. The majority of the infants could be assigned, on the basis of the ultrasound scan at discharge, either to a large group who were at low risk of neurodevelopmental disorders or to a small group who were at high risk; the remainder were at intermediate risk. These findings may be used as a guide to the prognosis for other infants whose ultrasound scans show similar appearances.

Atrophy↗

PubMed2006

Interference phenomena in temporal evolution of accident probability in workplaces.

The aim of this article is to investigate some implications of complexity in workplace risk assessment. Workplace is examined as a complex system, and some of its attributes and aspects of its behavior are investigated. Failure probability of various workplace elements is examined as a time variable and interference phenomena of these probabilities are presented. Potential inefficiencies of common perceptions in applying probabilistic risk assessment models are also discussed. This investigation is conducted through mathematical modeling and qualitative examples of workplace situations. A mathematical model for simulation of the evolution of workplace accident probability in time is developed. Its findings are then attempted to be translated in real-world terms and discussed through simple examples of workplace situations. The mathematical model indicates that workplace is more likely to exhibit an unpredictable behavior. Such a behavior raises issues about usual key assumptions for the workplace, such as aggregation. Chaotic phenomena (nonlinear feedback mechanisms) are also investigated for in simple workplace systems cases. The main conclusions are (1) that time is an important variable for risk assessment, since behavior patterns are complex and unpredictable in the long term and (2) that workplace risk identification should take place in a holistic view (not by work post).

Accidents↗

PubMed1985

The probability of overlooking prostatic cancer in transurethrally resected material when different embedding practices are followed.

When all transurethrally resected material of 53 subsequent patients was microscopically examined, primary adenocarcinoma of the prostate was found in 18 patients and benign disease in 35. Only 9 of the patients with histologically confirmed malignancy of the prostate were clinically diagnosed. The proportion of prostatic chips that contained malignant tissue ranged from 1-96%. A mathematical analysis evaluating the probability of including a carcinoma when different numbers of blocks were processes was performed. The analysis showed that when the patient has a clinically malignant diagnosis the probability of 100% is reached by the processing of one block. If the patient has a clinically benign diagnosis, however, the probability of 98% is first reached by the processing of 8 blocks, if such an amount of material is available.

Adenocarcinoma↗

PubMed2006

Comparison of dynamic treatment regimes via inverse probability weighting.

Appropriate analysis of observational data is our best chance to obtain answers to many questions that involve dynamic treatment regimes. This paper describes a simple method to compare dynamic treatment regimes by artificially censoring subjects and then using inverse probability weighting (IPW) to adjust for any selection bias introduced by the artificial censoring. The basic strategy can be summarized in four steps: 1) define two regimes of interest, 2) artificially censor individuals when they stop following one of the regimes of interest, 3) estimate inverse probability weights to adjust for the potential selection bias introduced by censoring in the previous step, 4) compare the survival of the uncensored individuals under each regime of interest by fitting an inverse probability weighted Cox proportional hazards model with the dichotomous regime indicator and the baseline confounders as covariates. In the absence of model misspecification, the method is valid provided data are available on all time-varying and baseline joint predictors of survival and regime discontinuation. We present an application of the method to compare the AIDS-free survival under two dynamic treatment regimes in a large prospective study of HIV-infected patients. The paper concludes by discussing the relative advantages and disadvantages of censoring/IPW versus g-estimation of nested structural models to compare dynamic regimes.

Acquired Immunodeficiency Syndrome↗

PubMed1985

Noise, biased probability and serial reaction.

Recent studies have shown that moderate intensity noise does influence performance although most studies showing effects of this level of noise have used verbal materials. An experiment showed that moderate intensity noise (85 dBC) also influences attentional selectivity in a serial reaction task which involved the processing of sensory information. Noise decreased response times to signals with high probabilities of occurrence but increased latencies for signals which occurred less frequently. Although attentional selectivity in noise depended on signal probability, it was not influenced by the spatial location of the signal. When a mode of responding is adopted in noise, subjects are often rather inflexible and continue to use this strategy even though it is inappropriate. This was demonstrated in the present study because the noise-induced bias continued even when the signal probabilities were returned to normal. Previous studies using higher noise intensities have shown that noise often increases the number of errors or gaps. The moderate intensity noise used in the present study did not have this effect.

Attention↗

PubMed2002

How informed is consent? Understanding of pictorial and verbal probability information by medical inpatients.

Understanding probability information about treatment risks and benefits is a vital component of patients' decision making capacity. This study demonstrates extensive misunderstanding of verbal descriptions of probability by medical inpatients of all ages, questioning the extent of their capacity for giving informed consent. Pictorial descriptions of probability were well understood, suggesting their adoption into clinical practice.

