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P300, probability, and interstimulus interval.

The relationship between target stimulus probability and interstimulus interval on the P300 (P3) component of the event-related potential was assessed in three experiments. In each study an auditory discrimination paradigm was employed wherein subjects indicated with a finger tap response the occurrence of a randomly presented 2000 Hz target tone embedded in a series of 1,000 Hz tones. Target stimuli were presented with a probability of either .20 or .80 in different conditions which were combined factorially with different interstimulus intervals. Experiment 1 presented stimuli at 2.0, 2.5, or 3.0 second intervals; Experiment 2 presented stimuli at 2.0, 3.0, or 4.0 second intervals; Experiment 3 presented stimuli at 4.0, 6.0, or 10.0 second intervals. P3 amplitude was larger for the .20 relative to the .80 target probability conditions for the shorter interstimulus intervals but not for the longer intervals. P3 latency was consistently longer for the .20 relative to the .80 target probability conditions, with generally little effect observed for interstimulus interval changes. The results suggest that interstimulus interval affects component amplitude by determining the amount of processing resources available when the P3 is produced.

Adult↗

Measurement of expired carbon dioxide, oxygen and volume in conjunction with pretest probability estimation as a method to diagnose and exclude pulmonary venous thromboembolism.

BACKGROUND: The classical alveolar pCO(2)-pO(2) relationship predicts that pulmonary embolism (PE) causes a low ratio of pCO(2)/pO(2) at end expiration. Our purpose was to define a simple protocol to collect expired pCO(2)/pO(2) to diagnose PE. Emergency department patients with suspected PE were enrolled. Clinical pretest probabilities for PE were estimated prior to diagnostic testing using the Canadian score and clinicians' unstructured estimate. Patients provided three 30-s periods of tidal breathing, separated by three deep exhalations. Expired pCO(2), pO(2) and breath volume were measured. All patients underwent standardized objective testing for PE including 90-day follow-up. Diagnosis (PE+) required anticoagulation for image-proven PE within 90 days. RESULTS: Of 200 patients enrolled, 178 were included in final analysis (24 PE+). The mean coefficient of variability for the deep-exhaled and end-tidal pCO(2)/pO(2) ratios were 6.8 +/- 6.7 and 7.5 +/- 6.8%, respectively. Mean pCO(2)/pO(2) ratios were stable throughout the collection periods in both methods. When compared with the deep-exhaled ratio, the end-tidal mean ratio demonstrated slightly better diagnostic utility by the area under the receiver operating characteristic curve. The end-tidal ratios were divided into four interval likelihood ratios and coupled with pretest probability from the two methods to generate three sets of posttest probabilities. Receiver operating characteristic analysis demonstrated good overall diagnostic performance (areas under the curves >0.88) for both posttest probability sets. CONCLUSION: This preliminary work demonstrates that the end-tidal pCO(2)/pO(2) averaged from 30 s of breathing can produce clinically relevant likelihood ratios for the diagnosis and exclusion of PE.

Breath Tests↗

Perimetric probability maps to separate change caused by glaucoma from that caused by cataract.

We describe a new method for analysis of change in glaucomatous visual fields with the object to differentiate between changes caused by glaucoma from those caused by cataract. New pattern deviation change probability maps were developed from a prospectively collected glaucoma material and designed to be sensitive to changes in localized field loss, but to be unaffected by media-induced perimetric change. We compared the new change probability maps with the commercially available total deviation change probability maps in series of Humphrey perimetric tests in a glaucoma material of 43 eyes of 35 patients, who had undergone cataract surgery. When using the total deviation maps, considerable differences were seen between fields obtained before and after cataract surgery. Much smaller differences were seen when using the new change probability maps, that almost eliminated the common and disturbing effect of increasing cataract. This new tool could be of considerable help in differentiation between progressive glaucomatous visual field loss and deterioration caused by increasing media opacities.

Aged↗

The probability of having glaucoma at different IOP levels.

The probability of having glaucoma is indicated by the quotient (number of eyes with glaucoma)/(number of eyes in the total population). This quotient was calculated for each value of IOP. The number of eyes at each IOP value was taken from IOP frequency distribution curves for glaucomatous and normal eyes, calculated from values obtained by a population survey. By plotting the probability of having glaucoma vs IOP, a sigmoid curve was obtained. The curve indicates that while the glaucoma probability is near zero at IOP = 18 mmHg, it is 0.5 at 27-28 mmHg, and the probability approaches 1, i.e. certainty, at an IOP around 35 mmHg. The frequency distribution of the tolerance limit of IOP was calculated by derivation of this curve. The distribution of IOP tolerance limit was close to a normal distribution with average = 27.9 mmHg and standard deviation = 3.2 mmHg.

