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PubMed1976

On the regularities of distribution of Hypoderma bovis De Geer larvae parasitizing cattle herds in different parts of the range of this warble fly.

The type and parameters of the distribution of the second and third instar larvae of Hypoderma bovis in cattle herds in Czechoslovakia (54 herds, 7233 head), Mongolia (20 herds, 1809 head) and the USSR (48 herds, 4978 head) were studied. A statistical analysis showed a) that in the majority of cases negative binomial distribution serves as a model of the distribution of larvae with sufficient reliability; b) that the regularity of dependence of the distribution exponent k of the negative binomial distribution on the incidence of infestation remains constant in different parts of the range of this warble fly. The latter fact indicates that the regulatory systems limiting the population numbers of this warble fly are associated with host-parasite relationships and do not depend on a complex of conditions specific for various natural zones. In order to understand the regulatory processes in parasite populations it is necessary to study equally the regulatory mechanisms operating primarily on the level of specimens as well as the regulatory systems operating on the level of populations.

Animals↗

PubMed1976

On the regularities of distribution of Hypoderma bovis De Geer larvae parasitizine cattle herds in different parts of the range of this warble fly.

The type and parameters of the distribution of the second and third instar larvae of Hypoderma bovis in cattle herds in Czechoslovakia (54 herds, 7233 head), Mongolia (20 herds, 1809 head) and the USSR (48 herds, 4978 head) were studied. A statistical analysis showed a) that in the majority of cases negative binomial distribution serves as a model of the distribution of larvae with sufficient reliability; b) that the regularity of dependence of the distribution exponent k of the negative binomial distribution on the incidence of infestation remains constant in different parts of the range of thes warble fly. The latter fact indicates that the regulatory systems limiting the population numbers of this warble fly are associated with host-parasite relationships and do not depend on a complex of conditions specific for various natural zones. In order to understand the regulatory processes in parasite populations it is necessary to study equally the regulatory mechanisms operating primarily on the level of specimens as well as the regulatory systems operating on the level of populations.

Animals↗

PubMed1988

Doxapram dosage regimen in apnea of prematurity based on pharmacokinetic data.

To 18 premature apneic patients refractory to theophylline, doxapram (0.5-2.5 mg/kg/h) was administered in combination with therapeutic doses of theophylline. Doxapram concentrations in serum were measured 48 h after commencement of the infusion and then in 2-hour intervals during a 6-8 h withdrawal. Total body clearance (dose/Css) of the drug ranged from 0.20 to 0.56 liter/h in 13 patients and 1.14 to 1.75 liter/h in 4 patients suggesting a binomial distribution in the disposition kinetics of the drug. Other pharmacokinetic indices, although variable, did not exhibit binomial distribution. The mean volume of distribution and half-life of doxapram were 7.33 +/- 4.55 liter/kg and 8.17 +/- 4.13 h, respectively. Based on our calculations to accelerate the attainment of a steady-state plasma concentration (Css) of approximately 1.5 mg/l, a loading dose of 5.5 mg/kg and a maintenance dose of 1 mg/kg/h along with serum concentration monitoring are recommended.

Apnea↗

PubMed1986

Estimation and analysis of the concentration-response surfaces associated with multiple-agent combinations.

Chinese hamster cells (V79) were treated with ethylnitrosourea (ENU) and cis-diamminedichloroplatinum(II) (DDP) alone and in combination. Sister chromatid exchanges (SCEs) were quantified as measures of genotoxicity of the two agents. The combination experiment employed a factorial design in which cells were treated, in various concentration combinations, with both agents simultaneously. Response surface methodology, using a polynomial model based on a negative binomial distribution of SCE events, was employed for analysis of the interactions of the two genotoxic agents. The negative binomial distribution, a generalization of the Poisson distribution, is required since SCEs are discrete variables which, under the conditions of these experiments, have a distribution which exhibits extra-Poisson variability. The model of the ENU/DDP combinations indicated an increasingly less-than-additive effect resulting from increasing concentrations of each agent in the combination. The analysis of these experiments demonstrates the usefulness of a powerful statistical procedure for evaluating the biological effects resulting from exposure to multiple cytotoxic agents. The methodology can be used with many other types of endpoints and is not limited by the number of treatment agents.

