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At least 163 records · Page 9Linked to original sources
PubMed2002

Estimation in medical imaging without a gold standard.

RATIONALE AND OBJECTIVES: In medical imaging, physicians often estimate a parameter of interest (eg, cardiac ejection fraction) for a patient to assist in establishing a diagnosis. Many different estimation methods may exist, but rarely can one be considered a gold standard. Therefore, evaluation and comparison of different estimation methods are difficult. The purpose of this study was to examine a method of evaluating different estimation methods without use of a gold standard. MATERIALS AND METHODS: This method is equivalent to fitting regression lines without the x axis. To use this method, multiple estimates of the clinical parameter of interest for each patient of a given population were needed. The authors assumed the statistical distribution for the true values of the clinical parameter of interest was a member of a given family of parameterized distributions. Furthermore, they assumed a statistical model relating the clinical parameter to the estimates of its value. Using these assumptions and observed data, they estimated the model parameters and the parameters characterizing the distribution of the clinical parameter. RESULTS: The authors applied the method to simulated cardiac ejection fraction data with varying numbers of patients, numbers of modalities, and levels of noise. They also tested the method on both linear and nonlinear models and characterized the performance of this method compared to that of conventional regression analysis by using x-axis information. Results indicate that the method follows trends similar to that of conventional regression analysis as patients and noise vary, although conventional regression analysis outperforms the method presented because it uses the gold standard which the authors assume is unavailable. CONCLUSION: The method accurately estimates model parameters. These estimates can be used to rank the systems for a given estimation task.

Diagnostic Imaging↗
PubMed2000

Estimating age-related trends in cross-sectional studies using S-distributions.

Growth trends in children are often based on cross-sectional studies, in which a sample of the population is investigated at one given point in time. Estimating age-related percentiles in such studies involves fitting data distributions, each of which is specific for one age group, and a subsequent smoothing of the percentile curves. The first requirement for this process is the selection of a distributional form that is expected to be consistent with the observed data. If a goodness-of-fit test reveals significant discrepancies between the data and the best-fitting member of this distributional form, an alternative distribution must be found. In practice, there is seldom an objective argument for selecting any particular distribution. Also, different distributions can yield very similar fits, so that any selection is somewhat arbitrary. Finally, the shapes of the observed distributions may change throughout the age range so drastically that no single traditional distribution can fit them all in a satisfactory manner. To overcome these difficulties in population studies, non-parametric smoothing techniques and normalizing transformations have been used to derive percentile curves. In this paper we present an alternative strategy in the form of a flexible parametric family of statistical distributions: the S-distribution. We suggest a method that guides the search for well-fitting S-distributions for groups of observed distributions. The method is first tested with simulated data sets and subsequently applied to actual weight distributions of girls of different ages. As far as the results can be tested, they are consistent with observations and with results from other methods.

Adolescent↗
PubMed1999

Molecular evolution and phylogeny of the Drosophila saltans species group inferred from the Xdh gene.

The Drosophila saltans group of the subgenus Sophophora consists of five species subgroups whose phylogenetic relationships are poorly known. We have analyzed 2085 coding nucleotides from the xanthine dehydrogenase (Xdh) gene in six species, at least one from each subgroup. We follow a model-based maximum likelihood framework. We first model the substitution process using a tree topology that is approximately accurate. Then we evaluate several candidate tree topologies using a working model of nucleotide substitution. We found that a minimally realistic description of the substitution process along the Xdh region should allow two transition and four transversion rate parameters and different fixed rates for codon positions, which are distributed statistically according to different gamma distributions. The phylogeny obtained using this description differs in significant respects from a phylogeny based on anatomical criteria. We have also analyzed data from five additional (three nuclear and two mitochondrial) gene regions. In our analysis, these relatively short DNA sequences, either separately or jointly, fail to discriminate statistically among alternative phylogenies. When the data for these five gene regions are combined with the Xdh sequences, the strong phylogenetic signal emerging from Xdh becomes somewhat diluted rather than reinforced. The phylogeny of the species and biogeographical considerations suggest that the D. saltans group originated in the tropics of the New World, similarly as the closely related D. willistoni group.

