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PubMed1981

Application of Poisson's distribution model to the occurrence of acute viral hepatitis in the district of Sokolov.

The possibility of application of the Poisson's model of distribution in the field of epidemiology was analyzed on an example of actual distribution pattern of HBsAg-positive and HBsAg-negative cases of acute viral hepatitis notified weekly in a distinct during a period of 6 years. The results suggest that the distribution pattern of HBsAg-positive AVH is fully compatible with the Poisson's model of distribution, whereas the distribution pattern of HBsAg-negative AVH differs from it quite evidently. The observed Poisson's distribution of HBsAg-positive AVH offers some new theoretical and practical implications concerning the incidence, distribution and prophylaxis of this infection. It is also assumed that HBsAg-positive AVH is not the only one of the communicable diseases the occurrence of which is compatible with the Poisson's model of distribution.

Czechoslovakia↗
PubMed2001

Chromosome aberration analysis in radiotherapy patients and simulated partial body exposures: biological dosimetry for non-uniform exposures.

Chromosome aberration analysis was carried out in peripheral blood lymphocytes of cancer patients following radiotherapy of lungs, cervix and spine. Radiotherapy in the pelvic region involving large doses (6 Gy) showed an overdispersed distribution of dicentrics. However, when the doses were fractionated (three fractions of 2 Gy) distribution was found to be near Poisson. Spine irradiation covering almost all the lymphocytes pools, indicated a Poisson distribution. The data show that depending on the sites of exposure, the distribution of dicentrics in cells varies and hence there is a non-uniform distribution of lymphocytes in the body. The average dose to the lymphocytes was found to be one sixth of the partial body dose. Based on the non-Poisson distribution of aberrations, the fraction of lymphocytes irradiated, mean dose to the fraction and part of the body exposed was calculated in a case of acute 6 Gy pelvic irradiation. The fraction of cells irradiated was calculated to be 4.11% and the portion of the body exposed was approximately 16.8%. The dose to the irradiated fraction was found to be 5.4 Gy, which is in agreement with the given dose of 6 Gy. In simulated exposures the u values increased systematically with the decrease in fraction of irradiated cells and the calculated dose to the fraction was also in good agreement with the true dose.

Chromosome Aberrations↗
PubMed1999

Evidence that most radiation-induced HPRT mutants are generated directly by the initial radiation exposure.

Radiation-induced HPRT mutants are generally assumed to arise directly from DNA damage that is misrepaired within a few hours after X-irradiation. However, there is the possibility that mutations result indirectly from radiation-induced genomic instability that may occur several days after the initial radiation exposure. The protocols that commonly employ a 5-7 day expression period to allow for expression of the mutant phenotype prior to replating for selection of mutants would not be able to discriminate between mutants that occurred initially and those that arose during or after the expression period. To address this question, we performed a fluctuation analysis in which synchronous or asynchronous populations of human bladder carcinoma cells were treated with single doses of X-irradiation. For comparison, radiation was delivered during the expression period, either from an initial dose of 1.0 Gy followed by two 1.0 Gy doses separated by 24 h or from disintegrations resulting from I125dU incorporated into DNA. The mutation frequency observed at the time of replating was used to calculate the average number of mutants in the initial irradiated culture by assuming that the mutants were induced directly at the time of irradiation. Then, this average number was used to calculate the fraction of the irradiated cultures that would be predicted by a Poisson distribution to have zero mutants. There was reasonably good agreement between the predicted poisson distribution and the observed distribution for the cultures that received single doses. Moreover, as expected, when cultures were irradiated during the expression period, the fraction of the cultures having zero mutants was significantly less than that predicted by a Poisson distribution. These results indicate that most radiation-induced HPRT mutations are induced directly by the initial DNA damage, and are not the result of radiation-induced instability during the 5-7 day expression period.

DNA↗
PubMed2000

Justification of statistical overlap theory in programmed temperature gas chromatography: thermodynamic origin of random distribution of retention times.

