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PubMed1992

Comparison of logistic regression and Bayesian-based algorithms to estimate posttest probability in patients with suspected coronary artery disease undergoing exercise ECG.

Two multivariate methods, a logistic regression-derived algorithm and a Bayesian independence-assuming method (CADENZA), were compared concerning their abilities to estimate posttest probability of coronary disease in patients with suspected coronary disease. All patients underwent exercise testing within 3 months prior to coronary angiography. Coronary disease was defined as the presence of one or more vessels with greater than or equal to 50% luminal diameter narrowing. A group of 300 patients (disease prevalence = 37%) was used to derive the algorithm. Another group of 950 patients was used to validate the algorithm and compare it to CADENZA. Seven variables (age, sex, symptoms, diabetes, mm ST depression, ST slope, and peak heart rate) were used to generate posttest probabilities for each method. The receiver operating characteristic curve area for the logistic regression method (0.81 +/- 0.01) was significantly higher than CADENZA (0.75 +/- 0.01; p less than 0.05). There was, however, no difference in the calibration of the two methods. When given equivalent variable information, the logistic regression algorithm had better discrimination than CADENZA for estimating the probability of coronary disease following exercise electrocardiography.

Algorithms↗

PubMed1983

Membrane fluidity and the probability of complement fixation.

We develop a mathematical theory of the role of membrane fluidity in the initiation of the IgG mediated complement cascade. The basic assumption is that C1q must be at least doubly bound to activate C1r, but that once C1q is doubly bound, C1r still requires some mean finite time tau to become enzymatically active. If C1q dissociates during this time interval, C1r cannot be activated. We consider the consequences of the simplest model of fluidity--one in which the difference between "fluid phase" lipids and "non-fluid phase" lipids is to allow protein mobility, but not a change in protein conformation. We show that under these conditions fluidity will effect C1r activation only if the rate of formation of multiply bound C1q is limited by diffusion in the membrane. If diffusion in the membrane is not rate-limiting, then, within the framework of this model, fluidity has no effect whatsoever on C1r activation. Thus, an experimental determination that C1q binding is not rate-limited by diffusion in the surface, but that fluidity does effect activation, would suggest a protein conformational change resulting perhaps from altered lipid composition. If diffusion in the surface does rate limit multiple C1q binding, we predict the possibility of an optimum diffusion coefficient for activation. For suitably chosen and reasonable parameter values this optimum will occur in the range (10(-11) less than or equal to D less than or equal to 10(-8) cm2/sec. We predict further, under these circumstances, a precipitous drop in the probability of activation above the optimum. The abrupt switch from a high probability of activation to essentially no probability of activation suggests the possibility of a very sensitive control mechanism exploitable by relatively small changes in membrane lipid composition.

Animals↗

PubMed1989

Fixation probabilities for advantageous mutants: a note on multiplication and sampling.

If the average number of gametes produced by the individual is small, as may be the case for haploid organisms, then sampling with and without replacement can lead to considerable differences in the fixation probabilities of mutant alleles. As a function of the population size N, these probabilities converge quickly to the survival probabilities given by branching processes with Poisson or Bernoulli offspring distributions.

Biological Evolution↗

PubMed1981

Probabilities of success and failure in endodontic treatment: a Bayesian approach.

Bayes' theorem provides a mathematical rule for changing a (prior) probability into a new (posterior) probability incorporating additional information. Application of the theorem is a way to overcome some limitations that the human mind has in processing information. A Bayesian approach is useful for the processing of data and as a tool for decision making. Bayes' theorem is expounded, and examples are given of the use of the theorem for computing the odds on success or failure of endodontic treatment of a tooth, given a particular preoperative status and given also the results of the preparation and filling of the root canal of the tooth in question. Application of Bayes' theorem using data collected provides an insight based upon probabilities and odds in the way preoperative conditions and operative results affect the ultimate treatment result.

Bayes Theorem↗

PubMed1992

Clusters galore: insights about environmental clusters from probability theory.

The posterior probability of a causal explanation given that an environmental cancer cluster is statistically significant depends on the prior probability of an environmentally caused cluster, the sensitivity of the statistical test and its specificity. The prior probability is low, because it is rare to have enough carcinogen in the general environment to cause a relative risk of cancer high enough to achieve statistical significance in a small geographic area. The sensitivity and specificity are not great. The likelihood that a census tract escapes statistically significant elevations in all 80 types of cancer can be calculated. Many of the thousands of census tracts will, by chance alone, have at least one type of cancer whose elevation is statistically significant. Actual observation from a large cancer registry confirms this probabilistic prediction. Applying the principles of Bayes' Theorem would suggest that most statistically significant environmental cancer clusters are not due to environmental carcinogens. One would have to investigate hundreds of environmental cancer clusters to find one with a true environmental cause.

