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PubMed1989

[Family clustering analysis of HBV infection].

A family clustering analysis of HBsAg, anti-HBs, anti-HBc positive and total infected persons in 148 families on a farm was carried out by the methods of G statistic, binomial distribution and negative binomial distribution. The results consistently showed that there was significant clustering of HBsAg carriers in families, whereas there were not clustering was seen an overall HBV infected persons in families. The clustering of HBsAg carriers in families is due probably to the effect of some genetic factors. The results of G statistic analysis indicate that anti-HBc also have significant clustering in families.

Carrier State↗
PubMed1993

Estimating the variance of standardized rates of recurrent events, with application to hospitalizations among the elderly in New England.

Usual approaches for estimating the variance of a standardized rate may not be applicable to rates of recurrent events. Where individuals are prone to repeated health events, Greenwood and Yule (J R Stat Soc [A], 1920;83:255-79) advocated use of the negative binomial distribution to account for departures from the assumption of randomness of recurrent events required by the Poisson distribution. In this paper, the authors implemented the negative binomial distribution in the computation of annual hospitalization rates within certain hospital market areas. Data used were from 1,549,915 New England residents aged 65 years or more who were enrolled in Medicare between October 1, 1988, and September 30, 1989, and who had 458,593 hospital admissions during that year. New England was partitioned into 170 hospital market areas ranging in population size from 162 to 70,821 elderly Medicare enrollees. The negative binomial distribution demonstrated substantially better fits than the Poisson distribution to the numbers of hospitalizations within hospital market areas. Estimated standard errors for indirectly standardized rates based on the negative binomial distribution were 25-51 percent higher than estimated standard errors that assumed an underlying Poisson distribution. Using regression analysis to smooth overdispersion parameters across hospital market areas produced similar results. The approach described in this paper may be useful in estimation of confidence intervals for standardized rates of recurrent events when these events do not recur randomly.

Age Factors↗
PubMed1987

Statistics of neuromuscular transmitter release in young and old mouse muscle.

1. It was reported previously that in limb muscles of old (27-30 months) CBF-1 mice, quantal content (m) of evoked transmitter release was increased compared to that in young (9-12 months) mice. In diaphragm muscles there was no change with age. The object of the present study was to determine whether the age-related increase in transmitter release was due to increase in the binomial parameter n or the parameter p. The analysis also involved consideration of goodness-of-fit between observed and expected binomial distribution of the data. 2. Spontaneous miniature end-plate potentials (m.e.p.p.s) and evoked end-plate potentials (e.p.p.s) were recorded with intracellular techniques from soleus and diaphragm muscles bathed in low-Ca high-Mg medium. The goodness-of-fit between the observed e.p.p amplitude distribution and that expected from a binomial distribution was evaluated by chi 2 test. 3. In different muscles and at different ages, the percentage of fibres with binomial e.p.p. distributions varied from 17 to 44%, even though in all fibres there was a similar proportionality between direct quantal content and the reciprocal of the square of the coefficient of variation of e.p.p. amplitudes. In addition, apparent graphical agreement between observed and theoretical binomial e.p.p. distributions was often not substantiated by the chi 2 criterion. 4. In soleus muscles from young mice, lowering the stimulus frequency from 10 to 0.5 Hz and shortening the train length from 250 to 100 pulses increased the prevalence of binomial e.p.p. distributions, but the same result was not obtained in diaphragm or soleus muscles from old mice. If the mean amplitude of groups of 10 e.p.p.s in any train showed any drift (greater than 10%) then that train was excluded from the results. Thus, in order to make valid age comparisons, only fibres with binomial e.p.p. distributions were analysed further. 5. There was no change with age in m, n or p in diaphragm muscles, but in soleus muscles from old animals a nearly 2-fold increase in n entirely accounted for the increase in m. 6. If, as proposed by others, n represents the number of release sites, then the ageing soleus neuromuscular junction may have increased numbers or length of active zones or associated membrane components.

Action Potentials↗
PubMed1971

Fitting discrete probability distributions to evolutionary events.

