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PubMed1982

Quantitative studies of ovine haemonchosis. 3. The interpretation and diagnostic significance of the changes in serial egg counts of Haemonchus contortus in a sheep flock.

An examination of the level and distribution of egg counts of H. contortus within an extensively managed flock of Merino sheep in south-east Queensland was carried out on three occasions over a ten week period. During this time the geometric mean egg count increased from 527 to 1331 eggs per gram, and although 26.3% of the flock were responsible for this increase, clinical evidence of haemonchosis was not observed. Examination of the distribution of counts supported the hypothesis that counts followed a negative binomial distribution. The values obtained for "k" (the index of over-dispersion), ranged from 0.5 to 1.4. However, on the two latter examinations, counts showed a divergence from the expected pattern (P = 0.015; P = 0.014). Further examinations of flocks at higher mean levels of count are required to establish if the trend towards a more normal distribution were maintained. The evidence from the present study and from outbreaks previously reported, suggested that in extensively managed sheep, the level of variance remained high as the mean egg count increased. It therefore appeared likely that in outbreaks of acute haemonchosis under grazing conditions, only a small proportion of the flock may become seriously affected.

Animals↗
PubMed2004

Parasite aggregations in host populations using a reformulated negative binomial model.

The negative binomial distribution model is reformulated and used to demarcate a host population at a specific level of infection by defining an attribute spanning a range of parasite aggregations. The upper limit of the range specifies the boundary for the classification of the host population and provides a technique to determine the cumulative probability at any level of parasite infection to a high degree of accuracy. This approach also leads to the evaluation of the k parameter, i.e. an inverse measure of dispersion of parasite aggregation, for each fraction of the host population with a discrete level of infection. The basic mathematical premise of the negative binomial function is unaltered in developing this reformulation which was applied to data on the distribution of the trichostrongylid nematode Heligmosomoides polygyrus in populations of the field mouse, Apodemus sylvaticus.

Animals↗
PubMed1991

Binary methods for continuous outcomes: a parametric alternative.

Often a "disease" or "state of disease" is defined by a subdomain of a continuous outcome variable. For example, the subdomain of diastolic blood pressure greater than 90 mmHg has been used to define hypertension. The classical method of estimating the risk (or prevalence) of such defined disease states is to dichotomize the outcome variable according to the cutoff value. The standard statistical analysis of such risk of disease then exploits methods developed specifically for binary data, usually based on the binomial distribution. We present a method, based on the assumption of a Gaussian (normal) distribution for the continuous outcome, which does not resort to dichotomization. Specifically, the estimation of risk and its variance is presented for the one- and two-sample situations, with the latter focusing on risk differences and ratios, and odds ratios. The binomial approach applied to the dichotomized data is found to be less efficient than the proposed method by 67% or less. The latter is found to be very accurate, even for small sample sizes, although rather sensitive to substitutions of the underlying distribution by thicker tailed distributions. Canadian total cholesterol data are used to illustrate the problem. For the one-sample case, the approach is illustrated using data from a study of the arterial oxygenation of 20 patients during one-lung anesthesia for thoracic surgery. For the two-sample case, data from a prognostic study of the renal function of 87 lupus nephritic patients are used.

Binomial Distribution↗
PubMed1984

Characterization of the distribution of sister chromatid exchange frequencies: implications for research design.

Mitoses from 21 individuals were examined to characterize the within and between subjects distributions of sister chromatid exchange (SCE) frequencies. The importance of accounting for both the within subjects and between subjects variability in the design and interpretation of research is demonstrated. A computer simulation study was performed to evaluate the estimate of an individual's mean SCE rate. A power analysis was performed using our transformed descriptive data to determine the percentage difference in SCE which could be detected between two groups (with 95% probability) as a function of both the number of mitoses per individual and the number of individuals in each group. Tables are provided as guidelines. Conclusions from our work include: (1) The empirical distribution of SCEs within an individual is best described by a negative binomial distribution; (2) The predominant source of variability in baseline SCE rates is between cells within a given individual rather than between individuals and can be accounted for in experiments by counting adequate numbers of mitoses per individual; and (3) There is a systematic relationship between the mean and SD for SCEs which should be removed prior to hypothesis testing by taking either a logarithmic transformation or square root transformation of the data.

