SEARCH · PubMed Health
Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Explore the source record for details and available documents.
We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.
When analyzing Poisson-count data sometimes a lot of zeros are observed. When there are too many zeros a zero-inflated Poisson distribution can be used. A score test is presented to test whether the number of zeros is too large for a Poisson distribution to fit the data well.
Frailty models are often used to model heterogeneity in survival analysis. The most common frailty model has an individual intensity which is a product of a random factor and a basic intensity common to all individuals. This paper uses the compound Poisson distribution as the random factor. It allows some individuals to be non-susceptible, which can be useful in many settings. In some diseases, one may suppose that a number of families have an increased susceptibility due to genetic circumstances. Then, it is logical to use a frailty model where the individuals within each family have some shared factor, while individuals between families have different factors. This can be attained by randomizing the Poisson parameter in the compound Poisson distribution. To our knowledge, this is a new distribution. The power variance function distributions are used for the Poisson parameter. The subsequent appearing distributions are studied in some detail, both regarding appearance and various statistical properties. An application to infant mortality data from the Medical Birth Registry of Norway is included, where the model is compared to more traditional shared frailty models.
The generalized Poisson distribution is a distribution which approximates various forms of mixtures of Poisson distributions. The mean and variance of the generalized Poisson distribution, which are simple functions of the two parameters of the distribution, are more useful than the original parameters in test data analysis. Therefore, we adopted two types of transformations of parameters. The first model has new parameters of mean and standard deviation. The second model contains new parameters of mean and variance/mean. An example indicates that the transformed parameters are convenient to understand the properties of data.
Use of the Poisson distribution to estimate the quality of random mixtures was evaluated as a measure of the highest attainable degree of dose uniformity of tablets. Ingredient A was assumed to have a large particle size as compared to diluent B. In contrast to the more precise binomial distribution, for the simple Poisson approach no experiments are necessary to investigate the mean proportions of the apparent volume, av and bv, which A and B assume within the powder samples in the die. The range of volume ratios was defined where the Poisson distribution is valid. Accepting an error of 5% of the random content variation of A per sample, av may amount to up to 0.1 (10%). In terms of the proportion by mass of A, a, this range is wider, and commonly of the order of 0.2 or higher. This approach was tested with tablets prepared from mixtures of coarse sucrose A and a fine Avicel/talc diluent B at A:B (m:m) ratios from 10:90 to 50:50. Even with the 30:70 tablets, the variations of the sucrose content were still in good agreement with the content variations of the random mixtures as estimated from the Poisson distribution. Estimates of the 50:50 ratio, however, deviated from the Poisson distribution.
A method was devised that employs deviations from the Poisson distribution to analyze the spatial arrangement of neurons and glia in human cerebral cortex. A field of randomly distributed points equal in number of a sample field of neuronal or glial cells is generated by computer, and the proportion of cells in the sample field that are closer to the nearest neighboring cells than to the nearest randomly distributed point is determined. We call this proportion the "Poisson ratio." When the cells are randomly distributed, the Poisson ratio is equal to 0.5. If the Poisson ratio is less than 0.5, the cells are farther away from one another than a random distribution would predict (exclusionary pattern); if the Poisson ratio is greater than 0.5, the cells are closer to one another than a random distribution would predict (clustering). A simple nonparametric statistical test is used to determine the significance of differences in the ratios. This method was applied to samples of human cerebral cortex in order to test the hypothesis that patients with schizophrenic psychosis may have an altered pattern of neuronal clustering. The analysis revealed that there is no difference in the nearest-neighbor distribution of either neurons or glia between psychotic patients and controls. It was found, however, that there is a highly significant difference in the spatial distribution of neurons versus glia in human cerebral cortex. Neurons of layers II to VI in the human cortex show greater-than-expected distances among them and are distributed according to an exclusionary pattern, while neurons in layer I show a clustering pattern.(ABSTRACT TRUNCATED AT 250 WORDS)
The value of Poisson distribution theory in describing and predicting the nature of sperm-egg interaction in vitro has been investigated using an interspecific in-vitro fertilization system, incorporating zona-free hamster oocytes and human spermatozoa. The frequency distribution of polyspermic oocyte penetrations in 72 experiments exhibited good agreement with the Poisson distribution at all levels of fertilization indicating that each oocyte must be of equal penetrability and that there can be no block to polyspermy in this interspecific system. Poisson distribution theory also accurately described the relationship between oocyte penetration and sperm motility in 50 out of 54 separate experiments spread across 10 serial dilution curves. For each dilution series the shape of the fitted curve was fixed but its location along the x-axis varied from donor to donor. The fixed nature of the relationship between sperm motility and egg penetration enables the results of such in-vitro fertilization experiments to be corrected for the number of motile spermatozoa in the incubation media. On the basis of these findings a protocol is described for assessing the results of the zona-free hamster oocyte penetration assay, which involves analysis of the degree of polyspermy followed by the application of Poisson distribution theory to correct the results to a standard concentration of motile spermatozoa. Changes in the penetrating ability of human spermatozoa after vasectomy and characterization of the degree of inter-ejaculate variation in penetrating potential are two clinical examples of such analyses given in the text. The statistical methods described in this paper should also be of general relevance to the study of fertilization mechanisms, in providing a rationale by which to analyse the quantitative nature of sperm-egg interaction in vitro.