A specific distribution of compounds' standard-state changes of enthalpy and entropy between mobile and stationary phases in programmed temperature gas chromatography (PTGC) is shown to produce the Poisson distribution of retention times often postulated in statistical-overlap theory (SOT). A three-part model is proposed, in which the enthalpy change is Poisson distributed, the average entropy change depends on the enthalpy change, and the actual entropy change varies in a uniformly random manner about the average entropy change. To test the model, the entropy and enthalpy changes of 350 aliphatic and aromatic hydrocarbons in petroleum were calculated with commercial GC software. These changes are shown to follow the three-part model. The model then was used with Monte Carlo methods to mimic the enthalpy and entropy changes. The substitution of the mimicked enthalpy and entropy changes into an equation for the retention temperature in PTGC is shown to produce a Poisson distribution of retention times that is statistically significant. This finding establishes a scientific link between the thermodynamics governing retention in PTGC and the superficially ad hoc assumption of the Poisson retention time distribution in SOT. Similar thermodynamic distributions are found for flavors and fragrances and for tetrachlorodibenzo-p-dioxins and furans, which follow SOT based on the Poisson distribution, but not for polychloronaphthalenes, which do not follow that SOT.

Journal Article↗
PubMed1998

Patterns of macroparasite aggregation in wildlife host populations.

Frequency distributions from 49 published wildlife host-macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host-parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

Animals↗
PubMed1996

Establishment probability in fluctuating environments: a branching process model.

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.

Demography↗
PubMed2001

Maximum-likelihood expectation-maximization reconstruction of sinograms with arbitrary noise distribution using NEC-transformations.

The maximum-likelihood (ML) expectation-maximization (EM) [ML-EM] algorithm is being widely used for image reconstruction in positron emission tomography. The algorithm is strictly valid if the data are Poisson distributed. However, it is also often applied to processed sinograms that do not meet this requirement. This may sometimes lead to suboptimal results: streak artifacts appear and the algorithm converges toward a lower likelihood value. As a remedy, we propose two simple pixel-by-pixel methods [noise equivalent counts (NEC)-scaling and NEC-shifting] in order to transform arbitrary sinogram noise into noise which is approximately Poisson distributed (the first and second moments of the distribution match those of the Poisson distribution). The convergence speed associated with both transformation methods is compared, and the NEC-scaling method is validated with both simulations and clinical data. These new methods extend the ML-EM algorithm to a general purpose nonnegative reconstruction algorithm.

Algorithms↗
PubMed1988

Neurofilaments are spaced randomly in the radial dimension of axons.

The organization of the cytoskeleton is compared in the large myelinated parasympathetic and somatic motor axons of the avian oculomotor system. Electron microscopic studies demonstrate that neurofilaments are the chief structural elements in these axons, and quantitative analyses of the distribution of neurofilaments in axonal cross-sections found that the average neurofilament packing density is 25% greater in the parasympathetic axons than in the somatic motor axons. In both types of axon the distributions of neurofilaments matched a randomly generated (Poisson) distribution. In axoplasm, a Poisson distribution could arise if the neurofilaments were distributed in the cross-sectional plane by stochastic forces operating randomly and without significant neurofilament-neurofilament interactions. Thus, in these axons, the neurofilaments behave as if they are inert 'molecules' in a dilute solution-subject to non-specific stochastic forces that tend to distribute them at random. We propose that neurofilaments normally are relatively free to move apart from each other and to fill the available space within the axon.

Animals↗
PubMed1982

Incidence of disorders tested by systematic screening: confidence limits and comparison of programmes.

Using the data from screening done in Switzerland since 1965, we showed that the probability of finding cases with increased phenylalanine or leucine concentrations is compatible with a Poisson distribution. If there are no trends present from year to year and if the Poisson distribution is an accurate fit further statistical treatment is possible. The advantage of using the Poisson distribution is exemplified by the calculation of confidence limits for the incidence of hyperphenylalaninaemia, maple syrup urine disease and hypothyroidism. Furthermore, statistical comparisons between different screening programs are easily done.

Epidemiologic Methods↗
PubMed1991

A two-state Markov mixture model for a time series of epileptic seizure counts.

This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.

Biometry↗
PubMed1995

Calculation of the need for paediatric intensive care beds.