Analysis of Variance↗
PubMed1983

Statistics of the mouse bone-marrow micronucleus test: counting, distribution and evaluation of results.

The distribution of historical control results from male mice tested in the bone-marrow micronucleus test was used to optimize counting procedures and to develop decision rules for evaluating test results. The ratio of normochromatic to polychromatic erythrocytes followed a normal distribution, while the incidence of micronucleated polychromatic and normochromatic erythrocytes followed a binomial distribution. Recommendations for the number of cells to be scored per animal and for the evaluation of results are based on these distributions and the two-hypothesis multiple-decision approach of Selby and Olsen (1981).

Animals↗
PubMedDate not supplied

The epidemiology and population biology of Necator americanus infection in a rural community in Zimbabwe.

Baseline data from an epidemiological study of hookworm infection in a rural community in Zimbabwe are presented. The infection status of an age-stratified sample of the community was assessed using anthelmintic expulsion techniques. Necator americanus was the only helminth parasite found to be present. The age-prevalence and intensity profiles rose asymptotically to an adult prevalence of about 80% and adult mean burden of 7.7 worms per host. The overall mean burden was 4.8 worms per host. The frequency distribution of N. americanus was overdispersed and well described by the negative binomial distribution with a value for the aggregation parameter, k, of 0.346. Separate estimates of k were lower in males and older hosts. The distribution patterns were difficult to reconcile with any simple process of age-dependent acquisition of an effective immune response. A significant negative correlation was recorded between per caput fecundity and worm burden, providing evidence for a density-dependent regulation of female worm fecundity. The basic reproductive rate (R0 congruent to 2) was found to be similar to estimates from other geographical areas.

Adolescent↗
PubMed2006

Extraction of local hydrogen exchange data from HDX CAD MS measurements by deconvolution of isotopic distributions of fragment ions.

Hydrogen/deuterium exchange (HDX) coupled to protein fragmentation either in solution (by means of proteolysis) or in the gas phase (using collisional activation of protein ions) and followed by mass spectral measurements of deuterium content of individual fragments has become one of the major experimental tools to probe protein structure and dynamics. One difficulty, which often arises in the course of interpretation of HDX MS data, is a need to separate deuterium contribution to the observed isotopic patterns from that of naturally occurring isotopes. Another frequently encountered problem, especially when HDX in solution is followed by protein ion fragmentation in the gas phase, is a need to determine the deuterium content of an internal protein segment based on the measured isotopic distributions of overlapping fragments. While several algorithms were developed in the past several years to address the first problem, the second one did not enjoy as much attention. Here we report a new algorithm based on a maximum entropy principle, which is capable of extracting local exchange data form the isotope distribution of overlapping fragments, as well as subtracting the background due to the presence of natural isotopes and residual deuterium in exchange buffers. The new method is tested with several proteins and appears to generate stable solutions even under unfavorable circumstances, e.g., when the resolving power of a mass analyzer is not sufficient to avoid signal interference or when the isotopic distributions of individual fragments are complex and cannot be approximated with simple binomial distributions. The latter feature makes the algorithm particularly useful when the exchange in solution is correlated or semicorrelated, paving the way to precise structural characterization of non-native protein states in solution.

Algorithms↗
PubMed1997

Some quantitative aspects of natural babesial infection in the haemolymph of Boophilus microplus engorged female ticks.