The assumptions underlying the use of the Poisson distribution are essentially that the probability of an event is small but nearly identical for all occurrences and that the occurrence of an event does not alter the probability of recurrence of such events. These assumptions do not seem to be met for evolutionary events since (i) the probability of fixing nucleotide codon substitutions is not equal for all substitutions at a codon, and probably varies for the same substitution in different lineages; (ii) the probability of fixing codon substitutions varies among positions of a cistron; and (iii) the fixation of a nucleotide codon substitution at one position in a cistron modifies, and may even promote, the fixation of a codon substitution elsewhere along the cistron. Natural selection presumably is the causative factor that acts to modify the probability of a nucleotide codon substitution's being fixed in a population. The use of the negative binomial distribution is consistent with the evidence that selective pressure on amino acid or nucleotide codon positions varies both among codon positions of a cistron and at a particular position during evolutionary time. If the number of fixations of nucleotide codon substitutions per position of cistrons encoding cytochromes c are phyletically inferred (phylogeny based on a paleontological record) rather than phenetically inferred (based on paired comparisons of extant species' differences in the absence of a phylogeny) the distribution of these fixation data cannot be described adequately by a single Poisson distribution. The fit of these same data to a negative binomial distribution is very satisfactory. It has been argued that the fit of phenetically inferred fixation data, which do not take account of parallel or reverse fixations, to the Poisson distribution was supportive evidence for the hypothesis that protein evolution results from the fixation of selectively neutral codon substitutions. This argument now appears to be undercut by the evidence that data on nucleotide codon fixation are more probably distributed according to the negative binomial distribution. The fact that fixation data can be described by a particular discrete probability distribution does not of itself provide insight into the mechanisms of the evolutionary process. However, the facts-(i) that the assumptions underlying the use of the negative binomial distribution adequately deal with the varying probability of fixing amino acid or nucleotide codon substitutions at and among the positions of a cistron and (ii) that the negative binomial distribution provides an excellent fit for the phyletically inferred fixation data-suggest that the negative binomial is a very appropriate discrete probability distribution for describing evolutionary events. Amino acids or their nucleotide codon substitutions may be fixed at a position of a cistron as though selectively neutral relative to the codon being replaced, even though the codon position will not be selectively neutral, since many amino acids cannot function there. The negative binomial distribution treats this situation well whereas a single Poisson distribution could only be satisfactory if all codon positions that could vary were selectively neutral.

Amino Acid Sequence↗
PubMed1993

Analysis of aphidicolin-induced chromosome fragility in the domestic pig (Sus scrofa).

Aphidicolin (APC)-sensitive fragile sites were identified in chromosome preparations from peripheral lymphocyte cultures of 12 four-way crossbred pigs. A chi 2 analysis demonstrated that aphidicolin-induced breakage events and previously reported in vivo chromosome rearrangement events were not independent. Comparison of expected Poisson and negative binomial distributions to observed breakage patterns indicated that the negative binomial distribution provided a better fit to experimental data. The negative binomial distribution is consistent with a distribution of breakage rates, i.e., non-constant rates of breakage at chromosomal loci across the genome.

Animals↗
PubMed1999

An estimator of the mutant frequency in assays using transgenic animals.

The Poisson distribution is a fundamental probability model for count data, and is a natural model for the observed plaque counts in mutation assays using animals with lambda or PhiX174 transgenes. The Poisson likelihood for observed counts is a function of the mutant fraction, and it is straightforward to derive the associated maximum likelihood estimate of the mutant fraction and its variance. The estimate is easy to calculate, and if not the same, very similar to ad hoc estimates in current use. The model indicates the proper way to combine data from a number of plates, possibly prepared with different sample dilutions. The estimator of the mutant fraction is biased as a consequence of dividing by a random variable, the plaque count used to calculate the total recovered plaque-forming units. Fortunately, the bias becomes negligible as this count becomes large. On the other hand, increasing this count can increase the variance by decreasing the amount of sample assayed for mutant phages. Concurrent heed to the bias and the variance provides some guidance as to the optimum allocation of a sample into portions assayed for mutant phages and total recovered phages. The distribution of the estimate of the mutant fraction is related to the binomial distribution. This relationship implies a binomial distribution for the mutant count conditional on an overall count (either the sum of mutant and counted total plaques or the sum of counted mutant and non-mutant plaques). A special but important case occurs when each plate can be evaluated for mutant plaques and non-mutant plaques. Then, the observed proportion of mutants estimates the mutant fraction. More generally, the relationship to a binomial distribution provides a procedure for calculating a confidence interval.

Animals↗
PubMed1999

[Study on family aggregation of cases of advanced schistosomiasis japonica].

AIM: To explore the family aggregation of advanced schistosomiasis japonica. METHODS: Eighty-one cases of advanced schistosomiasis(AS) and 67 cases of non-advanced schistosomiasis with history of infections in Yushan County, Jiangxi Province were chosen as proband groups and control groups respectively, then grades 1 and 2 relatives of them were investigated on AS. Family aggregation of AS was analyzed through comparing the prevalence rate between the close and distant relatives of probands and controls and fitting the observed distribution of AS cases among the population by zero-truncated Poisson distribution and zero-truncated negative binomial distribution. RESULTS: The prevalence rate was higher in the close relatives (Group I relatives) of the probands than in the distant relatives(Group II relatives) of the probands and in the controls' relatives. The observed distribution of AS was beyond the probability of the zero-truncated Poisson distribution, but consistent with the zero-truncated negative binomial distribution. CONCLUSION: Family aggregation of advanced schistosomiasis does exist.