Bayes Theorem↗

PubMed1986

A program for training and feedback about probability estimation for physicians.

Medical decisions are rarely made under conditions of complete certainty. In the past decade there has been a rapid growth of interest in formal methods for optimizing medical decisions under uncertainty. Application of decision-analytic methods requires physicians to make probability estimates about clinical events for which extensive data are not available. This paper describes a computer program to train physicians to be better probability estimators: to make probability estimates that are numerically meaningful for use in formal decision analyses. It is designed to be a stand-alone application requiring about 2 hours of physician time. Use requires an IBM-PC or compatible microcomputer with graphics adaptor and monitor, and 8087 coprocessor.

Computer-Assisted Instruction↗

PubMed1981

Effect of task and stimulus probability on evoked potentials.

Some experimental data demonstrate the existence of at least two different P300s distinguished by latency, topography and functional significance. These positive waves are preceded by a negative component which has been labelled N200. The purpose of this study was to analyze the modifications of these negative and positive components according to probability and task (GO vs. NOGO) in order to better understand the significance of each of them in terms of stages of information processing. Six normal subjects were tested twice on separate days, in a GO-NOGO paradigm. Auditory stimuli - high pitch (GO) and low pitch (NOGO) - were presented in three different occurrence probability combinations: 0.2/0.8; 0.5/0.5; 0.8/0.2, in successive blocks. In both GO and NOGO responses, a vertex N200 component was followed by two positive waves - the first peaking at 300 msec at Cz (Cz : P300), the other one Ca 400 msec at Pz (Pz : P400). An inverse relation between amplitude and probability was seen for the three components but it was twice as large for P400 as for P300. A task effect was only seen for N200, the amplitude and latency of which increased in the GO condition. From the first session to the second, the amplitude of N200 decreased whereas that of P300 increased.

Adult↗

PubMed1989

Stimulus probability and motor response in young and old adults: an ERP study.

The effects of responding hand and stimulus probability were investigated in young and old subjects in an RT task in which both rare and frequent stimuli required a response. It was found that the effect of stimulus probability was less pronounced in old subjects than in young, and that the latency of P3 was longer in the elderly, although their RTs were not different from young subjects. ERPs for right hand responses were larger than for left hand responses; this difference was discernible already in the P2 and N2 peaks of the ERP. A tentative explanation is offered for these large and unexpected hand differences. An interpretation in terms of an age-related decrease in resources is proposed for the increased P3 latency and the decreased probability effect on P3 amplitude in old subjects.

Adolescent↗

PubMed1991

Histogram reduction method for calculating complication probabilities for three-dimensional treatment planning evaluations.

New tools are needed to help in evaluating 3-D treatment plans because of the large volume of data. One technique which may prove useful is the application of complication probability calculations. A method of calculating complication probabilities for inhomogeneously irradiated normal tissues is presented in this paper. The method uses clinical estimates of tolerance doses for a few discreet conditions of uniform partial organ irradiation, an empirical fit of a continuous function to these data, and a technique (the effective volume method) for transforming nonuniform dose-volume histograms into equivalent uniform histograms. The behavior of the effective volume histogram reduction method for various boundary conditions is reviewed. The use of complication probabilities in evaluating treatment plans is presented, using examples from an NCI 3-D treatment planning contract.

Humans↗

PubMed1992

Development and validation of a logistic regression-derived algorithm for estimating the incremental probability of coronary artery disease before and after exercise testing.

