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PubMed1995

Cluster sampling techniques in quantal response teratology and developmental toxicity studies.

This paper presents a model-free approach for evaluating teratology and developmental toxicity data involving clustered binary responses. In teratology studies, a major statistical problem arises from the effect of intralitter correlation, or the potential for littermates to respond similarly. Some statistical methods impose strict distributional assumptions to account for extra-binomial variation, while others rely on nonparametric resampling and empirical variance estimation techniques. Quasi-likelihood methods and generalized estimating equations (GEE), which model the marginal mean/variance relationship, also avoid strict distributional assumptions. The proposed approach, often used to analyze complex sample survey data, is based on a first-order Taylor series approximation and a between-cluster variance estimation procedure, yielding consistent variance estimates for binomial-based proportions and regression coefficients from dose-response models. The cluster sample technique, presented here in the context of a logistic dose-response model, incorporates many of the advantages of quasi-likelihood methods, are valid for any underlying nested correlation structure, and are adaptable to a variety of analytical settings. The results of a simulation study show the cluster sample technique to be a viable competitor to GEE methods currently receiving attention.

Abnormalities, Drug-Induced↗

PubMed1981

Lesion distribution, multiple infection, and the logistic increase of plant disease.

The lesions of few of the 112 observed cases of plant disease were randomly distributed; most were fitted by the negative binomial function with exponent approximately 1. The proportion of healthy hosts generally equaled the frequency of zero in the negative binomial. The same course of an epidemic is calculated for the logistic increase of infected plants or for plants infected by propagules produced in proportion to lesions and distributed with exponent equal 1.

Journal Article↗

PubMed1993

Spatial and temporal variations in prevalence, intensity and aggregation of microfilaria in the human host.

The prevalence, intensity and the frequency distribution of microfilaria (mf) of Wuchereria bancrofti in the human blood and their variation in time (pre-vector control, control and post control periods) and space have been examined. The prevalence and intensity showed significant variation between time and different areas of urban Pondicherry. The significant reduction in the prevalence and intensity of microfilaremia in the areas of high endemicity indicated that the effect of vector control was well marked in these areas. The distribution of microfilaria in human population was adequately described by the truncated negative binomial prior to interruption of transmission, and the dispersion parameter 'k' of the negative binomial varied between 0.17 and 0.68. A change in the distribution was observed after the 5 years of vector control, during which the transmission was completely interrupted. The increased 'k' values suggest that the distribution of mf is influenced by the degree of exposure to infection. Therefore, comparison of changes in the parameter 'k' can be considered as an additional tool for evaluating the control operations aimed at interrupting the transmission.

Animals↗

PubMed1994

The analysis of 2 x 1 and 2 x 2 contingency tables: an historical review.

This paper describes the historical development of analytic techniques for frequency data presented as 2 x 1 or 2 x 2 contingency tables. The issues raised include: the need for a continuity correction when estimating the exceedance probability of a discrete statistic; the vulnerability of such statistics to a conservative bias when used in hypothesis testing; and the different statistical models that may underlie contingency tables. In the case of 2 x 1 contingency tables the recommended technique is the binomial test with a modified decision procedure for hypothesis testing. In the case of 2 x 2 contingency tables there is a single statistic approximating the chi-square distribution which can be used to test the hypothesis of an association between the two relevant variables and which in most practical situations is robust with respect to the occurrence of small expected cell frequencies.

Bias↗

PubMed2003

A longitudinal study of a natural lice infestation in growing cattle over two winter periods.

