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PubMed1997

[A study on familial aggregation of hepatitis virus infection in Fujian province].

In nine disease surveillance points of Fujian Province, positive serum antibody against hepatitis A virus (anti-HAV), hepatitis B surface antigen (HBsAg), antibody against hepatitis Cvirus (anti-HCV) and antibody against hepatitis E virus (anti-HEV) in people of 1,237 families were determined and their distribution was analyzed to study familial aggregation of hepatitis virus infection by fitting to binomial distribution. Results showed that chi 2 of goodness-of-fit to binomial distribution was 49.89, 217.91 and 27.39 for anti-HAV, HBsAg and anti-HEV respectively, all with P < 0.001, indicating very obvious familial aggregation in HAV, HBV and HEV infection, with aggregation rates of 84.13%, 34.83% and 35.23% respectively. It suggests that familial aggregation is mainly caused by mother to infant transmission and horizontal transmission in families, and HEV infection can be transmitted through sex.

Binomial Distribution↗
PubMed1997

Density-Dependent Patch Exploitation and Acquisition of Environmental Information

We study density-dependent resource harvest patterns due to Bayesian foraging for different distributions of resources. We first consider a forager with information about the stochastic properties of its environment. In this case we show that when the number of food items per patch follows a distribution from the exponential family, the density dependence is given by the ratio sigma2/&mu; of the distribution of number of food items per patch. Bayesian foraging can therefore lead to positive (negative binomial distribution) or negative (binomial distribution) density dependent resource harvest and even to density independent (Poisson distribution) resource harvest, depending on the distribution of resources in the environment. In a second stage we incorporate learning about the distribution of resources in the whole environment. The mean of the distribution of number of food items per patch of a given environment is learnt faster than the variance of the distribution. Learning occurs faster in poorer than richer environments. Copyright 1997 Academic Press

Journal Article↗
PubMed1998

The processes influencing the distribution of parasitic nematodes among naturally infected lambs.

The impact of mixed, nematode infection upon a group of animals will depend upon the number of nematodes present, how they are distributed among hosts and whether individuals that are heavily parasitized with one species are more likely to be heavily parasitized with other species. A survey of over 500 six-month-old, Scottish Blackface lambs from a single farm in Southwest Strathclyde identified 7 different categories of nematodes in the abomasum and small intestine. There were considerable differences among years and among nematodes in the prevalence and mean intensity of infection. Ostertagia circumcincta was present in nearly all lambs and judged by prevalence and intensity is one of the most successful of all parasitic nematodes. Each category of nematodes had a skewed distribution; most animals had relatively few worms but a small proportion had many worms. The variance of the number of nematodes in each category were approximately equal to the square of the mean. The counts of adult O. circumcincta followed a negative binomial distribution, but the negative binomial distribution did not provide a good description of the observed values for the other species. These other species had a lower prevalence and possibly some sheep were not exposed to infection. There was no significant genetic variation among lambs in the number of nematodes present and therefore the differences among these lambs were unlikely to be a consequence of genetic differences in host susceptibility. Lambs with increased numbers of one species were more likely to be have increased numbers of the other species, but the correlations were weak and may reflect covariation in exposure to different parasites.

Abomasum↗
PubMed1998

The mirror effect and attention-likelihood theory: a reflective analysis.

The mirror effect refers to findings from studies of recognition memory consistent with the idea that the underlying "strength" distributions are symmetric around their midpoint separating studied and nonstudied items. Attention-likelihood theory assumes underlying binomial distributions of marked features and claims that old-item differences result from differential attention across conditions during study. The symmetry arises because subjects use the likelihood ratio as the basis for decision. The author analyzes the model and argues that one of the main criticisms (the complexity of the likelihood-ratio decision rule) is unwarranted. A further analysis shows that other distributions (the Poisson and the hypergeometric) can also produce a mirror effect. Even with the binomial distribution, a variety of parameter values can produce a mirror effect, and with the right combination of parameter values, differential attention across conditions is not necessary for a mirror effect to occur.

Attention↗
PubMed1999

Heterogeneity in the distribution of Strongyloides ratti infective stages among the faecal pellets of rats.

The distribution of helminth parasites within their host population is usually overdispersed and can be described by the negative binomial distribution. The causes of this overdispersion are poorly understood, but heterogeneity in the distribution of infective stages within the environment has been implicated as a possible factor. Here we describe the distribution of infective stages of the rat intestinal nematode parasite Strongyloides ratti among the faecal pellets of its host. The distribution of infective stages between faecal pellets is overdispersed and well described by the negative binomial distribution. This overdispersion increases during the course of infection and occurs over a range of infection intensities. Overdispersion of nematode infective stages among faecal pellets may result in increased spatial heterogeneity of the infective stages in the environment and thus may contribute to the generation of overdispersion of adult parasitic stages. In addition, these findings raise important issues regarding the accurate quantification of helminth egg counts from faecal samples.