Aged↗

PubMed1997

Probability of detecting antibodies to bovine herpesvirus 1 in bulk milk after the introduction of a positive animal on to a negative farm.

The purpose of this study was to assess the probability that the introduction of one or more bovine herpesvirus 1 (BHV-1)-seropositive animals would result in the bulk milk of a clean herd becoming BHV-1-positive. Probability calculations (stochastic and deterministic) were based on the distribution of the log(titre) of 828 positive animals and the daily milk production of the herds and of the individual cows. They showed that the probability in average sized herds of 45 dairy cows is only between 10 and 25 per cent and that even in small herds of 25 cows the introduction of a positive animal would go undetected in the majority of cases. It is concluded that if the bulk milk has become BHV-1-positive it is most likely that the infection has spread.

Animals↗

PubMedDate not supplied

Review of criteria appropriate for a very low probability of pulmonary embolism on ventilation-perfusion lung scans: a position paper.

The "low-probability" interpretation of ventilation-perfusion lung scans has been characterized as misleading or even dangerous because of the high prevalence of pulmonary embolism associated with such an interpretation. Since the completion of the Prospective Investigation of Pulmonary Embolism Diagnosis (PIOPED) study, analyses of the PIOPED database have allowed identification of several abnormalities seen on ventilation-perfusion scans that have a positive predictive value (PPV) for pulmonary embolism of less than 10%. These include nonsegmental perfusion abnormalities (PPV = 8%), perfusion defects smaller than the corresponding areas of increased opacity at chest radiography (PPV = 8%), matched ventilation-perfusion abnormalities in two or three zones of a single lung (PPV = 3%), one to three small segmental perfusion defects (PPV = 1%), triple matched defects in the upper or middle lung zone (PPV = 4%), and the stripe sign (PPV = 7%). Use of these abnormalities as interpretative criteria constitutes "very low probability" interpretation and will reduce the number of low-probability interpretations of ventilation-perfusion lung scans, which may be considered nondiagnostic because of the unacceptably high rate of false-negative results. This will enhance the utility of the ventilation-perfusion lung scan for screening patients with suspected pulmonary embolism.

Angiography↗

PubMed2003

Probability in radiology.

In this article, a summary of the basic rules of probability using examples of their application in radiology is presented. Those rules describe how probabilities may be combined to obtain the chance of "success" with either of two diagnostic or therapeutic procedures or with both. They define independence and relate it to the conditional probability. They describe the relationship (Bayes rule) between sensitivity, specificity, and prevalence on the one hand and the positive and negative predictive values on the other. Finally, the two distributions most commonly encountered in statistical models of radiologic data are presented: the binomial and normal distributions.

Bayes Theorem↗

PubMed1985

"Low-probability" ventilation-perfusion scintigrams: clinical outcomes in 99 patients.

To evaluate the reliability of "low probability" ventilation-perfusion (V-P) scintigrams in excluding pulmonary embolism (PE), we reviewed the clinical records of 99 consecutive patients (74 in-patients and 25 outpatients) whose V-P studies had been interpreted as indicative of a low probability of PE. None of the 99 patients were referred for pulmonary angiography. Venography was performed in four patients and was positive in three. No patients were treated specifically for pulmonary embolism, but five received full treatment with anticoagulants for other reasons (three for venous thrombosis, one for a history of venous thrombosis, and one for a ventricular aneurysm). Seven of the hospitalized patients died during the index admission and seven additional hospitalized patients (including one treated with anticoagulants) died 1-5 months after discharge from the hospital. None were thought clinically to have died as a result of PE, and autopsy disclosed no PE in two. Follow-up information was obtained for 69 surviving patients (49 inpatients and 20 outpatients) not treated with anticoagulants. None of these patients were thought clinically to have had PE during follow-up of at least 2 weeks duration (greater than 2 months in 93% and greater than 6 months in 75%). Our results suggest that major short-term morbidity or death attributable to PE are quite infrequent in patients with low-probability V-P scintigrams.

Adult↗

PubMed1999

What clinicians can offer: assessing and communicating probabilities for individual patient decision making.

Accurate diagnostic and prognostic probabilities are important for physicians and their patients because of their impact on decisions. For individual patient decision making, physicians have to rely on their own judgement. Research has shown that physicians' probability assessments are often not of high quality and that a variety of factors have a detrimental influence on their judgements. Using a formula or a model may produce superior assessments. Most treatment decisions involve uncertainty and value conflict in the sense that there is a trade off between the possible harms of alternative treatments and their benefits. The communication of diagnostic and prognostic probabilities to patients occurs largely in verbal terms, which can lead to ambiguity in communication. The precise words and context chosen for communication are very important and can have a major effect on patients' decisions.