Alcohol Dehydrogenase↗
PubMed1998

[Interpopulation diversity of the gene pool: beta distribution of Wright's F(ST) statistics].

The distribution of FST(i) estimates were studied in representative samples of ith genes for the gene pools of the major human populations, including the populations of Europe, Asia, Africa, Australia, America, North-eastern Eurasia, and five subregions of the latter. An average of 80 FST(i) estimates were analyzed for each sample of marker genes with a level of polymorphism (q) from 0.05 to 0.95. For each gene pool, the empirical distributions of FST(i) estimates were approximated by the main types of theoretical distributions--the normal, chi 2, Weibull, gamma, and beta distributions. In all gene pools, only beta distributions were good approximations of the empirical FST(i) distributions. The parameters of the beta distributions are reported in this study. It was demonstrated that the characteristics of beta distributions for all major gene pools studied could be interpolated to the smaller constituent gene pools. since the use of the traditional parametric tests starts from an assumption of normal distribution, they are inapplicable to analysis of FST statistics. Therefore, the obtained parameters of beta distributions should be used. These parameters allow the confidence intervals of the average FST values to be determined and permit correct comparison between the characteristics of both individual genes and gene pools to be performed.

Africa↗
PubMed2001

Spontaneous chiral separation in noncovalent molecular clusters.

A new method is introduced to determine the extent to which spontaneous chiral separation occurs in small noncovalently bound clusters. Soft-sampling electrospray ionization was used to transfer noncovalent complexes from solution to the gas phase. Mixing D and L enantiomers with one of the pair isotopically labeled reveals the effect of chirality on cluster stability. The observed cluster distribution is compared to the predicted statistical distribution to determine any preference for homo- or heterochirality. Arginine, for example, forms a stable trimer with no preference for the chirality of the individual amino acids. Serine, however, forms a protonated octamer with a pronounced preference for homochirality. The implications of these results for the structures of the complexes are discussed along with the broader implications for the origins of homochirality in living systems (homochirogenesis).

Journal Article↗
PubMed1998

Comparative study of different weighting methods in non-linear regression analysis: implications in the parametrization of carebastine after intravenous administration in healthy volunteers.

The influence of different weighting methods in non-linear regression analysis was evaluated in the pharmacokinetics of carebastine after a single intravenous dose of 10 mg in 8 healthy volunteers. Plasma concentrations were measured by HPLC using an on-line solid-phase extraction method and automated injection. The analytical method was fully validated and the function of the analytical error subsequently determined. The parametric approach was performed using different weighting methods, including the homoscedastic method (W = 1) and heteroscedastic methods using weights of 1/C, 1/C2, and the inverse of the concentration variance calculated through the analytical error function (1/V), and the results were statistically evaluated according to the normal distribution. Statistically significant differences were observed in the representative parameters of the disposition kinetics of carebastine. The use of a multiple comparison test for statistical analysis of all differences among group means indicated that differences were generated between the homoscedastic method (W = 1) and the heteroscedastic methods (1/C, 1/C2, and 1/V). The results obtained in the present study confirmed the utility of the analytical error function as a weighting method in non-linear regression analysis and reinforced the importance of the correct choice of weights to avoid the estimation of imprecise or erroneous pharmacokinetic parameters.

Adult↗
PubMed2000

Shear stress distribution in the trabeculae of human vertebral bone.

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

Adult↗
PubMed2001

Bayesian analysis of systems with random chemical composition: renormalization-group approach to Dirichlet distributions and the statistical theory of dilution.