OBJECTIVES: Our goals were to develop and validate a multivariate algorithm for estimating the incremental probability of the presence of coronary artery disease. BACKGROUND: Multivariate methods, including logistic regression analysis, have been extensively applied to diagnostic exercise testing. However, few previous studies have included both an incremental design and external validation. METHODS: A retrospective collection of clinical, exercise test and catheterization data was performed involving four U.S. referral medical centers. All patients had no prior history of coronary disease and had undergone coronary angiography < or = 3 months after exercise stress testing. An algorithm was developed in one center (590 patients with a 41% prevalence of coronary artery disease) with the use of logistic regression analysis and was validated in the other three centers (1,234 patients, 70% prevalence). The algorithm incorporated pretest variables (age, gender, symptoms, diabetes, cholesterol), exercise electrocardiographic (ECG) variables (mm of ST segment depression, ST slope, peak heart rate, metabolic equivalents [METs], exercise angina) and one thallium variable. Discrimination was measured with receiver operating characteristic curve analysis. Calibration (that is, reliability) was assessed from a comparison of probability estimates and the actual prevalence of disease. RESULTS: The overall incremental receiver operating characteristic curve areas for the validation group were pretest, -0.738 +/- 0.016; postexercise ECG, 0.78 (SE 0.017); and postthallium, 0.82 (SE 0.016); p < 0.01 for both increments. Within the three validation institutions, the institution with a disease prevalence closest to that of the derivation institution had the best incremental receiver operating characteristic curve areas. There was a stepwise incremental improvement in calibration especially from exercise ECG to thallium testing. CONCLUSIONS: An incremental multivariate algorithm derived in one center reliably estimated disease probability in patients from three other centers. The incremental value of testing was best demonstrated when the derivation and validation groups had a similar disease prevalence. This algorithm may be useful in decision making that relates to the diagnosis of coronary disease.

Algorithms↗

PubMed2004

The Dallas Heart Study: a population-based probability sample for the multidisciplinary study of ethnic differences in cardiovascular health.

The decrease in cardiovascular death rates in the United States has been slower in blacks than whites, especially in patients <65 years of age. The Dallas Heart Study was designed as a single-site, multiethnic, population-based probability sample to (1) produce unbiased population estimates of biologic and social variables that pinpoint ethnic differences in cardiovascular health at the community level and (2) support hypothesis-driven research on the mechanisms causing these differences using genetics, advanced imaging modalities, social sciences, and clinical research center methods. A probability-based sample of Dallas County residents aged 18 to 65 years was surveyed with an extensive household health interview. The subset of participants 30 to 65 years of age provided in-home fasting blood and urine samples and underwent multiple imaging studies, including cardiac magnetic resonance imaging and electron beam computed tomography. Completed interviews were obtained for 6,101 subjects (54% black), phlebotomy visits for 3,398 (52% black), and clinic visits for 2,971 (50% black). Participation rates were 80.4% for interviews, 75.1% for phlebotomy visits, and 87.4% for clinic visits. Weighted population estimates of many measured variables agreed closely with those of the United States census and were relatively stable from the interview sample to the phlebotomy and clinic subsamples. Thus, the Dallas Heart Study provides a phenotypically well-characterized probability sample for multidisciplinary research that will be used to improve the mechanistic understanding and prevention of cardiovascular disease, especially in black Americans.

Adolescent↗

PubMed2004

Effects of stop-signal probability in the stop-signal paradigm: the N2/P3 complex further validated.

The aim of this study was to examine the effects of frequency of occurrence of stop signals in the stop-signal paradigm. Presenting stop signals less frequently resulted in faster reaction times to the go stimulus and a lower probability of inhibition. Also, go stimuli elicited larger and somewhat earlier P3 responses when stop signals occurred less frequently. Since the amplitude effect was more pronounced on trials when go signals were followed by fast than slow reactions, it probably reflected a stronger set to produce fast responses. N2 and P3 components to stop signals were observed to be larger and of longer latency when stop signals occurred less frequently. The amplitude enhancement of these N2 and P3 components were more pronounced for unsuccessful than for successful stop-signal trials. Moreover, the successfully inhibited stop trials elicited a frontocentral P3 whereas unsuccessfully inhibited stop trials elicited a more posterior P3 that resembled the classical P3b. P3 amplitude in the unsuccessfully inhibited condition also differed between waveforms synchronized with the stop signal and waveforms synchronized with response onset whereas N2 amplitude did not. Taken together these findings suggest that N2 reflected a greater significance of failed inhibitions after low probability stop signals while P3 reflected continued processing of the erroneous response after response execution.

Adolescent↗

PubMed2006

Effects of spatial separation and stimulus probability on the event-related potentials elicited by occasional changes in sound location.