Animals↗
PubMed2004

The relationship between IgA activity against 4th-stage larvae and density-dependent effects on the number of 4th-stage larvae of Teladorsagia circumcincta in naturally infected sheep.

The number of Teladorsagia circumcincta 4th-stage larvae in naturally infected lambs from a single farm varied among lambs and among different years. Within each year the distribution of 4th-stage larvae among lambs was similar to that expected from a negative binomial distribution. The ratio of 4th-stage larvae to adult T. circumcincta was low in two years with a low mean intensity of infection but high in two years with a higher mean intensity of infection. The negative binomial distribution is defined by the mean and by k, a parameter that measures dispersion; k was low when mean infection intensity was low but higher when mean infection intensity was high. As k is an inverse index of overdispersion this indicated that the distribution of 4th-stage larvae was more overdispersed at low levels of infection. In a combined analysis, the number of adult T. circumcincta and the plasma IgA activity against 4th-stage larvae were both associated with increased numbers of 4th-stage larvae. There was a statistical interaction between the number of adults and IgA activity that moderated their combined effect.

Abomasum↗
PubMed2003

Phorbol esters and adenosine affect the readily releasable neurotransmitter pool by different mechanisms at amphibian motor nerve endings.

Phorbol esters and adenosine have been proposed to interact at common sites downstream of calcium entry at amphibian motor nerve endings. We thus studied the actions and interactions of phorbol esters and adenosine using electrophysiological recording techniques in conjunction with both binomial statistical analysis and high-frequency stimulation at the amphibian neuromuscular junction. To begin this study, we confirmed previous observations that synchronous evoked acetylcholine (ACh) release (reflected as endplate potentials, EPPs) is well described by a simple binomial distribution. We then used binomial analysis to study the effects of the phorbol ester phorbol dibutyrate (PDBu, 100 nM) and adenosine (50 microM) on the binomial parameters n (the number of calcium charged ACh quanta available for release) and p (the average probability of release), where the mean level of evoked ACh release (m) = np. We found that PDBu increased m by increasing the parameter n whilst adenosine reduced m by reducing n; neither agent affected the parameter p. PDBu had no effect on either the potency or efficacy of the inhibition produced by adenosine. Subtle differences between these two agents were revealed by the patterns of EPPs evoked by high-frequency trains of stimuli. Phorbol esters increased ACh release during the early phase of stimulation but not during the subsequent plateau phase. The inhibitory effect of adenosine was maximal at the beginning of the train and was still present with reduced efficacy during the plateau phase. When taken together with previous findings, these present results suggest that phorbol esters increase the immediately available store of synaptic vesicles by increasing the number of primed vesicles whilst adenosine acts at a later stage of the secretory process to decrease the number of calcium-charged primed vesicles.

Acetylcholine↗
PubMed2003

Modeling the dependence between number of trials and success probability in beta-binomial-Poisson mixture distributions.

Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.

Algorithms↗
PubMed2000

On a likelihood-based goodness-of-fit test of the beta-binomial model.

When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta-binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-fit test proposed by Brooks et al. (1997, Biometrics 53, 1097-1115) but find that it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.

Animals↗
PubMed1997

Clinical and biochemical patterns of presentation in monolateral and bilateral calcium nephrolithiasis.

To investigate patterns of monolateral and bilateral nephrolithiasis, we enrolled 196 patients with idiopathic calcium stone disease (ICaSD) and 36 with proven primary hyperparathyroidism (PHP). Monolateral disease occurred in 45 subjects with ICaSD and 3 with PHP. All had had three or more stone events. They were studied for a number of clinical and biochemical parameters. The expected prevalence of monolateral stone disease was calculated according to the binomial distribution of random events. Whereas the observed and expected prevalence of monolateral nephrolithiasis did not differ in PHP, the distribution did not follow a chance pattern in ICaSD, since monolateral disease was still frequent among patient with more than 6 episodes. To find out whether monolateral and bilateral ICaSD had distinct pathogenic mechanisms the two groups were compared for clinical and biochemical patterns: no differences emerged concerning metabolic derangements, urine saturation and diet-related biochemistries. Bilateral stone-formers had a higher recurrence rate, but a similar number of stone-operations or ESWL. In 81 of 151 bilateral idiopathic stone-formers in which we were able to assess the exact number of stone events in left and right kidney, the distribution of stones between kidneys did not differ from the binomial distribution. In conclusion, while PHP-associated nephrolithiasis presents predictable patterns, ICaSD comprises a subset in which the disease occurs monolaterally. These forms cannot be distinguished from bilateral forms with common clinical features or routine biochemistries.