Adult↗
PubMed1982

Accuracy of estimated phylogenetic trees from molecular data. I. Distantly related species.

The accuracies and efficiencies of four different methods for constructing phylogenetic trees from molecular data were examined by using computer simulation. The methods examined are UPGMA, Fitch and Margoliash's (1967) (F/M) method, Farris' (1972) method, and the modified Farris method (Tateno, Nei, and Tajima, this paper). In the computer simulation, eight OTUs (32 OTUs in one case) were assumed to evolve according to a given model tree, and the evolutionary change of a sequence of 300 nucleotides was followed. The nucleotide substitution in this sequence was assumed to occur following the Poisson distribution, negative binomial distribution or a model of temporally varying rate. Estimates of nucleotide substitutions (genetic distances) were then computed for all pairs of the nucleotide sequences that were generated at the end of the evolution considered, and from these estimates a phylogenetic tree was reconstructed and compared with the true model tree. The results of this comparison indicate that when the coefficient of variation of branch length is large the Farris and modified Farris methods tend to be better than UPGMA and the F/M method for obtaining a good topology. For estimating the number of nucleotide substitutions for each branch of the tree, however, the modified Farris method shows a better performance than the Farris method. When the coefficient of variation of branch length is small, however, UPGMA shows the best performance among the four methods examined. Nevertheless, any tree-making method is likely to make errors in obtaining the correct topology with a high probability, unless all branch lengths of the true tree are sufficiently long. It is also shown that the agreement between patristic and observed genetic distances is not a good indicator of the goodness of the tree obtained.

Base Sequence↗
PubMed2003

Study of recombinant micro-organism populations characterized by their plasmid content per cell using a segregated model.

Numerous observations from recombinant systems have shown that properties such as the specific cell growth rate and the plasmid-free cell formation rate are related, not only to the average plasmid content per cell, but also to the plasmid distribution within a population. The plasmid distribution in recombinant cultures can have an effect on the culture productivity that cannot be modelled using average values of the overall culture. The prediction of the behaviour of a plasmid content distribution and its causes and effects can only be studied using segregated models. A segregated model that describes populations of recombinant cells characterized by their plasmid content distribution has been developed. This model includes critical causes of recombinant culture instability such as the plasmid partition mechanism at cell division, plasmid replication kinetics and the effect of the plasmid content on the specific growth rate. The segregated model allows investigation of the effect of each of these causes and that of the plasmid content distribution on the observable behaviour of a recombinant culture. The effect of two partitioning mechanisms (Gaussian distribution and binomial distribution) on culture stability was investigated. The Gaussian distribution is slightly more stable. A small plasmid replication rate constant results in a very unstable culture even after short periods of time. This instability is dramatically improved for a larger value of this constant, hence improving protein synthesis. For a very narrow initial plasmid distribution, a given plasmid replication rate and partitioning mechanism can become broad even after a relatively short period of time. In contrast, a very "broad" initial distribution gave rise to a "Gamma-like" distribution profile. If we compare the results obtained in the simulations of the segregated model with those of the non-segregated one (average model), the latter model predicts much more stable behaviour, thus these average models cannot predict culture instability with the same precision. When compared with the experimental results, the segregated model was able to predict the practical behaviour with accuracy even in a system with a high plasmid content per cell and a high rate of plasmid-free cell formation which could not be achieved with a non-segregated model.

Journal Article↗
PubMed1984

[Dynamics of the distribution of variables in morphology].

This paper discusses examples of exponentially distributed, Poisson-distributed, and binomially distributed random variables from morphology and describes secular and historical processes as well as phenomena of aging as factors of the dynamics of such distributions, the major focus being on tests of morphometric variables for the existence of normal distributions. In those cases where hypotheses of the existence of particular distributions of random morphometric variables are established it is necessary that consideration be given to metrological and stereological factors pertaining to the process of measuring and the geometry of the structures being measured, respectively. Karyometric results are used to demonstrate the splitting of a single statistical population into several populations as a result of the process of aging of the human organism.

Aged↗
PubMed1986

The negative binomial model and the denominator problem in a rural family practice.