The ability to extract information about the spatial location of sounds plays an important role in auditory scene analysis. The present study examined the effects of spatial separation and stimulus probability on auditory event-related potentials (ERPs) to changes in sound location. In Experiment 1, we found that difference waves between ERPs elicited by standard and deviant stimuli showed a biphasic negative-positive response peaking around 126 and 226 ms after deviant onset. The amplitude of both responses increased with decreasing deviant stimulus probability, and increasing stimulus deviance. When the same stimuli were presented with equal probability for all locations (Experiment 2), there were no significant differences in the ERP amplitude and latency. These results suggest that the data reported in Experiment 1 are the result of contextual changes, rather than changes in simple acoustic features. Brain electrical source analyses are consistent with generators located in auditory cortices posterior to Heschel's gyrus. Although occasional changes in sound location elicit earlier peaks than the mismatch negativity (MMN) response reported for other types of deviation, their topographical distribution and behavior are consistent with MMN. The early latency of MMN for changes in sound location is interpreted in the context of an early-warning system to alert the organism to new sound sources in the environment.

Acoustic Stimulation↗

PubMed2005

Probability of mediastinal involvement in non-small-cell lung cancer: a statistical definition of the clinical target volume for 3-dimensional conformal radiotherapy?

PURPOSE: Conformal irradiation (3D-CRT) of non-small-cell lung carcinoma (NSCLC) is largely based on precise definition of the nodal clinical target volume (CTVn). A reduction of the number of nodal stations to be irradiated would facilitate tumor dose escalation. The aim of this study was to design a mathematical tool based on documented data to predict the risk of metastatic involvement for each nodal station. METHODS AND MATERIALS: We reviewed the large surgical series published in the literature to identify the main pretreatment parameters that modify the risk of nodal invasion. The probability of involvement for the 17 nodal stations described by the American Thoracic Society (ATS) was computed from all these publications. Starting with the primary site of the tumor as the main characteristic, we built a probabilistic tree for each nodal station representing the risk distribution as a function of each tumor feature. Statistical analysis used the inversion of probability trees method described by Weinstein and Feinberg. Validation of the software based on 134 patients from two different populations was performed by receiver operator characteristic (ROC) curves and multivariate logistic regression. RESULTS: Analysis of all of the various parameters of pretreatment staging relative to each level of the ATS map results in 20,000 different combinations. The first parameters included in the tree, depending on tumor site, were histologic classification, metastatic stage, nodal stage weighted as a function of the sensitivity and specificity of the diagnostic examination used (positron emission tomography scan, computed tomography scan), and tumor stage. Software is proposed to compute a predicted probability of involvement of each nodal station for any given clinical presentation. Double cross validation confirmed the methodology. A 10% cutoff point was calculated from ROC and logistic model giving the best prediction of mediastinal lymph node involvement. CONCLUSION: To more accurately define the CTVn in NSCLC three-dimensional conformal radiotherapy, we propose a software that evaluates the risk of mediastinal lymph node involvement from easily accessible individual pretreatment parameters.

Adult↗

PubMed2006

Reduction of cardiac and pulmonary complication probabilities after breathing adapted radiotherapy for breast cancer.

PURPOSE: Substantial reductions of cardio-pulmonary radiation doses can be achieved using voluntary deep inspiration breath-hold (DIBH) or free breathing inspiration gating (IG) in radiotherapy after conserving surgery for breast cancer. The purpose of this study is to evaluate the radiobiological implications of such dosimetric benefits. METHODS AND MATERIALS: Patients from previously reported studies were pooled for a total of 33 patients. All patients underwent DIBH and free breathing (FB) scans, and 17 patients underwent an additional IG scan. Tangential conformal treatment plans covering the remaining breast, internal mammary, and periclavicular nodes were optimized for each scan, prescription dose 48 Gy. Normal tissue complication probabilities were calculated using the relative seriality model for the heart, and the model proposed by Burman et al. for the lung. RESULTS: Previous computed tomography studies showed that both voluntary DIBH and IG provided reduction of the lung V50 (relative volume receiving more than 50% of prescription dose) on the order of 30-40%, and a 80-90% reduction of the heart V50 for left-sided cancers. Corresponding pneumonitis probability of 28.1% (range, 0.7-95.6%) for FB could be reduced to 2.6% (range, 0.1-40.1%) for IG, and 4.3% (range, 0.1-59%) for DIBH. The cardiac mortality probability could be reduced from 4.8% (range, 0.1-23.4%) in FB to 0.5% (range, 0.1-2.6%) for IG and 0.1% (range, 0-3.0%) for DIBH. CONCLUSIONS: Remarkable potential is shown for simple voluntary DIBH and free breathing IG to reduce the risk of both cardiac mortality and pneumonitis for the common technique of adjuvant tangential breast irradiation.