A study of paediatric intensive care usage and need was undertaken in the former English Northern region to define appropriate local provision in the light of apparently conflicting published evidence. It was hypothesised that daily bed need would follow a Poisson distribution. All admissions of children aged less than 15 years who required intensive care in the region were recorded retrospectively for the financial year 1993/4. The mean number of beds occupied was 11.7 per day, which is equivalent to 20.7 beds per million children per day. The distribution of numbers of beds used mirrored a Poisson distribution closely, and the predicted bed requirement to cover 95% of days in the year was in agreement with that observed. Review of recommendations for paediatric intensive care provision from other studies suggests that apparent differences arise largely from the effect of different sizes of population served, and that, when allowance is made for this, underlying rates of bed requirement are strikingly similar, with a mean of around 20 per million children per day. A formula is given for the application of this model to local populations.

Adolescent↗
PubMed1999

Experimental comparison of data transformation procedures for analysis of principal components.

Results of principal component analysis depend on data scaling. Recently, based on theoretical considerations, several data transformation procedures have been suggested in order to improve the performance of principal component analysis of image data with respect to the optimum separation of signal and noise. The aim of this study was to test some of those suggestions, and to compare several procedures for data transformation in analysis of principal components experimentally. The experiment was performed with simulated data and the performance of individual procedures was compared using the non-parametric Friedman's test. The optimum scaling found was that which unifies the variance of noise in the observed images. In data with a Poisson distribution, the optimum scaling was the norm used in correspondence analysis. Scaling mainly affected the definition of the signal space. Once the dimension of the signal space was known, the differences in error of data and signal reproduction were small. The choice of data transformation depends on the amount of available prior knowledge (level of noise in individual images, number of components, etc), on the type of noise distribution (Gaussian, uniform, Poisson, other), and on the purpose of analysis (data compression, filtration, feature extraction).

Computer Simulation↗
PubMed1982

Experimental design and statistical analysis considerations for in vitro mammalian cell transformation assays with BALB/3T3 cells.

Many mammalian cell assays testing for mutagenic activity have common features which cause statistical estimation and analysis problems. Such assays measure the number of cell alterations occurring in a plate containing an unknown number of cells at risk. The number of cells at risk can be estimated from a parallel cytotoxicity study. While the Poisson distribution has been assumed to apply to standardized frequencies, this is questioned. The failure of standardized frequencies to follow a Poisson distribution is attributed to the relatively small and dosage-dependent number of susceptible cells per plate. A minimum number of such cells per plate or random cluster of plates has been determined for each dose so that the measured variable approximates a Poisson distribution. A transformation is suggested to achieve reasonable normality and variance equality, thereby allowing the use of parametric analysis of variance and regression methods and an estimation of required sample size.

Animals↗
PubMed2001

Retinal capillary hemangioma: a comparison of sporadic cases and cases associated with von Hippel-Lindau disease.

OBJECTIVE: To report observations regarding the onset of tumors in patients with retinal capillary hemangiomas (RCH) and comparing sporadic cases with those associated with von Hippel-Lindau (VHL) disease. DESIGN: Retrospective consecutive case series. PARTICIPANTS: Sixty-eight patients with RCH managed at a tertiary referral center. MAIN OUTCOME MEASURES: The data were analyzed for age at diagnosis of RCH, two-hit mutation model, onset of new tumors, and random (Poisson) distribution. RESULTS: Among 68 patients, we identified 174 RCHs in 86 eyes. Thirty-one patients had VHL disease, and 37 patients were sporadic. The median age at diagnosis in cases with VHL disease was 17.6 years (range, 2.8-46.7 years), and in those without VHL disease it was 36.1 years (range, 7.0-74 years). The age distribution of RCH followed a two-hit mutation model. In eyes with VHL disease, the total number of RCH were distributed randomly as calculated by the Poisson distribution (mean number of tumors = 4). Overall onset of 33 new tumors was documented in 11 eyes (13%) over a median interval of 16 months (range, 3-235 months). All new tumors developed before the age of 47 years. The retinal location of new tumors was similar to the previous tumors with most new tumors located in the superotemporal quadrant (42%) and in the midperipheral retina (58%). Of the 50 patients initially manifesting solitary RCH, only 4 had new tumors develop over a median follow-up duration of 6.4 years (range, 0-33 years). All four cases had VHL disease. CONCLUSIONS: The median age at diagnosis of RCH in patients with VHL disease was almost 18 years less than those without VHL disease. The age distribution of RCH followed the two-hit mutation model. In VHL disease, the number of RCH is determined randomly. Most of the new RCH develop by the age of 47 years. In the absence of VHL disease, it is unlikely for patients with solitary RCH to develop new tumors.