Age of Onset↗
PubMed1996

Nonbinomial distribution of relative neurite outgrowth in PC-12 cells.

Previously we reported the results of a series of experimental tests using PC-12 cells to examine the biological effect of prescribed combinations of both nerve growth factor and magnetic fields. Because our assay of the PC-12 cells is based on binary classification of the cells following treatment, our data might be expected to have a binomial distribution. However, our data consistently show a smaller variability than that predicted by the binomial distribution model. In this paper, we examine some possible reasons for this reduction in variability in our results.

Algorithms↗
PubMed1988

The distribution of numbers of open channels in multi-channel patches.

Assumptions inherent in use of the binomial distribution are relaxed in order to identify alternative distributions with different variances, for fitting to the frequency distributions of numbers of open channels in multi-channel patches. The variance is less than that for the binomial distribution with the same expectation when either there is a negative interaction between channels or channels have different probabilities of being open. When the variance is greater, this may be because of positive interaction between channels or non-stationary behaviour. Use of the distributions and lack-of-fit statistics is illustrated.

Ion Channels↗
PubMed2005

Statistical kinematics of axillary nodal metastases in breast carcinoma.

The number of involved lymph nodes in individuals with breast cancer is highly variable, and of both prognostic and therapeutic importance. A statistical description for the frequency distribution of the numbers of involved nodes in an affected population could potentially reveal mechanisms of axillary metastasis, and eventually facilitate predictive models for tumor control and axillary sampling. A meta-analysis of 15 studies involving 24,757 axillary dissections was performed, including conventional dissections, sentinel node dissections and studies of occult metastases. Frequency histograms for the numbers of involved axillary lymph nodes from the populations were tested for clustering and they were fitted, as a first approximation, to a negative binomial distribution. Although the number of involved nodes per individual was quite variable, some individuals sustained more involved nodes than could be expected from a random (Poisson) distribution. The negative binomial distribution, however, provided acceptable descriptions for the distributions of involved nodes in all populations studied. Two mechanisms could explain these observations: (1) an apparent contagion model, where involved nodes seeded further nodal metastases, and (2) a spurious contagion model where the number of involved nodes per individual was randomly (Poisson) distributed and population heterogeneity accounted for the more severe cases. Both models were consistent with the hypothesis that the nodal metastasis is a chance event, with the probability of involvement greatest for nodes contiguous to the primary tumor and proportioned by lymphatic flow.

Biomechanical Phenomena↗
PubMed1980

Development and distribution of proximal caries in 303 9-20-year-old individuals in a Copenhagen suburb.

The purpose of the present study was to establish a theoretical basis for the practice of screening for identification of caries risk groups. Longitudinal data concerning the development of proximal caries in 303 persons from the age of 9 to the age of 20 were examined with regard to statistical distribution. Data from each year and from the entire period showed a close fit to the negative binomial distribution. This distribution can be the result of independent random occurrences, but varying susceptibility. Thus the consistent existence of a caries risk group is illustrated by this analysis, but no prediction is made. It is suggested that future evaluations of preventive measure directed toward caries risk groups should express the degree to which the similarity between the distribution of proximal caries and the negative binomial distribution can be eliminated.

Adolescent↗
PubMed1993

Modeling growth and individual differences in spatial tasks.