Much accurate health services and epidemiologic research in primary care is impeded by an inability to determine or estimate practice size in many countries. While the number of patients attending a practice is known, the number of non-attending members is not. Much of the work aimed at solving the denominator problem has focused on mathematical models for estimating the non-attenders. Of these, the negative binomial distribution of illness episodes received considerable early attention because of its success in British general practices. Enthusiasm for the negative binomial distribution waned when its application in non-capitated practices was largely unsuccessful. However, these American studies contained major biases, particularly in terms of independent knowledge of practice size and the potential for frequent usage of other primary care services. The negative binomial distribution was re-evaluated in a rural Canadian practice where there was only limited opportunity for external service utilization and where the practice's patient list had been subjected to separate validation. It fits well with the distribution of illness episodes in each of two consecutive 12-month periods and provided accurate estimates of practice size. It did not function well with the distribution of patient visits. This observation regarding the negative binomial distribution is discussed in the context of further searches for a solution to the denominator problem.

Adolescent↗
PubMed1998

Patterns of macroparasite aggregation in wildlife host populations.

Frequency distributions from 49 published wildlife host-macroparasite systems were analysed by maximum likelihood for goodness of fit to the negative binomial distribution. In 45 of the 49 (90%) data-sets, the negative binomial distribution provided a statistically satisfactory fit. In the other 4 data-sets the negative binomial distribution still provided a better fit than the Poisson distribution, and only 1 of the data-sets fitted the Poisson distribution. The degree of aggregation was large, with 43 of the 49 data-sets having an estimated k of less than 1. From these 49 data-sets, 22 subsets of host data were available (i.e. host data could be divided by either host sex, age, where or when hosts were sampled). In 11 of these 22 subsets there was significant variation in the degree of aggregation between host subsets of the same host-parasite system. A common k estimate was always larger than that obtained with all the host data considered together. These results indicate that lumping host data can hide important variations in aggregation between hosts and can exaggerate the true degree of aggregation. Wherever possible common k estimates should be used to estimate the degree of aggregation. In addition, significant differences in the degree of aggregation between subgroups of host data, were generally associated with significant differences in both mean parasite burdens and the prevalence of infection.

Animals↗
PubMed1996

Assembly and suppression of endogenous Kv1.3 channels in human T cells.

The predominant K+ channel in human T lymphocytes is Kv1.3, which inactivates by a C-type mechanism. To study assembly of these tetrameric channels in Jurkat, a human T-lymphocyte cell line, we have characterized the formation of heterotetrameric channels between endogenous wild-type (WT) Kv1.3 subunits and heterologously expressed mutant (A413V) Kv1.3 subunits. We use a kinetic analysis of C-type inactivation of currents produced by homotetrameric channels and heterotetrameric channels to determine the distribution of channels with different subunit stoichiometries. The distributions are well-described by either a binomial distribution or a binomial distribution plus a fraction of WT homotetramers, indicating that subunit assembly is a random process and that tetramers expressed in the plasma membrane do not dissociate and reassemble. Additionally, endogenous Kv1.3 current is suppressed by a heterologously expressed truncated Kv1.3 that contains the amino terminus and the first two transmembrane segments. The time course for suppression, which is maximal at 48 h after transfection, overlaps with the time interval for heterotetramer formation between heterologously expressed A413V and endogenous WT channels. Our findings suggest that diversity of K+ channel subtypes in a cell is regulated not by spatial segregation of monomeric pools, but rather by the degree of temporal overlap and the kinetics of subunit expression.

Cell Line↗
PubMed1993

Design and analysis of veterinary vaccine efficacy trials.

Vaccination-challenge tests that involve all-or-none responses and do not require a direct comparison between vaccinates and controls can be completely characterized by the binomial distribution. Consumer and producer risks associated with binomial distribution based tests can be adjusted by altering the number of animals involved and the criterion for acceptance. Clinical signs or other outcomes measured on an ordinal or ranking scale should generally be analyzed by nonparametric statistical procedures. Parametric statistical tests are the most appropriate for data measured on an interval scale if the necessary assumptions are met concerning the population sampled. The use of in vitro potency tests in quality control procedures for inactivated vaccines depends on the demonstration of a significant dose-response efficacy relationship in the host animal.

Analysis of Variance↗
PubMed1999

Analysis of geographical heterogeneity in live-birth ratio in Thailand.