We investigate the statistical properties of systems with random chemical composition and try to obtain a theoretical derivation of the self-similar Dirichlet distribution, which is used empirically in molecular biology, environmental chemistry, and geochemistry. We consider a system made up of many chemical species and assume that the statistical distribution of the abundance of each chemical species in the system is the result of a succession of a variable number of random dilution events, which can be described by using the renormalization-group theory. A Bayesian approach is used for evaluating the probability density of the chemical composition of the system in terms of the probability densities of the abundances of the different chemical species. We show that for large cascades of dilution events, the probability density of the composition vector of the system is given by a self-similar probability density of the Dirichlet type. We also give an alternative formal derivation for the Dirichlet law based on the maximum entropy approach, by assuming that the average values of the chemical potentials of different species, expressed in terms of molar fractions, are constant. Although the maximum entropy approach leads formally to the Dirichlet distribution, it does not clarify the physical origin of the Dirichlet statistics and has serious limitations. The random theory of dilution provides a physical picture for the emergence of Dirichlet statistics and makes it possible to investigate its validity range. We discuss the implications of our theory in molecular biology, geochemistry, and environmental science.

Algorithms↗
PubMed1984

The significance of morphometric procedures in the investigation of age changes in cytoarchitectonic structures of human brain.

The investigations were performed on NISSL-stained cytoarchitectonic images of totally 78 human brains (aged between 18 and 111 years) in the frontal area 11 (inside sulcus olfactorius) with 60 samples and in the visual cortex (area 17) with 45 samples. The morphometric measurements were taken by using a semiautomatic equipment. The largest projection areas of neurons were digitized over a drawing mirror. The arrangement of fields made it possible to get values for the total cortex and its layering. During the calculation the age-dependent embedding shrinkage was paid attention to. Therefore, the values concern the fresh tissue. The neuronal and glial densities, the neuronal sizes and size-distributions were calculated by using stereological and statistical principles. The results outline the following points: A basic description of the cytoarchitectonics is given in their qualitative and quantitative aspects. The individual variation shows high differences, which however, are in accordance with a normal statistical distribution. In area 11 we could find a significant difference of neuronal densities between males and females. The cell-sizes and the aging behavior are not different. In area 17 the amount of female brains was too small for statistics. The aging of both areas showed that the densities of neurons and glial cells do not decrease. A small increase may be possible. The neuronal sizes of area 11 are constant up to 60 years, then a distinct decrease can be observed. During aging the size decrease of neurons is very small in area 17. The layer III usually shows a distinct decrease of neuronal size during aging while layer V has a nearly constant size. The results were discussed and compared with other publications. The differences between our results and earlier publications seem to be mainly due to methodical problems. The older papers do and could probably not observe the stereological procedures of measuring and the age differences of the embedding procedures. The main result is that every gray structure of the brain has its own history.

Adolescent↗
PubMed1978

Distribution of membrane thickness determined by lineal analysis.

The expected statistical distributions of intercept length are derived in terms of geometrical probability density functions pertaining to plates with known thickness penetrated by lines with random orientation. These expressions provide arithmetic and graphical solutions for obtaining distributions of membrane thickness and reciprocal membrane thickness from empirical distributions of intercept lengths. Furthermore, general relationships between probability density functions of distributions of intercept length and membrane thickness are derived as well as those between their moments. Examples of the application of the method to biological samples are given, and estimated distributions of glomerular basement membrane thickness are compared to those obtained by an independent, direct method. Various sources of bias, which in practice may occur due to departures from the sample model, are discussed and the influence of some of them is estimated. The knowledge of the probability density function of reciprocal intercepts makes it possible to perform a correction of the distribution of measured intercept length, which to some extent eliminates bias.

Animals↗
PubMed2002

A new parametric method based on S-distributions for computing receiver operating characteristic curves for continuous diagnostic tests.