Aged↗

Discrete coding of reward probability and uncertainty by dopamine neurons.

Uncertainty is critical in the measure of information and in assessing the accuracy of predictions. It is determined by probability P, being maximal at P = 0.5 and decreasing at higher and lower probabilities. Using distinct stimuli to indicate the probability of reward, we found that the phasic activation of dopamine neurons varied monotonically across the full range of probabilities, supporting past claims that this response codes the discrepancy between predicted and actual reward. In contrast, a previously unobserved response covaried with uncertainty and consisted of a gradual increase in activity until the potential time of reward. The coding of uncertainty suggests a possible role for dopamine signals in attention-based learning and risk-taking behavior.

Animals↗

Predicting conditional probability distributions: a connectionist approach.

Most traditional prediction techniques deliver a single point, usually the mean of a probability distribution. For multimodal processes, instead of predicting the mean, it is important to predict the full distribution. This article presents a new connectionist method to predict the conditional probability distribution in response to an input. The main idea is to transform the problem from a regression problem to a classification problem. The conditional probability distribution network can perform both direct predictions and iterated predictions, the latter task being specific for time series problems. We compare this new method to fuzzy logic and discuss important differences, and also demonstrate the architecture on two time series. The first is the benchmark laser series used in the Santa Fe competition, a deterministic chaotic system. The second is a time series from a Markov process which exhibits structure on two time scales. The network produces multimodal predictions for this series. We compare the predictions of the network with a nearest-neighbor predictor and find that the conditional probability network is more than twice as likely a model.

Neural Networks, Computer↗

Probability density estimation for the interpretation of neural population codes.

1. Electrophysiological recording data from multiple cells in motor cortex and elsewhere often are interpreted using the population vector method pioneered by Georgopoulos and coworkers. This paper proposes an alternative method for interpreting coding across populations of cells that may succeed under circumstances in which the population vector fails. 2. Population codes are analyzed using probability theory to find the complete conditional probability density of a movement parameter given the firing pattern of a set of cells. 3. The conditional probability density when a single cell fires is proportional to the shape of the cell's tuning curve of firing rate in response to different movement parameters. 4. The conditional density when multiple cells fire is proportional to the product of their tuning curves. 5. Movement parameters can be estimated from the conditional density using statistical maximum likelihood or minimum mean-squared error methods. 6. Simulations show that density estimation correctly finds movement directions for nonuniform distributions of preferred directions and noncosine cell tuning curves, whereas the population vector method fails for these cases. 7. Probability methods thus provide a statistically based alternative to the population vector for interpreting electrophysiological recording data from multiple cells.

Cell Count↗

Effects of large excitatory and inhibitory inputs on motoneuron discharge rate and probability.

We elicited repetitive discharge in hypoglossal motoneurons recorded in slices of rat brain stem using a combination of a suprathreshold injected current step with superimposed noise to mimic the synaptic drive likely to occur during physiological activation. The effects of repetitive en mass stimulation of afferent nerves were simulated by the further addition of trains of injected current transients of varying shapes and sizes. The effects of a given current transient on motoneuron discharge timing and discharge rate were measured by calculating a peristimulus time histogram (PSTH) and a peristimulus frequencygram (PSF). The amplitude and time course of the simulated postsynaptic potentials (PSPs) produced by the current transients were calculated by convolving the current transient with an estimate of the passive impulse response of the motoneuron. We then compared the shape of the injected current transient and the simulated PSP to the profiles of the PSTH and the PSF records. The PSTHs produced by excitatory PSPs (EPSPs) were characterized by a large, short-latency increase in firing probability that lasted slightly longer than the rising phase of the EPSP, followed by a reduced discharge probability during the falling phase of the EPSP. In contrast, the PSF analysis revealed a proportionate increase in discharge rate over the entire profile of the EPSP, even though relatively few spikes occurred during the falling phase. The PSTHs associated with inhibitory PSPs (IPSPs) indicated a reduction in discharge probability during the initial, hyperpolarizing phase of the IPSP, followed by an increase in the discharge probability during its subsequent repolarizing phase. Using the PSF analysis, the initial phase of the IPSP appeared as a large hole in the record where a very small number or no discharges occurred. The subsequent phase of the IPSP was associated with frequency values that were lower than the background values. The primary features of both PSTHs and PSFs can be used to estimate the relative amplitudes of the underlying EPSPs and IPSPs. However, PSTHs contain secondary peaks and troughs that are not directly related to the underlying PSP but instead reflect the regular recurrence of spikes following those affected by the PSP. The PSF analysis is more useful for indicating the total duration and the profile of the underlying PSP. The shape of the underlying PSP can be obtained directly from the PSF records because the discharge frequency of the spikes follow the PSPs very closely, especially for EPSPs.

