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PubMed1997

Short- and long-term multilineage repopulating hematopoietic stem cells in late fetal and newborn mice: models for human umbilical cord blood.

Blood from late fetal and newborn mice is similar to umbilical cord blood obtained at birth in human beings, an important source of stem cells for clinical transplantation. The mouse model is useful because long-term functions can be readily assayed in vivo. To evaluate the functions of hematopoietic precursors in the blood and other tissues of late fetal and newborn mice, short- and long-term multilineage repopulating abilities were measured in vivo by competitive repopulation. Manipulations that might affect cell function, such as enrichment, tissue culture, or retroviral marking, were avoided. Hematopoietic stem cell functions of late fetal or newborn blood, liver, and spleen, were assayed as myeloid and lymphoid repopulating abilities relative to standard adult marrow cells. Donor cells from these tissues as well as adult control donor marrow cells were all of the same genotype. Cells from each donor tissue were mixed with portions from a pool of standard adult "competitor" marrow distinguished from the donors by genetic differences in hemoglobin and glucosephosphate isomerase. After 21 to 413 days, percentages of donor type myeloid and lymphoid cells in recipient blood were measured to assay the functional abilities of donor precursors relative to the standard. These relative measures are expressed as repopulating units, where each unit is equivalent to the repopulating ability found in 100,000 standard adult marrow cells. Thus, measures of repopulating units do not compare single cells but overall repopulating abilities of donor cell populations. Relative functional abilities in 1 million nucleated cells from late fetal or newborn blood were several times less than those found in adult marrow, but far more than in normal adult blood, and appeared to include long-term functional primitive hematopoietic stem cells (PHSC) similar to those in marrow. To estimate functional abilities of individual PHSC, variances among large groups of identical recipients were analyzed using both the binomial model and competitive dilution, a new model based on the Poisson distribution. The data best fit the hypothesis that individual PHSC from adult marrow, late fetal blood, or newborn blood each produce similar fractions of the total lymphoid and erythroid cells found in the recipient for many months.

Animals↗
PubMed1997

A technique for quantitation of protein deposits on rigid gas permeable contact lenses.

PURPOSE: The purpose of this study was to develop a method for quantitating protein on rigid gas permeable (RGP) lenses and apply it to worn lenses. METHODS: We built a video microscope and wrote software to measure light absorbance by contact lenses before and after protein staining with Coomassie brilliant blue. We corrected for the temporal stability and spatial uniformity of the system, and set the iris aperture so that both lens surfaces could be simultaneously focused. We examined four RGP lens types worn by 22 patients. Standard curves were prepared with plastic discs spiked with dialyzed Coomassie blue-stained bovine serum albumin. RESULTS: The method was linear (R2 = 0.99) from 14 to over 100 microg protein per image and independent of dioptric power from -6 to +14 diopters. Protein quantities on worn Equalens II, Advent, Quantum II, and Fluoroperm 92 lenses were not significantly different (123 +/- 36, 111 +/- 28, 110 +/- 23, and 83 +/- 15 microg/lens; means +/- SEMs, P > 0.7). Patients differed (P < 0.05) in protein deposition, independently of lens type, and fit a Poisson distribution. DISCUSSION: The method is adequate for quantitating protein on RGP lenses or for examining the efficacy of cleaning regimens or care systems. However, because of the non-Gaussian distribution of patient protein deposits, paired or cross-over experimental design and testing is recommended for studying protein deposition in clinical trials.

Animals↗
PubMed1997

[Cancer risk in asbestos-cement industry workers in Poland].