Receiver operating characteristic (ROC) curves provides a method for evaluating the performance of a diagnostic test. These curves represent the true positive ratio, that is, the true positives among those affected by the disease, as a function of the false positive ratio, that is, the false positives among the healthy, corresponding to each possible value of the diagnostic variable. When the diagnostic variable is continuous, the corresponding ROC curve is also continuous. However, estimation of such curve through the analysis of sample data yields a step-line, unless some assumption is made on the underlying distribution of the considered variable. Since the actual distribution of the diagnostic test is seldom known, it is difficult to select an appropriate distribution for practical use. Data transformation may offer a solution but also may introduce a distortion on the evaluation of the diagnostic test. In this paper we show that the distribution family known as the S-distribution can be used to solve this problem. The S-distribution is defined as a differential equation in which the dependent variable is the cumulative. This special form provides a highly flexible family of distributions that can be used as models for unknown distributions. It has been shown that classical statistical distributions can be represented accurately as S-distributions and that they occur in a definite subspace of the parameter space corresponding to the whole S-distribution family. Consequently, many other distributional forms that do not correspond to known distributions are provided by the S-distribution. This property can be used to model observed data for unknown distributions and is very useful in constructing parametric ROC curves in those cases. After fitting an S-distribution to the observed samples of diseased and healthy populations, ROC curve computation is straightforward. A ROC curve can be considered as the solution of a differential equation in which the dependent variable is the ratio of true positives and the independent variable is the ratio of false positives. This equation can be easily obtained from the S-distributions fitted to observed data. Using these results, we can compute pointwise confidence bands for the ROC curve and the corresponding area under the curve. We shall compare this approach with the empirical and the binormal methods for estimating a ROC curve to show that the S-distribution based method is a useful parametric procedure.

Area Under Curve↗
PubMed1990

Stationarity and normality of distribution of rat cortical brain waves.

Establishing the stationarity and statistical distribution of potentials recorded from the nervous system is crucial for the application of frequency analysis. Both parameters were determined in the electrocorticograms of six adult Wistar rats during wakefulness and desynchronized sleep, during both of which desynchronization prevails. Stationarity of the signals was found to occur during at least 20 s in both states of the wakefulness-sleep cycle. A normal distribution was also found for at least 6.7 s. These findings provide strong support for the use of frequency analysis of brain waves as a reliable method to quantify neural electro-oscillograms.

Animals↗
PubMed1983

Helical sidedness and the distribution of polar residues in trans-membrane helices.

Trans-membrane helices have often been claimed to show "sidedness" in the distribution of polar and hydrophobic residues. However, an analysis of the statistical distribution of polar residues in randomly generated helices shows that the degree of bias commonly observed in real helices is far from statistically significant. It is concluded that "patchy" distributions of residues in such helices should be interpreted with great care.

Bacteriorhodopsins↗
PubMed2001

Quantification and variability analysis of bacterial cross-contamination rates in common food service tasks.

This study investigated bacterial transfer rates between hands and other common surfaces involved in food preparation in the kitchen. Nalidixic acid-resistant Enterobacter aerogenes B199A was used as a surrogate microorganism to follow the cross-contamination events. Samples from at least 30 different participants were collected to determine the statistical distribution of each cross-contamination rate and to quantify the natural variability associated with that rate. The transfer rates among hands, foods, and kitchen surfaces were highly variable, being as low as 0.0005% and as high as 100%. A normal distribution was used to describe the variability in the logarithm of the transfer rates. The mean +/- SD of the normal distributions were, in log percent transfer rate, chicken to hand (0.94 +/- 0.68), cutting board to lettuce (0.90 +/- 0.59), spigot to hand (0.36 +/- 0.90), hand to lettuce (-0.12 +/- 1.07), prewashed hand to postwashed hand (i.e., hand washing efficiency) (-0.20 +/- 1.42), and hand to spigot (-0.80 +/- 1.09). Quantifying the cross-contamination risk associated with various steps in the food preparation process can provide a scientific basis for risk management efforts in both home and food service kitchens.