Cells, Cultured↗

PubMed1976

The distribution of fetal death in control mice and its implications on statistical tests for dominant lethal effects.

In dominant lethal testing fetal death is generally assumed to follow either a Poisson or binomial distribution. However, both of these models were found to be inappropriate when three large sets of mouse control data and other data sets from the literature were examined. The validity of statistical test procedures based on these inappropriate models was then studied in detail. It was found that chi-square tests (which assume an underlying binomial distribution) may seriously exaggerate the level of significance and hence should not be used. In contrast, the inappropriateness of the underlying Poisson or binomial model appeared to have little effect on the validity of pairwise comparisons by analysis of variance procedures. Unlike chi-square, these procedures regard the pregnant female rather than the individual implant as the experimental unit. However, a statistical analysis of dominant lethal data generally involves more than a series of pairwise comparisons, and it is unclear how an invalid underlying model may affect statistical test procedures in this more complex situation. Moreover, it is difficult to justify the use of statistical models that are demonstrably invalid when a reasonable alternative exists. Thus, until a satisfactory parametric model can be found and appropriate test procedures derived, we prefer to analyze dominant lethal data by non-parametric (distribution-free) methods. Proportion of dead implants per female appears to be a more meaningful measure of fetal death than number of dead implants per female for several seasons which include (1) analyses based on proportions take the total number of implants per female into account and (2) analyses based on proportions make more reasonable assumptions concerning pre-implantation losses and are more powerful when such losses occur. Despite our concern with the appropriateness of the underlying model, in practice we have found few instances in which non-parametric and analysis of variance procedures have led to markedly different conclusions.

Animals↗

PubMed1988

The statistical analysis of graft patency data in a clinical trial of antiplatelet agents following coronary artery bypass grafting.

Because most coronary artery bypass patients receive more than one graft at surgery, it is most important to determine whether statistical analysis of graft patency should be performed on the premise that the multiple grafts within patients are dependent or independent experimental units. Veterans Administration Cooperative Study No. 207 was a multicenter clinical trial comparing four different antiplatelet regimens to placebo in the prevention of graft occlusion following coronary artery bypass grafting. Using the results from the 1-week postoperative angiograms from the Veterans Administration Cooperative Study No. 207, in which there were 3.2 distal anastomoses per patient, we have tested the hypothesis that grafts within patients tend to act dependently with respect to patency or occlusion by comparing the graft patency data to a binomial distribution (i.e., that distribution that would have been manifest if grafts were independent). Because the graft patency results in Study No. 207 significantly deviated from the binomial distribution (p = 0.0003), a more appropriate analysis for graft patency data was applied using a ratio estimate as applied to cluster sampling. The statistical methods used in 11 previous clinical trials of antithrombotic therapy after coronary artery bypass grafting were examined. Only one of the previous studies used such an analysis, and three additional reports attempted to correct for dependency of grafts within patients in their analyses using other statistical methods. In seven of the studies the investigators did not address the potential problem of a dependent relationship between multiple grafts within patients. We conclude that grafts within patients act as dependent experimental units and that the ratio estimate as applied to cluster sampling may be appropriately applied to these data.

Clinical Trials as Topic↗

PubMed1979

[Falsely positive values in multi-channel analysis: An iniquiry into reference and patient groups (author's transl)].

The number of falsely positive values occurring in 12-channel analysis was determined in two groups of patients and reference individuals. It revealed that the portion of falsely positive values actually found was statistically significant beyond that calculated on the assumption of a binomial distribution. Partly distinct correlations of the parameters combined to a profile as well as clear deviations from the normal distribution have to be taken into consideration as reasons for this discrepancy between theory and reality. The results show that the application of the binomial distribution leads to statements which significantly differ from the conditions actually present.