Adolescent↗
PubMed1978

Statistical aspects of the treponemal counts in the TPI test.

A method of counting treponemes in randomly selected visual fields is described. It was found that Treponema pallidum is distributed as a Poisson distribution among the visual fields and also among samples drawn from the same suspension. Immobilized treponemes are binomally distributed among the total number of treponemes. Application of the parameters of the Poisson and the binomial distributions should be made in order to determine the dosage of T. pallidum in animal experimentation and to evaluate the outcome of the TPI test. Some statistical aspects of the investigation of treponemal survival are presented.

Probability↗
PubMed1995

[Use of the micronucleus test for biological dosimetry in cases of homogeneous or non-homogeneous exposure to ionizing radiations].

The dose effect relationship after homogeneous irradiation and the effect on the Poisson distribution of adding non-irradiated blood and thereby simulating non homogenous accidental exposure were studied for dicentric aberrations and micronuclei in lymphocytes exposed in vitro to 60Co gamma irradiation. The dose effect relationship for both parameters was of the linear quadratic type with the micronuclei responding slightly less to radiation than the dicentrics but a greater number of cells can easily be screened for micronuclei than for dicentrics. Except for one dose level in micronuclei, no deviations from the Poisson distribution were observed, after homogeneous tradition, but such a deviation was evident when non-irradiated blood was added to the irradiated one. With the help of the method of the "contaminated Poisson distribution" the proportion as well as the dose of the exposed blood could be approximately estimated. In order to test the suitability of the micronucleus test in vivo, both dicentrics and micronuclei were determined in patients treated for seminoma to an abdominal field. The data showed a consistent increase in both parameters without a significant difference between patients. The increase of both types of anomalies corresponded about to that expected from the size of the field exposed. The data from micronuclei appear, therefore, about as reliable for biological dosimetry as those from dicentrics for biological dosimetry after homogeneous and non-homogeneous exposure to ionizing radiations.

Adult↗
PubMed1995

Somatic intrachromosomal homologous recombination events in populations of plant siblings.

Intrachromosomal homologous recombination in whole tobacco plants was analyzed using beta-glucuronidase as non-selectable marker. We found that recombination frequencies were additive for transgenes in allelic positions and could be enhanced by treatment of plants with DNA-damaging agents. We compared the patterns of distribution of recombination events of different transgenic lines of tobacco and Arabidopsis with the respective Poisson distributions. Some lines showed Poisson-like distributions, indicating that recombination at the transgene locus was occurring in a random fashion in the plant population. In other cases, however, the distributions deviated significantly from Poisson distributions indicating that for specific transgene loci and/or configurations recombination events are not randomly distributed in the population. This was due to overrepresentation of plants with especially many as well as especially few recombination events. Analysis of one tobacco line indicated furthermore that the distribution of recombination events could be influenced by treating the seedlings with external factors. Our results suggest that different plant individuals, or parts of them, might exhibit different transient 'states' of recombination competence. A possible model relating 'recombination silencing' and transcription silencing to heterochromatization of the transgene locus is discussed.

Arabidopsis↗
PubMed1998

Aggregated parasite distributions on hosts in a homogeneous environment: examining the Poisson null model.

Parasites are typically aggregated on their hosts in nature. The null hypothesis is that parasites should follow a Poisson distribution if environment, parasites and hosts are homogeneous. From this starting point, models have shown that factors such as heterogeneity in host susceptibility and spatial aggregations of parasites may cause parasite aggregations on hosts. I used computer simulations to show that parasites typically become aggregated on their hosts even in a homogeneous environment where parasites do not differentially prefer any host, and hosts do not differ in susceptibility, provided that hosts are randomly distributed and spatial distance between host and parasite influences the likelihood of colonisation.

Animals↗