PURPOSE: The current chromosomal biodosimetry system is practically limited to the estimation of equivalent whole-body dose in the low or moderate dose range. To circumvent this problem, a new dosimetry system was developed which was effective over a wide dose range and dose gradient. MATERIALS AND METHODS: In order to establish a quantitative formalism of a comprehensive dose-response kinetics, chromosome aberration frequencies were studied in human peripheral blood lymphocytes irradiated in vitro with gamma-rays in a dose range of 0.01-50Gy. Using the dose-yield relationship thus established, a new model of biodosimetry was developed which involved unfolding the chromosome aberration distribution into a mixed Poisson distribution and thence into a dose-distribution profile. The model was then tested with chromosome aberration data in lymphocytes irradiated in vitro, simulated partial body irradiation, accidental radiation exposure, therapeutic local irradiation and protracted exposure by internal deposit of Thorotrast. RESULTS: The dose-yield relations over a wide dose range fit satisfactorily a multiparametric dose-response curve, which included the first approximation kinetics of linear-quadratic dose-response and its distortion by mutual interference among multiple breaks on a chromosome arm. The unfolding strategy using these dose-response kinetics was successfully applied to the various types of radiation exposures; the reconstructed dose profile showing a sharp unimodal peak for moderate or high doses of gamma-rays in vitro irradiation, broadening for high-linear energy transfer radiation, discrimination of doses in the mixed culture of irradiated and unirradiated blood, and reasonable dose distribution for the in vivo exposures. CONCLUSION: A novel biodosimetry system was developed. The system is innovative in that it provides information not only on the macroscopic dose inhomogeneity, but also on the microscopic spectrum of doses stemming from the variability of energy transfer by charged particles as well as the multiple ionization events to which the target cell nucleus is exposed.
Earlier reports indicated that sperm from 25% of patients from infertile couples, but not from normal or fertile donors, show deviations from the theoretical Poisson distribution of the number of sperm penetrating zona-free hamster ova. Using semen samples from 15 grandfathers (aged 60 to 84 years) and 24 young fathers (aged 25 to 36 years), this study analyzed whether age also has an effect on the distribution. It was found that the overall fit to the Poisson distribution of the samples from grandfathers was very poor; in contrast, the samples from young fathers fit well. The observed deviations from the Poisson distribution among grandfathers may be a consequence of their long periods of sexual abstinence. Decrease in sexual activity produces age-different populations of sperm that probably differ in penetrating ability. Samples from older fathers also show a worse fit to the Poisson distribution than do those from younger fathers. These results suggest that the duration of sperm storage in the genital tract after maturation has an effect on sperm function.