Autoanalysis↗

PubMed1986

The question of the total gene number in Drosophila melanogaster.

A statistical analysis has been carried out on the distribution and allelism of nearly 500 sex-linked, X-ray-induced, cytologically normal and rearranged lethal mutations in Drosophila melanogaster that were obtained by G. Lefevre. The mutations were induced in four different regions of the X chromosome: (1) 1A1-3E8, (2) 6D1-8A5, (3) 9E1-11A7 and (4) 19A1-20F4, which together comprise more than one-third of the entire chromosome.--The analysis shows that the number of alleles found at different loci does not fit a Poisson distribution, even when the proper procedures are taken to accommodate the truncated nature of the data. However, the allele distribution fits a truncated negative binomial distribution quite well, with cytologically normal mutations fitting better than rearrangement mutations. This indicates that genes are not equimutable, as required for the data to fit a Poisson distribution.--Using the negative binomial parameters to estimate the number of genes that did not produce a detectable lethal mutation in our experiment (n0) gave a larger number than that derived from the use of the Poisson parameter. Unfortunately, we cannot estimate the total numbers of nonvital loci, loci with undetectable phenotypes and loci having extremely low mutabilities. In any event, our estimate of the total vital gene number was far short of the total number of bands in the analyzed regions; yet, in several short intervals, we have found more vital genes than bands; in other intervals, fewer. We conclude that the one-band, one-gene hypothesis, in its literal sense, is not true; furthermore, it is difficult to support, even approximately.--The question of the total gene number in Drosophila will, not doubt, eventually be solved by molecular analyses, not by statistical analysis of mutation data or saturation studies.

Alleles↗

PubMed1987

Temporal changes in aggregation: a laboratory study.

Changes in the variance to mean ratio and the parameter k of the negative binomial distribution were used to study temporal changes in the degree of aggregation of the monogenean parasite, Gyrodactylus turnbulli in free-running laboratory populations of the guppy, Poecilia reticulata. The parasite undergoes recurrent epidemic cycles in the host population under conditions of regular immigration of uninfected guppies. During the early phase of the epidemic, heterogeneity among fish together with direct reproduction are thought to contribute to the increasing degree of aggregation. During the increasing phase of the epidemic cycle, parasites become increasingly aggregated in the host population, presumably because of the direct reproduction of the parasite on the surface of a single host. As the peak prevalance and abundance are approached, the parasites become less aggregated with lowest clumping occurring during the declining phase of the cycle. This is thought to be a function of density-dependent death of infected hosts, and density-dependent reduction in parasite survival and reproduction on hosts that recover from infection. This study clearly indicates that the variance to mean ratio and the parameter k of the negative binomial distribution do not quantify the same aspect of the frequency distribution. It is suggested that the variance to mean ratio is a better measure when the prevalence and/or mean burden are changing and when the tail of the distribution is of particular interest, and that k may be a preferred parameter when the zero class or the lightly infected hosts are of primary interest.

Animals↗

PubMed1977

[Use of various accordance measures in the study of sick leave frequency distribution per man-year].

In the studies of a wide number of phenomena very often an attempt to describe their distributions with the help of certain theoretical distributions is undertaken. Pearson's chi2 and Kolmogorovs lambda traditional tests, when applied to the evaluation of accordance between the empirical distribution and the distribution calculated on the basis of theoretical probability function, depend directly on the dimensions of population studied, and they are not useful in the case of big quantities. In the paper the author presents a great number of measures for two (empirical and theoretical) distributions accordance and their application to the study of sick-leave frequency distribution per man per year. On the basis of received results a high level of distributions accordance between the sick leave cases distribution and the negative binomial distribution has been observed. The distribution of sick leave shows a high accordance with the logarithmically-normal distribution. In the light of the above mentioned distribution study, the imperfection of Pearson's chi2 and Kolmogorov's lambda tests can be ascertained. In the case of big quantities the evaluation of distributions accordance seems to require the application of the accordance measures based on relative quantities.