Animals↗

Effect of age on the performance of a diagnostic strategy based on clinical probability, spiral computed tomography and venous compression ultrasonography: the ESSEP study.

As the prevalence of PE increases with age, the effect of age on the diagnostic work-up in front of a clinical suspicion of PE deserves exploration. In this retrospective analysis, we used the data from 1041 consecutive suspected PE patients. The patients were divided into three groups according to tertiles of age: under 54 years, 54 to 73 years and above 73 years. The prevalence of PE in patients with respectively low, intermediate and high pretest clinical probability was expressed within each age group. We studied the effect of age on the results observed in three main groups of patients, after performing CT scan and ultrasonography (CUS): (1) patients with inconclusive results; (2) patients with negative findings on both exams and non high pretest clinical probability; (3) patients with positive findings.The prevalence of PE increased significantly with age, in overall, as well as in patients with low or intermediate pretest clinical probability. An analysis according to the three main diagnostic groups showed that: (1) the distribution of inconclusive spiral CT or CUS examinations was not different between age groups; (2) no thromboembolic event occurred in untreated patients with low or intermediate clinical probability aged under 54 years of age, whereas 7 events were diagnosed in patients aged over 73 years (p<0.001); (3) a higher proportion of older patients had a positive result at both spiral CT and CUS examinations. The percentage of positive CT scans in the case of negative or inconclusive CUS results was not different between age groups; conversely, in the case of a negative or inconclusive CT scan, the percentage of positive CUS was higher in older patients. In conclusion, management of elderly suspected PE patients appears to be different from both the work-up and the outcome perspectives.

Age Distribution↗

Influence of specific alternative diagnoses on the probability of pulmonary embolism.

The presence and likelihood of an alternative diagnosis to pulmonary embolism is an important variable of the Wells' prediction rule for establishing clinical probability. We assessed whether evoking specific alternative diagnoses would reduce the probability of pulmonary embolism enough to forego further testing. We retrospectively studied a cohort of 965 consecutive patients admitted for suspicion of pulmonary embolism at three medical centers in Europe in whom the presence of an alternative diagnosis at least as likely as pulmonary embolism was recorded before diagnostic testing. We divided the patients into 15 categories of alternative diagnoses evoked. We then assessed the prevalence of pulmonary embolism in each diagnostic category and compared it to the prevalence of pulmonary embolism in a reference group (patients with no alternative diagnosis or a diagnosis less likely than pulmonary embolism). The prevalence of pulmonary embolism in the reference group was 48%. The presence of an alternative diagnosis as or more likely strongly reduced the probability of pulmonary embolism (OR 0.15, 95% CI: 0.1-0.2, p < 0.01). In almost every diagnostic category, the prevalence of pulmonary embolism was much lower than in the reference group with an odds ratio below or near 0.2. Bronchopneumonia (OR 0.4, 95% CI 0.2 to 0.7) and cancer (OR 0.6, 95% CI 0.3 to 1.5) reduced the likelihood of pulmonary embolism to a lower extent. Evoking an alternative diagnosis at least as likely as pulmonary embolism reduces the probability of the disease, but this effect is never large enough to allow ruling it out without further testing, especially when bronchopneumonia or cancer are the alternative diagnoses considered.

Bronchopneumonia↗

A set probability technique for detecting relative time order across multiple neurons.