The goal of the present research is to understand individual differences and growth of children's and adolescents' performance on two spatial tasks through a formal model framework. In Study 1, 579 subjects aged 7-16 years old drew lines to represent their water-level task predictions for eight tilted rectangular vessels. In the verticality task, called the "van task," subjects drew lines representing their predictions concerning the orientation of a plumb line suspended from the ceiling of a van parked on eight different inclines. In Study 2, 185 subjects aged 9-16 years were presented with video displays on a computer monitor and were instructed to adjust lines on the screen to indicate their predictions for the same stimuli used in Study 1. Later, they responded to a multiple-choice verbal analogies test and answered interview questions concerning their task performance strategies for the van and water-level tasks. In both studies, responses on the van and water-level tasks were scored as correct or incorrect on the basis of empirically derived scoring criteria that varied with age. The number of correct responses for each subject on the van and water-level tasks was modeled as a binomial random variable. Individual differences, growth differences, and sex differences in task performance were modeled as mixtures of binomial distributions, a model that may be viewed as a latent class model. Data for Study 1 subjects 11 years and older were combined so that the joint structure of the water-level and van tasks could be studied. This structure was modeled as a mixture of bivariate binomial distributions. On the basis of their task performance, subjects in Study 1 were assigned to their corresponding latent classes. Once classified, the original response distributions of subjects within each latent class were explored in an effort to understand their various response strategies. Additionally, the correspondence between verbal explanations and van and water-level task performance was investigated in Study 2. Results include the following: 1. A two-component binomial mixture distribution fit well the van and water-level task data for each age and sex group; each binomial component may be viewed as a different latent class. Variance accounted for under the model often exceeded 90%. One binomial component (latent class) modeled the poor performers with poor task success rates, and the second component modeled the remaining good performers who consistently performed well.(ABSTRACT TRUNCATED AT 400 WORDS)

Adolescent↗
PubMed1998

Sister chromatid exchange data and Gram-Charlier series.

Bowman et al. [K.O. Bowman, M.A. Kastenbaum, L.R. Shenton, Fitting multi-parameter distributions to SCE data, Mutat. Res., 358 (1996) 15-24.] showed how discrete Pearson and discrete Johnson translation-system distributions may be fitted to sister chromatid exchange (SCE) data presented by Bender et al. [M.A. Bender, R.J. Pearston, R.C. Leonard, B.E. Pyatt, P.C. Gooch, On the distribution of spontaneous SCE in human peripheral blood lymphocytes, Mutat. Res., 281 (1992) 227-232.]. When their performances were measured by the chi-squared test of goodness of fit, these distributions proved to be only moderately better alternatives to the poorly fitting Poisson, binomial, and negative binomial distributions. In this paper, we extend our search for better characterizations of the SCE data by calling upon the Gram-Charlier type B approximation of the negative binomial distribution. We introduce an innovative extension of methods described in a little-known paper by Aitken and Gonin [A.C. Aitken, H.T. Gonin, On fourfold sampling with and without replacement, Proc. R. Soc. Edinburgh, 55 (1934) 114-125.], and show how this leads to fits of the SCE data that, in general, are within acceptable levels of probability. Moreover, we show how a theorem by Cramér [H. Cramér, Mathematical Methods of Statistics, Princeton Univ. Press, 1946.], relating to the scale factor m2/m'1 and its asymptotic distribution, may be used to discriminate between smokers and nonsmokers of the same gender.

Biometry↗
PubMed1991

Frequency of elevated urinary beta 2-microglobulin levels in relatives of patients with asymptomatic low-molecular-weight proteinuria.

We studied urinary beta 2-microglobulin levels in a total of 29 apparently healthy relatives (aged 0.8-70 years) of 8 male patients with asymptomatic low-molecular-weight proteinuria in six families. The frequency of levels above the age- and sex-associated 95% confidence limit was 7 of 29 (24%), 4 of 12 (33%) in first-degree relatives, 2 of 6 (33%) fathers, and 2 of 6 (33%) mothers. These frequencies were significantly above those in the general population (P less than 0.01, by a normal distribution test, a binomial distribution, and Poisson distribution test for the sample proportion). The increased frequency in fathers argues against an X-linked pattern of inheritance for this entity, suggesting that there is heterogeneity in the inheritance.

Adolescent↗
PubMed1989

Word recognition functions for the CID W-22 test in multitalker noise for normally hearing and hearing-impaired subjects.

Word recognition functions for Auditec recordings of the CID W-22 stimuli in multitalker noise were obtained using subjects with normal hearing and with mild-to-moderate sensorineural hearing loss. In the first experiment, word recognition functions were generated by varying the signal-to-noise ratio (S/N); whereas in the second experiment, a constant S/N was used and stimulus intensity was varied. The split-half reliability of word recognition scores for the normal-hearing and hearing-impaired groups revealed variability that agreed closely with predictions based on the simple binomial distribution. Therefore, the binomial model appears appropriate for estimating the variability of word recognition scores whether they are obtained in quiet or in a competing background noise. The reliability for threshold (50% point) revealed good stability. The slope of the recognition function was steeper for normal listeners than for the hearing-impaired subjects. Word recognition testing in noise can provide insight into the problems imposed by hearing loss, particularly when evaluating patients with mild hearing loss who exhibit no difficulties with conventional tests. Clinicians should employ a sufficient number of stimuli so that the test is adequately sensitive to differences among listening conditions.

Adult↗