BACKGROUND: Live-birth (male-female) ratios are a standard measure used in demography. Recently, live-birth ratios have been considered as a potential indicator for various environmental hazards. In this paper, mixture modeling is applied to analyse the geographic heterogeneity of live-births in their composition of male and female proportions (live-birth ratio) in the Kingdom of Thailand. METHODS: Live-birth data are taken from the 1990 census of the Kingdom of Thailand. The level of aggregation is the province, of which there are 73 in Thailand. The analysis is based on the simple observation that a logical equivalent to the live-birth ratio is available, namely the proportion of male live-births. Based on this measure a simple and exact statistical model is easily derived: conditional on the number of live-births, the number of male live-births forms a binomial distribution, with parameter lambda. If there is homogeneity in the proportion of male live-births, then all provinces can be described by means of a single binomial distribution. However, if there is heterogeneity in the proportion parameter lambda, then a mixture of binomial distributions will occur. RESULTS: For the 1990 census data, three groups could be identified: a majority group containing 84% of the provinces and a proportion parameter of lambda = 0.513, a group of five provinces having a reduced proportion parameter of lambda = 0.500 (fewer male live-births), and a group of four provinces having an increased proportion parameter of lambda = 0.525. CONCLUSIONS: It is unclear how this can be explained, although some potential explanations are offered. The stability of these groups in time should be confirmed and regularly monitored.

Bias↗
PubMed1979

The micronucleus test: statistical design and analysis.

Alternative statistical procedures are discussed which may be employed to compare the incidences among treatment groups of micronucleated polychromatic and normochromatic erythrocytes and their ratios. Comparison of incidences of micronucleated polychromatic erythrocytes using a sequential sampling strategy based on the negative binomial distribution is shown to require fewer animals for the same sensitivity of test than a similar procedure based on the binomial distribution. The sequential test is superior, both in power and number of animals required, to an alternative 1-stage test based on the same distribution. The procedure described permits the investigator to optimize the number of animals in each test group and the number of cells counted per animal to detect a predetermined increase in the incidence of micronucleated cells over that observed in the control population within chosen limits of type I and type II error. An alternative sequential approach based on the binomial distribution is presented, which is applicable when the number of cells analyzed per animal is variable.

Animals↗
PubMed1997

Theoretical basis for sampling statistics useful for detecting and isolating rare cells using flow cytometry and cell sorting.

This paper describes new approaches to calculating the number of cells that need to be processed using flow cytometry (FCM) techniques and the subsequent time required in order to isolate a specific number of cells having selected characteristics. The methods proposed use probabilistic assumptions about the contents of the sample to be sorted, logarithmic/exponential transformations to avert the computer "underflow" and "overflow" limitations of brute force calculations for the parameters of the binomial distribution imposed by existing computer hardware, and an established mathematical procedure for calculating error bounds for the normal approximation to the binomial distribution. Estimates are derived for the total number of cells in the FCM sample volume that must be available for processing and, for given FCM cell sorting decision speeds, the total elapsed times necessary to conduct particular experiments. The proposed approach obviates the need to resort to calculation expediencies such as the theoretically limited Poisson approximation for what can be considered a Bernoulli process mathematically characterized by the binomial distribution. Tables and graphs illustrate the projected times required to complete FCM experiments as a function of "effective" cell sorting decision speeds. Results from this paper also demonstrate that, as the "effective" cell sorting decision speed increases, there may not be a corresponding linear decrease in the time required to sort a given number of cells with selected statistical properties. The focus of this paper is on the use of innovative mathematical techniques for the design of experiments involving rare cell sorting. However, these same computational approaches may also prove useful for the high-speed enrichment sorting of non-rare cell subpopulations.

Cell Separation↗
PubMed1985

Bilateral distribution of implantation sites in small mammals of 22 North American species.

The distribution of activity between the left and right sides of the reproductive tract, as measured by numbers of CL, embryos and placental scars, was studied in small mammals of 22 species. Shrews ovulate from the two ovaries in a distribution that does not differ from the binomial. Implantation of blastocysts in the two uterine horns is more nearly even ('balanced') than would be predicted from the binomial distribution. Balance in this group apparently is achieved by transuterine migration of blastocysts, perhaps in conjunction with some spacing mechanism within the uterus. Some cricetid rodents show little or no balance, but in others the distribution of activity sites (embryos, CL and placental scars) departs significantly from the binomial distribution. Reproductive activity sites of heteromyid and geomyid rodents (Geomyoidea) are highly balanced; uterine balance apparently is achieved by means of ovarian rather than uterine control. We know of no previous reports of ovarian balance and suggest that physiological mechanisms controlling numbers of ovulations in the species exhibiting this characteristic may differ from those in species exhibiting a random distribution of ovulation sites. Hypotheses regarding evolutionary aspects of balance are considered in phylogenetic and ecological terms, generating several testable research questions for physiologists, anatomists, and evolutionary ecologists.

Animals↗