Aged↗

PubMed2005

Errors in the estimation of the variance: implications for multiple-probability fluctuation analysis.

Synapses play a crucial role in information processing in the brain. Amplitude fluctuations of synaptic responses can be used to extract information about the mechanisms underlying synaptic transmission and its modulation. In particular, multiple-probability fluctuation analysis can be used to estimate the number of functional release sites, the mean probability of release and the amplitude of the mean quantal response from fits of the relationship between the variance and mean amplitude of postsynaptic responses, recorded at different probabilities. To determine these quantal parameters, calculate their uncertainties and the goodness-of-fit of the model, it is important to weight the contribution of each data point in the fitting procedure. We therefore investigated the errors associated with measuring the variance by determining the best estimators of the variance of the variance and have used simulations of synaptic transmission to test their accuracy and reliability under different experimental conditions. For central synapses, which generally have a low number of release sites, the amplitude distribution of synaptic responses is not normal, thus the use of a theoretical variance of the variance based on the normal assumption is not a good approximation. However, appropriate estimators can be derived for the population and for limited sample sizes using a more general expression that involves higher moments and introducing unbiased estimators based on the h-statistics. Our results are likely to be relevant for various applications of fluctuation analysis when few channels or release sites are present.

Animals↗

PubMed2006

An information theoretic approach for non-rigid image registration using voxel class probabilities.

We propose two information theoretic similarity measures that allow to incorporate tissue class information in non-rigid image registration. The first measure assumes that tissue class probabilities have been assigned to each of the images to be registered by prior segmentation of both of them. One image is then non-rigidly deformed to match the other such that the fuzzy overlap of corresponding voxel object labels becomes similar to the ideal case whereby the tissue probability maps of both images are identical. Image similarity is assessed during registration by the divergence between the ideal and actual joint class probability distributions of both images. A second registration measure is proposed that applies in case a segmentation is available for only one of the images, for instance an atlas image that is to be matched to a study image to guide the segmentation thereof. Intensities in one image are matched to the fuzzy class labels in the other image by minimizing the conditional entropy of the intensities in the first image given the class labels in the second image. We derive analytic expressions for the gradient of each measure with respect to individual voxel displacements to derive a force field that drives the registration process, which is regularized by a viscous fluid model. The performance of the class-based measures is evaluated in the context of non-rigid inter-subject registration and atlas-based segmentation of MR brain images and compared with maximization of mutual information using only intensity information. Our results demonstrate that incorporation of class information in the registration measure significantly improves the overlap between corresponding tissue classes after non-rigid matching. The methods proposed here open new perspectives for integrating segmentation and registration in a single process, whereby the output of one is used to guide the other.

Algorithms↗

PubMed2004

An MRI study of spatial probability brain map differences between first-episode schizophrenia and normal controls.

We created a spatial probability atlas of schizophrenia to provide information about the neuroanatomic variability of brain regions of patients with the disorder. Probability maps of 16 regions of interest (ROIs) were constructed by taking manually parcellated ROIs from subjects' magnetic resonance images (MRIs) and linearly transforming them into Talairach space using the Montreal Neurological Institute (MNI) template. ROIs included temporal, parietal, and prefrontal cortex subregions, with a principal focus on temporal lobe structures. Subject Ns ranged from 11 to 28 for the different ROIs. Our global measure of the spatial distribution of the transformed ROI was the sum of voxels with 50% overlap among subjects. The superior temporal gyrus (STG) and fusiform gyrus (FG) had lower values for schizophrenic subjects than for normal controls, suggestive of greater spatial variability for these ROIs in schizophrenic subjects. For the computation of statistical significance of group differences in portions of the ROI, we used voxel-wise comparisons and Fisher's exact test. First-episode schizophrenic patients compared with controls showed lower probability (P < 0.05) at dorso-posterior areas of planum temporale and Heschl's gyrus, lateral and anterior regions in the left hippocampus (HIPP), and dorsolateral regions of fusiform gyrus. Importantly, most ROIs of schizophrenic subjects showed a significantly lower spatial overlap than controls, even after nonlinear spatial normalization, suggesting a greater heterogeneity in the spatial distribution of ROIs. There is consequently a need for caution in neuroimaging studies where data from schizophrenic subjects are normalized to a particular stereotaxic coordinate system based on healthy controls. Apparent group differences in activation may simply reflect a greater heterogeneity of spatial distribution in schizophrenia.

Adult↗