A group of 61 cattle which were naturally infested with lice was followed over two winter periods. Data were collected on the number of lice found at various body sites over this period. Summary statistics were produced and due to the repeated measured and hierarchical structure of the data, multi-level analysis was used to model the population dynamics of Bovicola bovis and assess the influence of the various hierarchical levels. A four level Poisson model was produced--level one, the individual number of lice at each parting; level two, the body site examined (shoulder, midline or rump); level three, the time of the inspection and level four, the animal. Seasonal fluctuation in lice numbers was modelled using a cosine function transformation of time. A seasonal pattern was seen in both year's with lice counts higher in the first than the second year. The midline area was the most sensitive to detection of B. bovis. Variance contributed by the individual animal was less than that contributed by the body site examined and the time of the inspection. The model suggested that lice numbers within the shoulder and rump sites were near random following a Poisson distribution, but aggregation of lice occurred at the midline site with the distribution between animals following a Negative Binomial Pattern. The midline site was the most sensitive site for detecting B. bovis. Infestation numbers were higher in the first winter when cattle were younger. In the second winter, there was no difference in lice numbers between cattle exposed to infection for the first or second time.

Animals↗

PubMed1996

Order-restricted tests for stratified comparisons of binomial proportions.

The data set presented relates a binomial response to ordered levels of an explanatory variable, representing doses of a drug, with data collected at several centers. A study goal is to test independence of the response and the ordinal factor, assuming under the alternative only that the binomial parameter is a monotonically increasing function of the ordinal predictor. We present two likelihood-ratio tests that are sensitive to order-restricted alternatives. Simulating the exact distributions of the test statistics yields nearly exact P-values. We also discuss related analyses for comparing two groups on an ordinal response, and we propose a test that is sensitive to a stochastic ordering alternative.

Binomial Distribution↗

PubMedDate not supplied

Methodological issues in assessing the incidence of peritoneal dialysis-associated peritonitis in children.

OBJECTIVES: To evaluate the distribution of peritonitis incidence and assess the usefulness of patient-specific peritonitis rates in children. DESIGN: 49 children on automated peritoneal dialysis (PD) followed during a 2-year observation period. SETTING: Single-center, academic children's hospital. PATIENTS: 49 children aged 2 months to 18 years; 24 prevalent, 25 incident during the observation period. Cumulative observation time was 639 patient-months. MAIN OUTCOME MEASURES: Cohort-specific peritonitis incidence, median patient-specific peritonitis incidence, mean peritonitis incidence by gamma-Poisson (negative binomial) modeling, peritonitis-free survival by Kaplan-Meier life-table analysis. RESULTS: 68 new peritonitis episodes and 21 relapses occurred in 27 patients. The distribution of patient-specific peritonitis incidence was bimodal, with a large group experiencing no or very few episodes, and another cluster around 1 episode per 6-9 months. Overall cohort-specific peritonitis incidence was 1.28, median subject-specific incidence 0.99, and mean incidence according to negative binomial modeling 1.04 (95% confidence interval 1.02-1.06) episodes per patient-year. Median peritonitis-free survival time was 6.9 months. In those patients who developed peritonitis, subject-specific peritonitis incidence was inversely correlated with patient age (r = -0.42, p < 0.05) and duration of chronic PD at last observation (r = -0.42, p < 0.05). CONCLUSIONS: Since the distribution of peritonitis in children is non-Gaussian, the average risk of peritonitis is more accurately expressed by the median of the individual subject-specific peritonitis rates or by the mean incidence estimate obtained by the negative binomial distribution model. The assignment of a personal peritonitis risk to each patient permits risk factor analysis by routine statistical methods, even in smaller populations.

Adolescent↗

PubMed1991

Probabilistic secretion of quanta from nerve terminals in toad (Bufo marinus) muscle modulated by adenosine.