Absenteeism↗

PubMed1990

Applicability of presence-absence and sequential sampling for ovitrap surveillance of Aedes (Diptera: Culicidae) in Chiang Mai, northern Thailand.

Applicability of presence or absence sampling for ovitrap surveillance of Aedes aegypti (L.) and Aedes albopictus (Skuse) was examined for data collected in Chiang Mai, northern Thailand. Distribution of eggs per trap was contagious but did not fit the negative binomial distribution with a common k. The relationship between the mean number of eggs per trap and the proportion of positive traps was described using Gerrard & Chiang's model, which does not assume particular distribution patterns. Using this relation, the mean number of eggs per trap with confidence limits can be estimated without egg counts. Potential usefulness of presence or absence sequential sampling for decision making (when to initiate vector control for prevention of dengue hemorrhagic fever) was shown.

Aedes↗

PubMed1990

Frequency distribution of Wuchereria bancrofti microfilariae in human populations and its relationships with age and sex.

This paper examines the effects of host age and sex on the frequency distribution of Wuchereria bancrofti infections in the human host. Microfilarial counts from a large data base on the epidemiology of bancroftian filariasis in Pondicherry, South India are analysed. Frequency distributions of microfilarial counts divided by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. Parameter estimates from the fits indicate a significant trend of decreasing overdispersion with age in the distributions above age 10; this pattern provides indirect evidence for the operation of density-dependent constraints on microfilarial intensity. The analysis also provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors (around 5% of the total negatives). This allows the construction of corrected mf age-prevalence curves, which indicate that the observed prevalence may underestimate the true figures by between 25% and 100%. The age distribution of mf-negative individuals in the population is discussed in terms of current hypotheses about the interaction between disease and infection.

Adolescent↗

PubMed1991

Frequency distribution of Brugia malayi microfilariae in human populations.

This study examines the effects of host age and sex on the frequency distribution of Brugia malayi infections in the human host. Microfilarial (mf) counts for a large data base on the epidemiology of brugian filariasis in Shertallai, Kerala, South India are analysed. Frequency distributions of microfilarial counts partitioned by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. This analysis provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors, allowing the construction of corrected mf age-prevalence curves, which indicate that the observed prevalence may under-estimate the true figures by between 18 and 47%. There is no evidence from these results for a decrease in the degree of over-dispersion of parasite frequency distributions with host age, such as might be produced by the acquired immunity to infection. This departure from the pattern in bancroftian filariasis (where there is evidence of such decreases in over-dispersion; Das et al. 1990) is discussed in terms of the long history of filariasis control (and consequently low infection prevalence) in Shertallai.

Adolescent↗

PubMed1990

Variability in expression of common fragile sites: in search of a new criterion.

Fragile sites are nonrandom, heritable sites on chromosomes that can be induced to form gaps, breaks, and rearrangements under specific conditions. There is currently no established criterion to define a common fragile site. We applied seven published criteria to our data from three groups of subjects: (1) three pairs of like-sexed twins, (2) four unaffected von Hippel-Lindau (VHL) family members, and (3) six patients affected with VHL disease. Substantial differences were present in the numbers of sites considered positive by these criteria. While some of this variability can be attributed to technical factors, our data illustrate the problems in comparing results from different studies to assess the significance of fragile sites. A recently published criterion is based upon the Poisson distribution. We found this criterion to be flawed in its presentation, and furthermore, the Poisson distribution did not provide an adequate approximation to our data. We propose here an alternative approach based upon the negative binomial distribution.

Binomial Distribution↗

PubMed1990

The relationship between the frequency distribution of Ascaris lumbricoides and the prevalence and intensity of infection in human communities.