Communication↗

PubMed1994

Ovarian tumors: prediction of the probability of malignancy by using patient's age and tumor morphologic features with a logistic model.

An attempt was made to predict the probability of malignancy of a given ovarian tumor in a certain patient by using the age and simple morphologic features of the tumor. A cohort of 959 patients with ovarian tumors was analysed retrospectively according to the patient's age and tumor characteristics such as greatest diameter, consistency, bilaterality and diagnosis as malignant (271 patients) or benign (688 patients). All variables were entered unconditionally in a logistic regression. The presence of solid/multilocular elements has a 9.6-fold increased risk of malignancy, where a bilateral tumor has a 2.8-fold increase. Significant increase in risk of malignancy was observed in ages under 20 and over 40 years, as well as in tumors with a diameter larger than 9 cm. All variables were highly significant associated with the discrimination between benign and malignant. A formula including all variables has been developed so that the probability of malignancy can be estimated by a scientific calculator. In conclusion, simple, easily determined by ultrasound and reproducible criteria such as patient's age, tumor size, consistency and bilaterality were assembled in a logistic model in order to predict the probability of malignancy for a given ovarian tumor, in an individual patient.

Adult↗

PubMed1992

Sodium-lithium countertransport and probability of hypertension in Caucasians 47 to 89 years old.

The objectives of the present study were to determine whether sodium-lithium countertransport contributes to predicting the probability of having hypertension and to determine whether it does so after other predictor traits have been considered. We used logistic regression to model the relation between sodium-lithium countertransport and the probability of having hypertension, estimated by the prevalence of hypertension among 172 men and 252 women, aged 47-89 years, from the Caucasian population of Rochester, Minn. When sodium-lithium countertransport was the only predictor trait considered, it made a statistically significant contribution to prediction both in men (model chi(2)1df = 20.50, p < 0.001) and in women (model chi(2)1df = 16.69, p < 0.001). For each standard deviation increase in sodium-lithium counter-transport, the expected odds of having hypertension increased 2.25 times in men (95% confidence interval [CI], 1.44-3.51) and 1.77 times in women (95% CI, 1.32-2.37). When sodium-lithium countertransport was not considered, the other traits identified as predictors were age, body mass index, and plasma apolipoprotein CII and CII squared; plasma apolipoprotein AI was an additional predictor in women but not in men. When sodium-lithium countertransport was added to models that included the other predictors, it improved prediction both in men (increase in model chi(2)1df = 12.29, p < 0.001) and in women (increase in model chi(2)1df = 4.86, p < 0.027). Based on these complete models, when the other predictors remained at their mean values, each standard deviation increase in sodium-lithium countertransport increased the expected odds of having hypertension 2.06 times in men (95% CI, 1.31-3.22) and 1.48 times in women (95% CI, 1.04-2.21). These results establish that sodium-lithium countertransport provides information that is helpful in predicting the probability of having hypertension and is not reflected in other identified predictor traits.

Aged↗

PubMed2000

An accurate measure of the instantaneous discharge probability, with application to unitary joint-even analysis.

We present an estimate for the instantaneous discharge probability of a neurone, based on single-trial spike-train analysis. By detecting points where the neurone abruptly changes its firing rate and treating them specially, the method is able to achieve smooth estimates yet avoid the blurring of significant changes. This estimate of instantaneous discharge probability is then applied to the method of unitary event analysis. We show that the unitary event analysis as originally conceived is highly sensitive to firing-rate nonstationarities and covariations, but that it can be considerably improved if calculations of statistical significance use an instantaneous discharge probability instead of a firing-rate estimate based on averaging across multiple trials.

Action Potentials↗

PubMed2000

A general probability estimation approach for neural comp.

We describe an analytical framework for the adaptations of neural systems that adapt its internal structure on the basis of subjective probabilities constructed by computation of randomly received input signals. A principled approach is provided with the key property that it defines a probability density model that allows studying the convergence of the adaptation process. In particular, the derived algorithm can be applied for approximation problems such as the estimation of probability densities or the recognition of regression functions. These approximation algorithms can be easily extended to higher-dimensional cases. Certain neural network models can be derived from our approach (e.g., topological feature maps and associative networks).

Algorithms↗

PubMed2005

Estimating the posterior probabilities using the k-nearest neighbor rule.

In many pattern classification problems, an estimate of the posterior probabilities (rather than only a classification) is required. This is usually the case when some confidence measure in the classification is needed. In this article, we propose a new posterior probability estimator. The proposed estimator considers the K-nearest neighbors. It attaches a weight to each neighbor that contributes in an additive fashion to the posterior probability estimate. The weights corresponding to the K-nearest-neighbors (which add to 1) are estimated from the data using a maximum likelihood approach. Simulation studies confirm the effectiveness of the proposed estimator.

Biometry↗