With the development of multielectrode recording techniques, it is possible to measure the cell firing patterns of multiple neurons simultaneously, generating a large quantity of data. Identification of the firing patterns within these large groups of cells is an important and a challenging problem in data analysis. Here, we consider the problem of measuring the significance of a repeat in the cell firing sequence across arbitrary numbers of cells. In particular, we consider the question, given a ranked order of cells numbered 1 to N, what is the probability that another sequence of length n contains j consecutive increasing elements? Assuming each element of the sequence is drawn with replacement from the numbers 1 through N, we derive a recursive formula for the probability of the sequence of length j or more. For n<2j, a closed-form solution is derived. For n>or=2j, we obtain upper and lower bounds for these probabilities for various combinations of parameter values. These can be computed very quickly. For a typical case with small N (<10) and large n (<3000), sequences of 7 and 8 are statistically very unlikely. A potential application of this technique is in the detection of repeats in hippocampal place cell order during sleep. Unlike most previous articles on increasing runs in random lists, we use a probability approach based on sets of overlapping sequences.

Action Potentials↗

Psychosis and physical aggression in probable Alzheimer's disease.

OBJECTIVE: The purpose of this study was to determine the frequency and type of psychotic symptoms in patients with probable Alzheimer's disease and to test whether there is a relationship between specific psychotic symptoms and episodes of physical aggression. METHOD: From 209 patients with possible or probable Alzheimer's disease who had been assessed in a research clinic every 6 months for up to 4.5 years, 181 subjects with probable Alzheimer's disease were selected for study. On the basis of the summary note for each visit in the patients' charts, the presence of delusions, hallucinations, misidentifications, and episodes of physical aggression was determined. Data regarding psychotic symptoms and aggression were available for 170 and 169 subjects, respectively. RESULTS: Delusions had been reported for 74 (43.5%) of the patients and were the most frequent psychotic symptom; persecutory delusions were the most common type. Physical aggression had been noted for 50 (29.6%) of the patients. Delusions and misidentifications frequently preceded and were significantly associated with episodes of physical aggression. The presence of delusions was a significant predictor of physical aggression but accounted for only 3.5% of the variance. CONCLUSIONS: This study suggests that delusions are a risk factor for physical aggression in patients with probable Alzheimer's disease who have moderate to severe cognitive impairment. As delusions accounted for only a small percentage of the variance, further research is needed to identify other variables that may be significant predictors of physical aggression in this population.

Aged↗

Conversion from mild cognitive impairment to probable Alzheimer's disease predicted by brain magnetic resonance spectroscopy.

OBJECTIVE: Mild cognitive impairment has been regarded as a pre-Alzheimer condition, but some patients do not develop dementia. Given the available therapies for Alzheimer's disease, early diagnosis is of paramount importance. The authors' objective was to determine whether findings from magnetic resonance spectroscopy (MRS) of the hippocampus and other cortical areas would predict conversion from amnestic mild cognitive impairment to probable Alzheimer's disease. METHOD: A longitudinal inception cohort of 53 consecutive and incident subjects fulfilling the criteria of amnestic mild cognitive impairment was followed for a mean period of 3 years. At baseline, a neuropsychological examination (Mini-Mental State Examination, Blessed Dementia Rating Scale, Clinical Dementia Rating, verbal fluency test, and memory tests) and standard blood tests were performed, and three cortical areas were examined by proton MRS: left hippocampus, right parietal cortex, and left occipital cortex. The patients were evaluated periodically to detect conversion to probable Alzheimer's disease. The statistical analysis of predictions was based on receiver operating characteristic curves. RESULTS: By the follow-up assessment that occurred on average after 3 years, 29 patients (55%) had developed probable Alzheimer's disease. An occipital cortex N-acetylaspartate/creatine ratio < or =1.61 predicted dementia at 100% sensitivity and 75% specificity (area under the curve=0.91, 95% CI=0.80-0.97). The positive predictive value was 83%, and the negative predictive value was 100%, with an overall cross-validated classification accuracy of 88.7%. None of the values in the hippocampus and parietal cortex had significant predictive value. CONCLUSIONS: MRS of the brain performed on patients with mild cognitive impairment is a valuable tool in predicting conversion to probable Alzheimer's disease. Occipital values were more reliable than hippocampal values in this prediction.

Aged↗

Intervals for posttest probabilities: a comparison of 5 methods.

BACKGROUND: Several medical articles discuss methods of constructing confidence intervals for single proportions and the likelihood ratio, but scant attention has been given to the systematic study of intervals for the posterior odds, or the positive predictive value, of a test. METHODS: The authors describe 5 methods of constructing confidence intervals for posttest probabilities when estimates of sensitivity, specificity, and the pretest probability of a disorder are derived from empirical data. They then evaluate each method to determine how well the intervals' coverage properties correspond to their nominal value. RESULTS: When the estimates of pretest probabilities, sensitivity, and specificity are derived from more than 80 subjects and are not close to 0 or 1, all methods generate intervals with appropriate coverage properties. When these conditions are not met, however, the best-performing method is an objective Bayesian approach implemented by a simple simulation using a spreadsheet. CONCLUSION: Physicians and investigators can generate accurate confidence intervals for posttest probabilities in small-sample situations using the objective Bayesian approach.