Quantitative aspects of the natural babesial (Babesia bovis and Babesia bigemina) infection in Boophilus microplus engorged female ticks obtained from two herds of Holstein heifers positive by the immunofluorescent antibody test to both protozoan were evaluated. The number of kinetes/microscope field of haemolymph was determined for each tick from day 5 to 10 post-collection. A close relationship between daily and cumulative babesial infection was detected. Correlation and determination coefficients between days post-collection and the daily and cumulative infection rates, including heavily infected ticks (those ticks carrying at least 3.0 kinetes/microscope field of haemolymph), were always higher than 0.9 (P < 0.01) in ticks of both herds. The median was found to be a more representative measure than the mean to define the distribution of kinetes number amongst infected ticks since this is a negative binomial distribution. The analysis of the sequential order of days of infection more accurately showed the amplification of the babesial infection in the tick haemolymph than the evolution of kinetes number in relation to days post-collection. Sampling ticks on days 8, 9 and 10 post-collection would have detected all ticks infected with Babesia spp. from both herds. A categorization of infected or non infected ticks would be of greater epidemiological importance than the haemolymph infection level, based upon previous laboratory studies that showed a poor relationship between haemolymph infection in the female ticks and the infection rate in their eggs. However, further studies in natural infected ticks and better techniques to differentiate B. bovis and B. bigemina kinetes are needed before these laboratory results can be applied to field conditions.

Animals↗
PubMed1998

The statistical distribution of wrist movements during sleep.

The purpose of this work was to describe the basic statistical properties of the process of production of movements measured with a wrist actimeter, along a complete sleep period in normal human subjects. Two distinct types of random magnitudes were considered to analyze the data, the times between successive groups of movements and the number of movements at each fixed time (1 min) measurement epoch. Suitable probabilistic models for the two variates were chosen, fitting theoretical distribution functions to the observed data. It is concluded that interval data fit a one-parameter exponential distribution, while the number of movements fit a two-parameter negative binomial distribution. The estimated values of these parameters, besides being necessary to perform further statistical analysis, are a measure of the intensity and frequency of the movements. Finally the relationship between polysomnography measures and the elicited parameters was studied.

Adult↗
PubMed2002

Epidemiological study of the intestinal helminths of wild boar (Sus scrofa) and mouflon (Ovis gmelini musimon) in central Italy.

Since 1995 the population of wild ungulates increased significantly in the "Parco provinciale dei Monti Livornesi" (Livorno, Tuscany, Central Italy). We studied the intestinal macroparasites of two hosts, the wild boar (Sus scrofa) and the mouflon (Ovis gmelini musimon). In the case of wild boars we found a dominant parasite species, Globocephalus urosubulatus. For this parasite the frequency distribution of the number of parasites per host agrees with a negative binomial distribution. There is not a significant correlation between the age of the animals and the parasitosis. Furthermore the mean parasite burden of male and female wild boars does not differ significantly. In the case of mouflons we found a dominant parasite species Nematodirus filicollis with Trichuris ovis as codominant species.

Age Factors↗
PubMed1990

[The epidemiological study of esophageal cancer at Yangcheng County in Shanxi].

This paper indicated that counties with higher incidence of esophageal cancer in Shanxi were found to centre round Yangcheng, Jincheng, Qinshui etc. by means of an analysis of the gathered areas on mortality of esophageal cancer in every county or city in Shanxi. These form a higher incidence area of noticeable and centric distribution together with other counties in Henan and Hebei. In all towns in Yangcheng, however, there is no gathered areas. Since 1974, the observed tendency of esophageal cancer in Yangcheng has shown that the mortality ranges from 120-150/100,000, without change in male and in female. However, among the population, the mortality in male is always higher than in female. And it increases with age in people over 30 years. Hereditary epidemiological data at Yanli Town in the county has demonstrated that there is significant difference between the distribution of incidence and mortality of esophageal cancer and the probability of binomial distribution, showing obvious familiar gathering of esophageal cancer.

Adult↗
PubMed1984

[Longitudinal study of the evolution of the frequency of dental caries in a school milieu: a statistical model].

Following a 3-year epidemiological study of the appearance of dental caries in a population of children aged 6 to 9 years (and examined every 12 months), a model of the evolution of the frequency of caries based on a Poisson "with zeros" distribution is proposed. The multivariate distribution of the above phenomena appears as a mixture of multiple negative binomial distribution (MNB) of the following form: sigma mjMNB(a;k0jb,k1jb,k2jb) with sigma mj = 1. The experimental data from the sample of 501 children validate the model in its successive stages. Simulations using the bootstrap method show that the estimates of the model parameters remain stable in the neighbourhood of the distribution observed; at the same time they permit establishing the margins of confidence. Finally, it is shown why the total number of dental faces affected during the experimental period remained strongly asymmetrical.

