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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↗

PubMed1961

Localization of macromolecules in Escherichia coli. I. DNA and proteins.

If thin sections of Escherichia coli, labeled uniformly with tritium, are radioautographed calculations, based on the distribution of section sizes show that the number of H(3) decays per section should be very close to a Poisson distribution. We might, therefore, expect that the distribution of radioautographic grain counts among random cross-sections should follow a Poisson distribution. It can then be inferred that a deviation from a Poisson indicates a high concentration of label in a preferred region. This region can then be identified by analysis of serial section and comparison with electron micrographs. Sections of cells labeled with leucine-H3 gave a Poisson distribution of grain counts, and it was concluded that proteins were distributed fairly uniformly throughout the cell. The situation was not changed if labeled cells were placed in chloramphenicol or if very short pulses of label were used. When Escherichia coli is grown in presence of chloramphenicol a major morphological change concerns the nuclear region: it becomes more regular in outline, nearly spherical, and occupies a smaller proportion of the cell length. The previously described association between DNA labeled with thymidine-H3 and the nuclear region was confirmed by showing that the distribution of the label in the cell followed exactly the morphological changes of the nuclear region. It was also shown that the concentration of DNA in the nuclear region was at least 45 times higher than that of the cytoplasm. Several morphological features of cells grown in chloramphenicol and examined in the electron microscope are discussed.

Autoradiography↗

PubMed1962

On the increase of sites for chromosome exchange formation after chromosome duplication.

Although radiation-induced chromosome exchanges are not distributed among cells according to a Poisson distribution, chromatid interchanges are. In Vicia faba the lack of fit to a Poisson distribution has been attributed to the occurrence of only two sites per cell where the chromosomes are close enough to form exchanges if broken. When chromatid aberrations are induced, after chromosomal duplication, the number of sites more than doubles.

Chromatids↗

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↗

PubMedDate not supplied

The expanded application of most probable number to the quantitative evaluation of extremely low microbial count.

This paper is about the evaluation of the extremely low microbial counts from the field by expanding the most probable number (MPN) methodology when the data follow Poisson distribution in order to achieve more accurate estimation with limited number of data. Several data sets with extremely low microbial counts from pharmaceutical clean room and laboratory clean bench monitoring were found with good Poisson distribution fitness by chi2 test (P < 0.05), and the MPN calculations were conducted for these data by using the Halvorson and Ziegler equation. The MPN values are generally larger than the arithmetic average, indicating a higher sensitivity of the data assay. This approach is justified because Poisson distribution is the mathematical background of the MPN procedure, with the Halvorson and Ziegler equation as its foundation. It is considered that the MPN methodology has a potential application for quality control in the extremely low level microbial counting environment in the clean rooms levels ISO class 7 or above. Further studies on the precision of this method and development of a sampling plan based on careful mathematical analysis will help to refine the approach.

Air Microbiology↗

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↗

PubMed2005

Statistical evaluation for detection of peptide specific interferon-gamma secreting T-cells induced by HIV vaccine determined by ELISPOT assay.

Interferon-gamma (IFN-gamma) secreting T-cells play an important role in immunodeficiency virus (HIV) disease pathogenesis. A common technique to determine the efficacy of the HIV vaccines in murine models is to compare the number of IFN-gamma secreting T-cells induced by HIV vaccine to a control group. The measurement of IFN-gamma secreting T-cells relies on an ELISPOT assay. This assay is carried out in triplicate wells from the same mouse on the same ELISPOT plate. The numbers of spot forming cells (SFC) from these wells are correlated counts. Traditionally, simple statistical methods, such as ANOVA or Kruskall-Wallis tests, are performed on means by mouse. These approaches ignore the fact that the data are correlated counts. Count data are usually assumed to follow the Poisson distribution. However, some count data exhibit overdispersion that can affect the test statistics. The negative binomial distribution is an alternative to the Poisson distribution in the presence of overdispersion. Hence, negative binomial regression is a more suitable approach for overdispersed count data. In this study, we used a negative binomial regression to determine that IL-12 was a good adjuvant. The results of the study using a negative binomial regression are discussed.

AIDS Vaccines↗

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↗

PubMed2004

Assessment by monte carlo simulation of thermodynamic correlation of retention times in dual-column temperature programmed comprehensive two-dimensional gas chromatography.