Bayes Theorem↗

Derived thresholds. Determining the diagnostic probabilities at which clinicians initiate testing and treatment.

The medical decision making literature has previously considered the test and test-treatment thresholds in a normative fashion. In the normative approach, the analyst calculates the optimal threshold--the likelihood of disease at which testing or treatment should be undertaken. In contrast, we describe a method of deriving the threshold in a descriptive fashion, by determining the probabilities of disease at which clinicians actually make the decision to test or to initiate specific treatment without further testing. In applying this method, the analyst first asks clinicians to provide an estimate of the prior probability of disease, and to select one of three options: test, treat, or do neither. After receiving new information about the patient, the clinicians are asked to revise the probability estimate and to select a new option. Correlation of changes in the probability of a disease with changes in the clinicians' selections of options to test or treat enables the analyst to estimate the test and test-treatment thresholds used by the clinicians in medical decision making. Knowledge of these thresholds also enables the analyst to calculate the clinicians' ratio of the benefits to the costs of the therapy being considered, considering the risks of the test itself.

Cost-Benefit Analysis↗

Probability judgement in medicine: discounting unspecified possibilities.

Research in cognitive psychology has indicated that alternative descriptions of the same event can give rise to different probability judgments. This observation has led to the development of a descriptive account, called support theory, which assumes that the judged probability of an explicit description of an event (that lists specific possibilities) generally exceeds the judged probability of an implicit description of the same event (that does not mention specific possibilities). To investigate this assumption in medical judgment, the authors presented physicians with brief clinical scenarios describing individual patients and elicited diagnostic and prognostic probability judgments. The results showed that the physicians tended to discount unspecified possibilities, as predicted by support theory. The authors suggest that an awareness of the discrepancy between intuitive judgments and the laws of chance may provide opportunities for improving medical decision making.

Bias↗

On the probability of cost-effectiveness using data from randomized clinical trials.

BACKGROUND: Acceptability curves have been proposed for quantifying the probability that a treatment under investigation in a clinical trial is cost-effective. Various definitions and estimation methods have been proposed. Loosely speaking, all the definitions, Bayesian or otherwise, relate to the probability that the treatment under consideration is cost-effective as a function of the value placed on a unit of effectiveness. These definitions are, in fact, expressions of the certainty with which the current evidence would lead us to believe that the treatment under consideration is cost-effective, and are dependent on the amount of evidence (i.e. sample size). METHODS: An alternative for quantifying the probability that the treatment under consideration is cost-effective, which is independent of sample size, is proposed. RESULTS: Non-parametric methods are given for point and interval estimation. In addition, these methods provide a non-parametric estimator and confidence interval for the incremental cost-effectiveness ratio. An example is provided. CONCLUSIONS: The proposed parameter for quantifying the probability that a new therapy is cost-effective is superior to the acceptability curve because it is not sample size dependent and because it can be interpreted as the proportion of patients who would benefit if given the new therapy. Non-parametric methods are used to estimate the parameter and its variance, providing the appropriate confidence intervals and test of hypothesis.

Cost-Benefit Analysis↗

Post-test probability of asthma following methacholine challenge.

Using recently published data, a nomogram was constructed to estimate the likelihood of asthma following methacholine challenge. Based on Bayes' theorem, the nomogram makes use of the sensitivity and specificity of methacholine challenge to calculate the post-test probability of asthma once the physician makes a determination of the pretest probability, that is, the likelihood of asthma before the test results are considered. A family of curves is presented to cover several levels of cumulative breath units at which the test could become positive, and a single curve is presented for a negative test after 224 cumulative breath units. Separate curves are presented for smokers and nonsmokers. The estimate of pretest probability is most crucial in negative tests where likelihood of asthma is considered high, and in positive tests in patients in whom asthma is considered unlikely. Although these curves will not apply precisely to a different data base, the concept of the relationship between pretest and post-test probability helps in the interpretation of the test results and stresses the importance of using all available information in making a diagnosis.

Asthma↗