Child↗
PubMed1981

Sample size for detection of Y-chromosomes in lymphocytes of possible freemartins.

The number of metaphases that need to be examined to detect a Y-chromosome in a lymphocyte of a possible freemartin with a prescribed degree of certainty depends on the distribution of % XY cells among freemartins. To quantify this, the beta-binomial distribution was fit by maximum likelihood to% XY cells observed in blood samples of 70 freemartins (twin births only). The estimate mean and standard deviation of XY cells frequency in 70 freemartins (12,885 metaphases) was 0.48 and 0.30, respectively. These estimates correspond to a U-shaped distribution of XY cell frequency, i.e., one in which either an XX or an XY cell type predominates in most freemartins. These values indicate that sample sized of 26 and 168 are required to by 95% and 99% confident, respectively, that a female co-twin will not be misclassified.

Animals↗
PubMed1999

Visible evidence for differences in synaptic effectiveness with activity-dependent vesicular uptake and release of FM1-43.

Activity-dependent uptake and release of the fluorescent probe FM1-43 were used to compare synaptic performance (rates of transmitter release and synaptic vesicle turnover) at different frequencies in phasic and tonic motor neurons innervating the crayfish leg extensor muscle and in the tonic motor neuron of the opener muscle. The phasic extensor motor neuron, which has a high quantal content of transmitter release, accumulated and released FM1-43 more rapidly than the tonic motor neuron, especially at low frequencies of stimulation. Individual bright spots appeared on the varicosities of the junctional terminals during stimulation in FM1-43; these spots corresponded to zones of immunostaining for the synaptic vesicle associated protein synaptotagmin, but they were larger and less numerous than synapses identified by electron microscopy and appear to represent one to several synapses with their associated clusters of synaptic vesicles. The number of bright spots observed on varicosities of the tonic terminal after stimulation at >/=20 Hz is generally similar to values for responding units (n) calculated from binomial distributions derived from quantal analysis. At frequencies of </=10 Hz, bright spots did not usually appear on tonic extensor varicosities, and the quantal release patterns were best fitted with Poisson distributions. Another tonic motor neuron, the excitor of the opener muscle, showed individual bright spots at lower frequencies of stimulation, consistent with its higher quantal output at these frequencies and corresponding with the binomial fits for quantal release distributions. In this axon, the number of distinctive bright spots increased with frequency in the 2- to 20-Hz range, indicating increased participation of synapses during frequency facilitation. In the tonic extensor neuron terminals, the brightness and the size of the individual spots increased with frequency, and new foci of dye uptake appeared at the edges of preexisting spots. Relative intensity change varied considerably among individual spots during dye loading at different frequencies. Similarly, individual spots on a single tonic terminal destained at different rates when stimulated after previous loading with FM1-43. These results suggest differential performance of individual synapses or small groups of synapses, some being more effective in transmitter release than others, as inferred from previous ultrastructural and quantal analysis studies. The large overall differences between phasic and tonic synapses suggest differential regulation of transmitter release at individual synapses in the two neurons.

Animals↗
PubMed2026

HiCPotts: An R/Bioconductor package to identify significant interactions in chromosome conformation capture data and model sources of bias.