In dental epidemiological studies, an analysis of variance assuming a normal distribution is commonly used to compare caries indices, which are often not normally distributed. As these indices represent discontinuous data, it would be preferable to use the negative binomial or the Poisson distribution. In this study, in order to compare the DMFS indices of adults working in the confectionery manufacturing industry in France, the results of the generalised linear model obtained using the normal and the Poisson distribution with identity or log built-in link function were compared. The negative binomial distribution was not used because it is very often unavailable in the most used statistical software. Analysis of the caries indices showed that the use of the normal distribution could lead to an incorrect interpretation of the data. Therefore it is concluded that the generalised linear model with Poisson distribution and over dispersion is to be preferred when comparing caries levels.
The common and convenient assumption in accident count analysis, that accidents are Poisson-distributed, is reexamined. Two statistical tests, for evaluating the assumption are described and compared. It is shown that a test based upon a combinatorial analysis is much more accurate than the alternative chi-square test when accident counts are expected to be small. The more accurate test is used to reinterpret data on accident count variability, the results indicating that the Poisson distribution is appropriate for the analysis of accidents at individual sites.
By using a generalization of the Poisson process, distributions can be constructed that show appropriate amounts of underdispersion relative to the Poisson distribution that may be apparent from observed data. These are then used to examine the differences between the distributions of numbers of fetal implants in mice corresponding to different doses of the herbicide 2,4,5-T.
Since 1980 the German Children's Cancer Registry has documented all childhood malignancies in the Federal Republic of Germany. Various statistical procedures have been proposed to identify municipalities or other geographic units with increased numbers of malignancies. Usually the Poisson distribution, which requires the malignancies to be distributed homogeneously and uncorrelated, is applied. Other discrete statistical distributions (so-called cluster distributions) like the generalized or compound Poisson distributions are applicable more generally. In this paper we present a first explorative approach to the question of whether it is necessary to use one of these cluster distributions to model the data of the German Children's Cancer Registry. In conclusion, we find no indication that the Poisson approach is insufficient.
We have investigated the consequences of having multiple fusion complexes on exocytotic granules, and have identified a new principle for interpreting the calcium dependence of calcium-triggered exocytosis. Strikingly different physiological responses to calcium are expected when active fusion complexes are distributed between granules in a deterministic or probabilistic manner. We have modeled these differences, and compared them with the calcium dependence of sea urchin egg cortical granule exocytosis. From the calcium dependence of cortical granule exocytosis, and from the exposure time and concentration dependence of N-ethylmaleimide inhibition, we determined that cortical granules do have spare active fusion complexes that are randomly distributed as a Poisson process among the population of granules. At high calcium concentrations, docking sites have on average nine active fusion complexes.
Vital cells number (VCN) in the sampling of E. coli populations was experimentally measured and distribution histograms were obtained. In most cases distributions show considerable deviation from Poisson model. VCN distribution histograms are polymodal, dispersion/arithmetical mean ratio may essentially differ from 1. The more essential differences from Poisson distribution were observed for populations with the higher cell concentration. Computer simulation of the VCN histograms indicated that additional parameters (such as those describing cellular interaction of different nature and/or other factors that influence random behaviour of cells) should be introduced into Poisson model to explain observed variations in VCN distribution histograms.
An example of the use of the truncated Poisson distribution in an immunogold assay of dystrophin, a gene product of importance in the study of muscular dystrophies, is presented. The practical benefit of using minimum variance unbiased estimators of relevant functions of the parameter of the distribution is considered.
Transgenic mutation assays generally use mutant frequencies to estimate mutation frequencies but the degree to which clonal expansion inflates mutant frequencies is largely unknown. Mutant frequency is defined as the fraction of cells carrying mutations in the gene of interest and, according to the standard Big Blue protocol, is determined by dividing the number of mutant plaques by the total number of plaques screened. Mutation frequency is determined as the fraction of cells carrying definitely independent mutations and therefore requires correction for clonal expansion. Mutant and mutation frequencies were determined for brain, thymus and male germ cells of four mice from two age groups (3-versus 10-month old). The mutant frequency in thymus differed significantly between 3- and 10-month old mice (P < 0.05). By sequencing all mutants, the mutation frequency (i.e., corrected for jackpot mutations) in thymus was determined and was not significantly different between 3- and 10-month old mice. Mutant frequency does not fit a Poisson distribution, but mutation frequency corrected for jackpot mutations is substantially less variable and does fit a Poisson distribution.