Observed field data from a range of geographically distinct human communities suggest a consistent non-linear relationship between prevalence and mean intensity of Ascaris lumbricoides infection. Utilizing the negative binomial distribution as a description of observed aggregation, maximum-likelihood analysis reveals that the degree of aggregation is a negative linear function of mean worm burden. The factors responsible for this relationship in human populations require further study but may involve some combination of (i) density-dependent reduction in worm numbers within individuals, (ii) density-dependent parasite-induced host mortality or (iii) self-treatment by heavily infected hosts. Variability in the degree of aggregation appears dependent on the level of infection in a community and independent of geographical differences in the host or parasite populations.

Animals↗

PubMed1988

Quantitative genetic analysis of bi-iliac breadth.

Bi-iliac breadth, the frontal maximum diameter between right and left iliac crests, was measured in 1,547 male and 2,085 female residents of a rural area in Japan. All subjects were over 14 years of age. The bi-iliac breadth showed an increase related to age but little sex difference. Modification of age and sex variations from the measured value was obtained by calculation of the score, represented by arithmetical means and standard deviations. Distribution of these scores appeared to be binomial, and since binomial distribution approaches normal distribution when n is large, it is presumed that this trait gains normal distribution. Thus variation of bi-iliac breadth in subjects 20-79 years of age enables us to analyze inheritance. No significant difference was found between husband and wife in the correlation coefficients or between father and daughter (0.13 +/- 0.08). Significant differences were found as follows: father-son (0.35 +/- 0.05) (P less than 0.001), mother-son (0.28 +/- 0.05) (P less than 0.001), and mother-daughter (0.28 +/- 0.06) (P less than 0.001). There was no indication of maternal or paternal effects, since no significant difference was found in father-child and mother-child correlation coefficients. It is concluded that bi-iliac breadth is a quantitative genetic trait under control of polygenes on autosomes. Regression coefficient of child on midparental value was 0.55 +/- 0.05, approximately twice the means of four pairs of correlation coefficients between parent-offspring. Narrowly, heritability was estimated as 0.54 approximately 0.55. Contribution of dominance to total variance was small (VD = 0.11), in contrast to the larger additive genetic variance (VA = 0.54).

Adolescent↗

PubMed1976

Evoked neurotransmitter release: statistical effects of nonuniformity and nonstationarity.

Recent studies of the mechanism of quantal neurotransmitter release have assumed that the number of quanta released at each stimulation is binomially distributed and have sought to estimate the binomial parameters n and p. Mathematical analysis and computer simulations show that temporal variation in the number of eligible or filled release sites and either spatial or temporal variation in the probability of release at a site can drastically bias such estimates, while the experimental histograms remain statistically indistinguishable from those predicted by the binomial law. Interpretation of the estimates n and p in terms of ultrastructural or physiological characteristics of the nerve terminal is liable to significant error if departures from the binomial assumptions are not suitably assessed.

Computers↗

PubMed1977

Capillary lengths, anastomoses, and estimated capillary transit times in skeletal muscle.

Total capillary length, capillary segment length, and number of anastomoses per capillary were measured in rat gracilis muscle at rest and after 2 min of phasic contraction. Mean values of the foregoing variables at rest (+/-SD) were, respectively, 1,012 micronm +/- 484, 409 micron +/- 274, and 0.83 +/- 1.09. Total capillary lengths are well described by the gamma distribution, number of anastomoses by the negative binomial distribution, and segment length by the Weibull distribution. Contraction has no significant effect on the means or the frequency distributions, indicating that: 1) pressure gradients between adjacent capillaries are small, and 2) intercapillary anastomoses do not improve flow distribution in exercise. Erythrocyte velocities observed in resting muscle (Burton, K. S., and P. C. Johnson. Am J. Physiol. 223: 517-524, 1972) were shown to be adequately characterized by the gamma distribution. From these velocities and the observed distribution of path lengths, we computed an estimated distribution of capillary transit times. Mean transit time was 4.29 s. The median was 2.45 s, and 11% of values exceeded 8 s. The range was 90 ms-43 s. This heterogeneity of transit times should profoundly affect calculations of O2 transport and the shape of indicator dilution curves.

Animals↗