MOTIVATION: Chromosome Conformation Capture methods, including Hi-C, micro-C or Capture-C, are used to map chromatin interactions genome-wide. Most of the existing computational methods do not account for sources of bias (such as DNA accessibility, GC content or TE content) in the data. RESULTS: We previously developed ZipHiC, a Bayesian method based on the hidden Markov random field (HMRF) model and the Approximate Bayesian Computation (ABC), that uses zero-inflated Poisson distribution to model the noise, signal and false signal of the data and showed that this approach was able to detect bias from DNA accessibility, GC content and TE content in both Hi-C and micro-C data. Here, we present HiCPotts, another Bayesian method based on the HMRF model and the ABC that uses a zero-inflated Negative Binomial distribution instead to model the noise and signal of the data. We systematically show that HiCPotts reduces false positives and increases recovery of true interactions compared to ZipHiC, but also compared to other methods such as FastHiC, Juicer and HiCExplorer. Most importantly, we provide an R/Bioconductor package that allows modelling the noise, signal and false signal using various distributions such as the zero-inflated Negative Binomial (ZINB) and the zero-inflated Poisson distribution (ZIP). AVAILABILITY AND IMPLEMENTATION: https://bioconductor.org/packages/HiCPotts/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Approximate Bayesian Computation↗
PubMed1985

Heterotrophic bacteria in water distribution systems. I. Spatial and temporal variation.

The drinking water distribution system of the city of Metz in France was sampled intensively during six, monthly surveys which were designed to determine the spatial and temporal distribution of total heterotrophic bacteria in the network. A non-hierarchical nearest-centroid clustering method was used for dividing the water distribution system into zones corresponding to different levels of bacterial density. The general pattern of the spatial heterogeneity showed a high degree of reproducibility. Since the frequency distribution of total heterotrophic bacteria within the zones was compatible with the negative binomial distribution, the water distribution system studied may be considered as being composed of several heterogeneous subsystems. The consistency of this structured spatial dispersion pattern of bacteria in light of some physical and chemical characteristics of the system is evident. In consideration of the principal features of flow in the system relevant to the layout of water mains, the location of zones of highest bacterial concentrations have been attributed to lower levels of chlorine residuals and prolonged retention time of the water in the network, especially in the storage units, before reaching the various distribution areas. Although the monthly variation in the bacterial concentration of the entire system showed a marked increase which was concomitant with warmest water temperatures, the zones were subject to noticeable discrepancies in the range of temporal variation.

Bacteria↗
PubMed1993

Follicular development and ovulation in the marmoset monkey as determined by repeated laparoscopic examination.

This paper describes the course of follicular development in vivo in the marmoset monkey, the only anthropoid primate with a relatively high (2-4) and variable ovulation number. Results are presented in relation to predictions from a mathematical model of control of follicle selection and ovulation number. Repeated laparoscopic examinations during the follicular phase were conducted for 14 cycles. Ovulatory follicles were 1.0 mm (median) in diameter at Day 6 and could be distinguished from nonovulatory follicles by Day 8, at which point they were 2.0 mm in diameter. Ovulations were not synchronous; the most common observation 1-2 days after the estradiol peak was ovulation of one follicle but not the other. Examination of the course of follicular development within a cycle and the distribution of ovulation sites both supported predictions stemming from a mathematical model of follicle selection developed by Lacker et al. [Biol Reprod 1987; 37:570-580]. Specific findings were the following: 1) Variations in patterns of follicle growth within a cycle resembled those generated by the model; in 64% of cycles, the 2-3 ovulatory follicles grew at similar rates. However, in 36% of cycles, ovulatory follicles displayed disparate rates of growth. 2) An examination of the distribution of ovulation sites (right versus left) revealed no significant difference from a binomial distribution, suggesting the likelihood that interovarian (rather than intraovarian) factors control this distribution.

Animals↗
PubMedDate not supplied

[Ecoepidemiology of Haemonchus contortus bahiensis, ecotype present in sheep of arid zones of Venezuela].

The frequency distribution of female Haemonchus contortus bahiensis Grisi, 1974 in sheep from Venezuelan arid zones is 15.32% for the type with vulvar flap, 51.6% for the vulvar-knob and 33.07% for smooth type. A Shannon-Weaver diversity index corresponding to 1.44 bits was calculated for these forms with similarities in the general size, egg-size and in the number of the longitudinal cuticular ridges. An aggregated kind of distribution in the host population according to the K parameter of a negative binomial distribution was recorded for male and female worms. A complicated interaction was observed between the abundance, aggregation and prevalence of this ecotype and the importance of these findings is discussed with regard to host-parasite relationships.

Animals↗