A cohort study was carried out in order to evaluate the cancer risk in the asbestos-cement industry workers. The cohort consisted of workers employed in four asbestos-cement plants. One of those plants was established in 1924, the other three in the 1960s and 1970s. Currently only two of these plants continue their production. The plants used mainly chrysotile asbestos as well as crocidolite and amosite. Amphibolite asbestos was used before the mid-nineteen eighties in production of pressure pipes utilising about 15% of the total quantity of asbestos used. The measurements of the asbestos fibre concentration at work-sites have been taken occasionally since the mid 1980s, thus, the determination of a cumulative dose for individual persons in the cohort and the evaluation of the dose-effect relationship were not feasible. It could only be supposed that the concentrations at the preparatory work-site during first years of the plants' operation accounted for several tens fibres/cm3 in the production that employed the dry method. The cohort consisted of workers employed in the plant for at least three months between beginning of the plant during the post-war period, and 1980, that is during the period when amphibolite asbestos was in use. The retrospective observation was completed on 31 December 1991. The analysis of the death risk by causes was based on a standardized mortality ratios (SMRs) calculated using the person-years method. Statistical significance of SMRs was assessed by means of Poisson distribution one-sided test. The general population of Poland was used as the reference population to estimate the death risk. The cohort comprised 4,712 persons (3,563 males and 1,149 females). Of this number 4,500 persons (3,405 males and 1,095 females) were followed. The cohort availability were 95.5%. Male mortality, both total (473 deaths; SMR = 83) and due to malignant neoplasms (108 deaths; SMR = 86) was lower than in the general population. An excess of deaths from neoplasm of the pleura was by about 23 times higher (5 deaths; SMR = 2,288) and from neoplasm of the large intestine by two times higher (7 deaths; SMR = 214). Among females (41 deaths; SMR = 50) death risk was lower than in the reference population. At a low level of total mortality from neoplasms (13 deaths; SMR = 52) a statistically significant excess of deaths from neoplasm of the pleura (2 deaths; SMR = 2,112) was observed. In the plants investigated the analysis revealed a considerably diversified mortality from asbestos-related neoplasms. The incidence of pleura mesothelioma should be attributed to the use of considerable quantities of crocidolite asbestos and high concentrations of fibres in the air in plants II and IV, particularly during the first years after their establishment. In view of a long period of latency the excess of this neoplasm can be expected till 2020.

Aged↗
PubMed2006

The Gamma-Poisson model as a statistical method to determine if micro-organisms are randomly distributed in a food matrix.

The Gamma-Poisson model, i.e., a Poisson distribution where the parameter lambda is Gamma distributed, has been suggested as a statistical method for determining whether or not micro-organisms are randomly distributed in a food matrix. In this study, we analyse the Gamma-Poisson model to explore some of the properties of the Gamma-Poisson model left unexplored by the previous study. The conclusion of our analysis is that the Gamma-Poisson model distinguishes poorly between variation at the Poisson level and the Gamma level. Estimated parameter values from simulated data-sets showed large variation around the true values, even for moderate sample sizes (n=100). Furthermore, at these sample sizes the likelihood ratio is not a good test statistic for discriminating between the Gamma-Poisson distribution and the Poisson distribution. Hence, to determine if data are randomly distributed, i.e., Poisson distributed, the Gamma-Poisson distribution is not a good choice. However, the ratio between variation at the Poisson level and the Gamma level does provide a measure of the amount of overdispersion.

Computer Simulation↗
PubMed2005

Responder cell frequency estimation and binomial three-level nonlinear mixed effects model in limiting dilution assays.

Responder cell frequencies (RCF), which describe vaccine-boosted immune responses in herpes zoster (HZ) prevention studies, have been estimated by using limiting dilution assays (LDA). The theoretical linearity assumption between the logarithm of the proportion of nonresponding wells (s) and the cell concentration (N) (or dilution level) in LDA, based on the single-hit Poisson model, is often violated with observed data resulting in biased estimates of RCF. In this article, the Poisson assumption is modified by applying a mixture of Poisson and gamma distributions, resulting in a negative binomial assumption, which presents a better fit between s and N. In LDA for HZ prevention studies, binary responses (responder or non-responder wells) are measured repeatedly at different cell concentrations and over time. To account for the correlation between responses to varying dilution levels from individuals, and the correlation between repeated assays of individuals over time simultaneously, a binomial three-level nonlinear mixed-effects model is proposed. For parameter estimation, a maximum likelihood method is applied via adaptive Gaussian quadrature. There is a lack of non-Gaussian multilevel nonlinear mixed-effects software, which can execute such a complicated fit. In this article, an algorithm for the three-level nonlinear mixed-effects model, which can be inserted into the code in the SAS procedure NLMIXED, is suggested.

Cell Count↗
PubMed2005

A comparative study of a theoretical neural net model with MEG data from epileptic patients and normal individuals.

OBJECTIVE: The aim of this study was to compare a theoretical neural net model with MEG data from epileptic patients and normal individuals. METHODS: Our experimental study population included 10 epilepsy sufferers and 10 healthy subjects. The recordings were obtained with a one-channel biomagnetometer SQUID in a magnetically shielded room. RESULTS: Using the method of x2-fitting it was found that the MEG amplitudes in epileptic patients and normal subjects had Poisson and Gauss distributions respectively. The Poisson connectivity derived from the theoretical neural model represents the state of epilepsy, whereas the Gauss connectivity represents normal behavior. The MEG data obtained from epileptic areas had higher amplitudes than the MEG from normal regions and were comparable with the theoretical magnetic fields from Poisson and Gauss distributions. Furthermore, the magnetic field derived from the theoretical model had amplitudes in the same order as the recorded MEG from the 20 participants. CONCLUSION: The approximation of the theoretical neural net model with real MEG data provides information about the structure of the brain function in epileptic and normal states encouraging further studies to be conducted.