The correlation of retention times in comprehensive two-dimensional gas chromatography caused by correlation of enthalpy and entropy changes between two stationary phases, methylsilicone and poly(ethylene glycol), was examined using commercial GC software and in-house Monte Carlo simulation. The enthalpy change, deltaH0, and entropy change, deltaS0, of 93 compounds were predicted from isothermal one-dimensional gas chromatograms predicted by the software. These values then were mimicked by Monte Carlo simulation, which removed the strong correlation of deltaH0 and modest correlation of deltaS0 between the two phases. Retention times in a comprehensive two-dimensional gas chromatogram (GC x GC) and in simulations of it were predicted for typical dual-capillary temperature-programmed conditions using the actual, correlated values of deltaH0 and deltaS0 and their uncorrelated Monte Carlo counterparts, respectively. The uncorrelated deltaH0 and deltaS0 values caused the retention-time range of the simulations' second dimension to expand substantially beyond that in the GC x GC. Other simulations were developed using a restricted range of uncorrelated deltaH0 and deltaS0 values to mimic more closely the retention-time range of the GC x GC's second dimension. The intervals between nearest neighbor retention-time coordinates were calculated in both the latter simulations and the GC x GC. The intervals were larger in the simulations than in the GC x GC because the former contained uncorrelated coordinates and the latter contained correlated ones, which clustered along or near the diagonal. The retention times in the first dimension of the GC x GC were Poisson distributed, as assessed by statistical-overlap theory. In contrast, the two-dimensional reduced retention-time coordinates in the GC x GC were not Poisson distributed, because retention times were correlated. However, the reduced retention-time coordinates in the simulations were Poisson distributed.

Journal Article↗

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↗

PubMed2006

Modeling Sage data with a truncated gamma-Poisson model.

BACKGROUND: Serial Analysis of Gene Expressions (SAGE) produces gene expression measurements on a discrete scale, due to the finite number of molecules in the sample. This means that part of the variance in SAGE data should be understood as the sampling error in a binomial or Poisson distribution, whereas other variance sources, in particular biological variance, should be modeled using a continuous distribution function, i.e. a prior on the intensity of the Poisson distribution. One challenge is that such a model predicts a large number of genes with zero counts, which cannot be observed. RESULTS: We present a hierarchical Poisson model with a gamma prior and three different algorithms for estimating the parameters in the model. It turns out that the rate parameter in the gamma distribution can be estimated on the basis of a single SAGE library, whereas the estimate of the shape parameter becomes unstable. This means that the number of zero counts cannot be estimated reliably. When a bivariate model is applied to two SAGE libraries, however, the number of predicted zero counts becomes more stable and in approximate agreement with the number of transcripts observed across a large number of experiments. In all the libraries we analyzed there was a small population of very highly expressed tags, typically 1% of the tags, that could not be accounted for by the model. To handle those tags we chose to augment our model with a non-parametric component. We also show some results based on a log-normal distribution instead of the gamma distribution. CONCLUSION: By modeling SAGE data with a hierarchical Poisson model it is possible to separate the sampling variance from the variance in gene expression. If expression levels are reported at the gene level rather than at the tag level, genes mapped to multiple tags must be kept separate, since their expression levels show a different statistical behavior. A log-normal prior provided a better fit to our data than the gamma prior, but except for a small subpopulation of tags with very high counts, the two priors are similar.

Algorithms↗

PubMed1999

Psoralen cross-linking as probe of torsional tension and topological domain size in vivo.

DNA within a cell is organized with unrestrained torsional tension, and each molecule is divided into multiple individual topological domains. Psoralen photobinding can be used as an assay for supercoiling and topological domain size in living cells. Psoralen photobinds to DNA at a rate nearly linearly proportional to superhelical density. Comparison of the rate of photobinding to supercoiled and relaxed DNA in cells provides a measure of superhelical density. For this, in vivo superhelical tension is relaxed by the introduction of nicks by either ionizing radiation or photolysis of bromodeoxyuridine in the DNA. Since nicks are introduced in a random fashion, the distribution of nicks is described by a Poisson distribution. Thus, after nicking, the fraction of topological domains containing no nicks is described by the zero term of the Poisson distribution. From measurement of the number of nicks introduced in the DNA and the fraction of torsional tension remaining, an average topological domain size can be estimated. Using this logic, procedures were designed and described for measuring supercoiling and domain size at specific sites in eukaryotic genomes.

Amanitins↗

PubMed2005

Effect of noise on defect chaos in a reaction-diffusion model.

The influence of noise on defect chaos due to breakup of spiral waves through Doppler and Eckhaus instabilities is investigated numerically with a modified Fitzhugh-Nagumo model. By numerical simulations we show that the noise can drastically enhance the creation and annihilation rates of topological defects. The noise-free probability distribution function for defects in this model is found not to fit with the previously reported squared-Poisson distribution. Under the influence of noise, the distributions are flattened, and can fit with the squared-Poisson or the modified-Poisson distribution. The defect lifetime and diffusive property of defects under the influence of noise are also checked in this model.

Artifacts↗