Animals↗
PubMed1998

The frequency distribution of the number of ion pairs in irradiated tissue.

The statistical distribution of the number of ion pairs per ionizing event in a small volume simulating a tissue sphere was obtained by applying the Expectation-Maximization (EM) algorithm to experimental spectra measured by exposing a Rossi-type spherical proportional counter to gamma radiation. The normalized experimental spectrum, r(x), which is the distribution of the number of ion pairs per event from both the primary track and the subsequent electron multiplication, can be represented as Sum(n) p(n) x f(n,x), where the f(n,x)'s for n = 1, 2, 3, ..., n are the normalized spectra for exactly 1, 2, 3, ..., n primary ion pairs and are calculated by convoluting the single-electron spectrum. The coefficients pn represent the mixing proportions of the spectra corresponding to 1, 2, 3, ..., n ion pairs in forming the experimental spectrum. The single-electron spectrum used in our calculations is the distribution of the number of ion pairs due to the multiplication process, and it is represented in analytical form by the Gamma distribution f(1,x) = a x x(b) x e(-cx), where x is energy, usually in eV, and a, b and c are constants. The EM algorithm is an iterative procedure for computing the maximum likelihood or maximum a posteriori estimates of the mixing proportions p(n), which we also refer to as the primary distribution of ion pairs in a microscopic spherical tissue-equivalent volume. The experimental and primary spectra are presented for simulated tissue spheres ranging from 0.25 to 8 microm in diameter exposed to 60Co gamma radiation.

Cobalt Radioisotopes↗
PubMed1982

Distribution of aflatoxin in whole peanut kernels, sampling plans for small samples.

It is well known that the distribution of aflatoxin in a lot of whole peanut kernels is extremely heterogeneous. Several different statistical distribution models have been proposed, fitting the experimental data reasonably well as long as the samples are very large, but differing considerably when applied to small samples. Therefore, it is important to know the real distribution between single kernels for the evaluation of the effectiveness of sampling plans for small samples. It is shown by the analysis of 368 samples of 1-10,000 kernels from the same lot of peanuts that the negative binomial distribution represents a good statistical model. The variance can be estimated from the mean concentration of the analysed samples, as confirmed by the comparison of data from several independent investigations. Decisions based on small samples are especially unfavourable to the consumer, as even a lot with a high mean concentration will tend to give negative results. A reasonably small risk of a false decision, both to the consumer and to the producer, can be reached only if very large samples are analysed.

Aflatoxin B1↗
PubMed2003

Digital karyometry in pancreatic adenocarcinoma.

OBJECTIVE: To characterize nuclei from pancreatic adenocarcinoma and nonneoplastic pancreatic tissue by digital karyometry, demonstrating specific nuclear signatures for each of them. STUDY DESIGN: Of cells from malignant and nonmalignant pancreatic tissue, 1,300 nuclei were assessed by digital karyometry from paraffin blocks stored at the Pathology Service of Hospital de Clinicas de Porto Alegre. A set of 40 features descriptive of the spatial and statistical distribution of nuclear chromatin was computed for each nucleus. Signatures were created for both types of tissue, and a distance metric from "normal" was defined and calculated for them. RESULTS: There were significant differences in 11 features between the 2 groups, allowing the creation of digital signatures. CONCLUSION: Nuclear chromatin texture signature can offer a specific digital characterization for both pancreatic adenocarcinoma and nonmalignant pancreatic tissue. Several isolated nuclear features serve as markers for the diagnosis of pancreatic adenocarcinoma. The present karyometric study of normal and malignant pancreatic tissue may be of use as a continuing tool to early diagnosis of pancreatic adenocarcinoma as it can be applied to cytologic specimens, also. In the future, studies using this technique should assess the chemopreventive potential of different agents as well as prognosis and treatment options for pancreatic adenocarcinoma.

Adenocarcinoma↗