Epilepsy↗
PubMed1981

Bacterial density in water determined by poisson or negative binomial distributions.

The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different locations and over time were illustrated by two examples. In cases where the negative binomial distribution was appropriate, a procedure was given for characterizing the variability by dividing the bacterial counts into homogeneous groups. The usefulness of this procedure was illustrated for the second example based on survey data for Lake Erie. A further illustration of the difference between results based on the Poisson and negative binomial distributions was given by calculating the probability of obtaining all samples sterile, assuming various bacterial densities and sample sizes.

Journal Article↗
PubMed1995

The distribution of rare alleles.

Population geneticists have long been interested in the behavior of rare variants. The definition of a rare variant has been the subject of some debate, centered mainly on whether alleles with small relative frequency should be considered rare, or whether alleles with small numbers should be. We study the behavior of the counts of rare alleles in samples taken from a population genetics model that allows for selection and infinitely-many-alleles mutation structure. We show that in large samples the counts of rare alleles--those represented once, twice, ...--are approximately distributed as a Poisson process, with a parameter that depends on the total mutation rate, but not on the selection parameters. This result is applied to the problem of estimating the fraction of neutral mutations.

Alleles↗
PubMed2005

Intraresidue distribution of energy in proteins.

Boltzmann-like distributions appear in many properties and energy-related quantities of proteins. A few examples are hydrophobicity, various types of side-chain/side-chain interactions, proline isomerization, hydrogen bonds, internal cavities, interactions at the level of specific atom types, and the propensity of the phi/'phi' ratio. Here, we conjecture that the Boltzmann hypothesis also holds for the intra-residue energy distribution. We confirm the conjecture by calculating the energies of 41,672 residues of the structures of highly resolved proteins, where at least 12 out of 20 naturally occurring amino acids follow Boltzmann's law. We further examine the entire set of all residue energies and find that the convolution of the individual distributions gives a Poisson function, which is followed by approximately 50% of individual proteins' structures.

Amino Acids↗
PubMed2002

Statistical methods for analysing discrete and categorical data recorded in performance analysis.

In this paper, we identify appropriate statistical methods for analysing categorical differences in discrete variables or 'performance indicators' resulting from performance analysis. The random mechanisms associated with discrete events do not follow a normal distribution; that is, the normal distribution is a continuous not a discrete probability distribution. We propose appropriate statistical methods based on two key discrete probability distributions, the Poisson and binomial distributions. Two approaches are proposed and compared using examples from notational analysis. The first approach is based on the classic chi-square test of significance (both the goodness-of-fit test and the test of independence). The second approach adopts a more contemporary method based on log-linear and logit models fitted using the statistical software GLIM. Provided relatively simple one-way and two-way comparisons in categorical data are required, both of these approaches result in very similar conclusions. However, as soon as more complex models or higher-order comparisons are required, the approach based on log-linear and logit models is shown to be more effective. Indeed, when investigating those factors and categorical differences associated with binomial or binary response variables, such as the proportion of winners when attempting decisive shots in squash or the proportion of goals scored from all shots in association football, logit models become the only realistic method available. By applying log-linear and logit models to discrete events resulting from notational analysis, greater insight into the underlying mechanisms associated with sport performance can be achieved.

Humans↗
PubMed2006

Generalized additive modeling with implicit variable selection by likelihood-based boosting.

The use of generalized additive models in statistical data analysis suffers from the restriction to few explanatory variables and the problems of selection of smoothing parameters. Generalized additive model boosting circumvents these problems by means of stagewise fitting of weak learners. A fitting procedure is derived which works for all simple exponential family distributions, including binomial, Poisson, and normal response variables. The procedure combines the selection of variables and the determination of the appropriate amount of smoothing. Penalized regression splines and the newly introduced penalized stumps are considered as weak learners. Estimates of standard deviations and stopping criteria, which are notorious problems in iterative procedures, are based on an approximate hat matrix. The method is shown to be a strong competitor to common procedures for the fitting of generalized additive models. In particular, in high-dimensional settings with many nuisance predictor variables it performs very well.

Biometry↗
PubMed2001

Estimation of the average burst size of Phix174 am3, cs70 for use in mutation assays with transgenic mice.

In mutation assays using transgenic mice, with recoverable vectors such as PhiX174 am3, cs70, mutations originate from two sources: (1) in vivo mutations, that is, mutations that were fixed in the mouse, or (2) ex vivo mutations, that is, mutations that were fixed during recovery or plating. When a bacteriophage infects a bacterium, it multiplies and bursts the cell, releasing a number of phages referred to as the burst size. Our method for distinguishing between in vivo mutations and ex vivo mutations estimates the average number of bursts, the denominator of in vivo mutant frequencies, by dividing the total plaque-forming units (PFU) by the average number of phages in a burst. Herein, we outline a probability model relating observed plaque counts to the burst size and present the statistical method used to estimate the burst size. The average size of a single burst from nonrevertant phages was estimated in eight studies under the conditions of our mutation assay. The average burst size was stable across studies at 182.5 plaques per burst (standard error, 14.25). The probability that a burst is a specific size was approximated by a negative binomial distribution, which implies a Poisson-Pascal distribution for the observed plaque counts. The observed plaque counts were adequately fit by this approximation. Environ. Mol. Mutagen. 37:356-360, 2001 Published 2001 Wiley-Liss, Inc.

Animals↗
PubMed1969

Exclusion of protein from high polymer media. I. Derivation of probability distribution for the number of fiber centers within any sphere of radius r.

Ogston's (1958) fiber model based on Poisson's distribution function gives the average number of fibers making contact and no contact inside a sphere of radius r. The probability of penetration of spherical particles within a fibrous network was derived from the moment generating function [Formula: see text] A is the number of particles that intrude into a sphere of radious r. alpha(mu) is the probability that a particle, whose center is mu units away from the origin, intrudes into a sphere of radius r. A has a Poisson distribution with a mean value E(A) = 4pinualpha(mu)mu(2)dmu. The theoretical derivation of the distribution function of A gives Ogston's fiber model.

Biological Transport↗
PubMed1984

Relation between structural and release parameters at the frog sensory-motor synapse.

The sensory-motor synaptic connexions in the frog lumbar cord have been used to examine the relationship between the statistical characteristics of the unitary excitatory post-synaptic potential (e.p.s.p.) and the number and organization of synaptic contacts determined when the primary afferent fibre used in evoking the e.p.s.p., and a motoneurone in which it was recorded, were both labelled with horseradish peroxidase (HRP). A significant correlation is found between the number of contacting boutons and the amplitude of the chemical component of the unitary e.p.s.p.s generated at the same connexions. The amplitude fluctuation patterns of the single-fibre e.p.s.p.s could be fitted by both Poisson and binomial distribution. The number of presumed Poisson release sites as estimated from the ratio Vmax/v (where Vmax is the maximal amplitude of the chemical component of e.p.s.p. and v is quantal size) is always less than or equal to the total number of boutons observed histologically. In three connexions there was a close correspondence between the number of binomial release units, n, and the number of contact regions formed by the tight clusters of contacting boutons. The unit potential amplitude estimated from the Poisson distribution is found to be two to three times smaller than the quantal size calculated from binomial distribution. A similar numerical relationship was found between the number of contacting boutons and the number of contact regions. It is suggested that at a single bouton, transmission results in release of a single quantum of transmitter, whereas the binomial quantum probably reflects the multi-quantal release occurring simultaneously at boutons comprising a contact region. A significant correlation is found between the mean quantum content estimated either from Poisson or binomial distribution and the number of contacting boutons and contact regions respectively, indicating the dependence of quantal release on the magnitude of synaptic surface. No correlation is found between the motoneuronal soma diameter and the quantal size, although the former is significantly correlated with the number of contacting boutons.

Action Potentials↗
PubMed2001

Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks.

The statistical aggregation of parasites among hosts is often described empirically by the negative binomial (Poisson-gamma) distribution. Alternatively, the Poisson-lognormal model can be used. This has the advantage that it can be fitted as a generalized linear mixed model, thereby quantifying the sources of aggregation in terms of both fixed and random effects. We give a worked example, assigning aggregation in the distribution of sheep ticks Ixodes ricinus on red grouse Lagopus lagopus scoticus chicks to temporal (year), spatial (altitude and location), brood and individual effects. Apparent aggregation among random individuals in random broods fell 8-fold when spatial and temporal effects had been accounted for.

Animals↗