1. A study has been made of the effect of blocking endogenous adenosine on the statistics of quantal secretion at nerve terminals in toad (Bufo marinus) muscle during summer and winter. 2. Exogenous adenosine (10-50 microM) reduces the mean quantal content of the endplate potential (EPP) recorded with an intracellular microelectrode (m) by 36 +/- 6% (mean +/- S.E.M.), independent of the control value of m in both summer and winter. The variance of the EPP (S2) was reduced by adenosine in proportion to m, so that the probability of quantal secretion (p) remained relatively constant. 3. Exogenous adenosine reduces the mean quantal content of secretion recorded with an extracellular electrode (m(e)) to a similar extent (47 +/- 6%) at different relatively high secreting sites along nerve terminal branches in both summer and winter. 4. Both theophylline (20-100 microM) and adenosine deaminase (2.5 i.u./ml) increase the amplitude of the EPP in summer in a [Ca2+]o of 0.5 mM or greater; a maximum increase of about 40% is reached at a [Ca2+]o of 1.2 mM. The amplitude of the EPP in winter is usually reduced by theophylline in a [Ca2+]o of 0.5 mM, but is always increased in a [Ca2+]o greater than 0.9 mM to reach a maximum increase of about 40% at high [Ca2+]o. 5. The variance of the EPP (S2) was always increased by theophylline to a greater extent than m in summer, so that p decreased and Poisson rather than binomial statistics could be used to describe the distribution of EPP amplitudes. In winter, theophylline generally increased m and S2 to about the same extent, so that p did not change much. 6. An autocorrelation analysis of the amplitude of successive EPPs in a long train at 0.5 Hz in high [Ca2+]o showed that these are likely to be independently distributed. Adenosine secreted by one impulse is then unlikely to affect secretion by a subsequent impulse in the train. 7. These observations are discussed in terms of the hypothesis that endogenously secreted adenosine at a release site inhibits secretion by nearby release sites in summer; this has the effect of reducing m and to a greater extent S2 so that binomial rather than Poisson statistics can describe the frequency distribution of EPP amplitudes.

Acetylcholine↗

PubMed2006

Inter-rater reliability of nursing home surveys: a Bayesian latent class approach.

In the U.S., federal and state governments perform routine inspections of nursing homes. Results of the inspections allow government to generate fines for findings of non-compliance as well as allow consumers to rank facilities. The purpose of this study is to investigate the inter-rater reliability of the nursing home survey process. In general, the survey data involves 191 binary deficiency variables interpreted as 'deficient' or 'non-deficient'. To reduce the dimensionality of the problem, our proposed method involves two steps. First, we reduce the deficiency categories to sub-categories using previous nursing home studies. Second, looking at the State of Kansas specifically, we take the deficiency data from 1 year, and use Bayesian latent class analysis (LCA) to collapse the sub-categories to a binary variable. We evaluate inter-rater agreement using deficiency data from two separate survey teams on one facility, a matched-pair design. We evaluate the agreement of the two raters on binary data using the weights from the LCA. This allows a two-by-two contingency analysis using a Bayesian beta-binomial model. We elicit informative prior distributions from the nursing home providers. Together, with the experimental data, this provides a posterior distribution of the kappa agreement of the raters for nursing home deficiency citation data.

Bayes Theorem↗

PubMed1991

Statistical methods for analyzing developmental toxicity data.

A description and review of methods for performing per-litter analyses involving extrabinomial proportion response is provided. It is stressed that the litter should be regarded as the appropriate experimental unit for quantitative analysis in studies for teratogenic or heritable mutagenic effects. Attention is directed at statistical identification of possible treatment effects, such as a positive dose response to a chemical stimulus. The methods range from distribution-free, nonparametric analyses to models involving parametric distributions such as the beta-binomial density. It is seen that most current methods require computer implementation. When concern is raised over misspecification of assumptions critical to the statistical analysis, it is argued that relatively parameter-free methods are appropriate for use. These include statistical bootstrapping and rank-based analyses.

Models, Statistical↗

PubMed1976

Frequency Distribution Of Enterobius Vermicularis In A Highly Endemic Population.

The distribution patterns of worm burden of Enterobius vermicularis were studied in a primary school in rural part of Korea, on July, September and November 1976, for successively three times on 285 children. Out of the subjected children treated with pyrantel pamoate at the dose of 10 mg/kg body weight, 107 in the first, 55 in the second and 43 in the third trials were cooperative in the satisfactory collection of whole amount of feces for three days in respective trials. The distribution patterns of worm burden in these subjected children were considered by statistical analyses for the fitness with theoretical lognormal and negative binomial frequencies. The theoretical values from equations of lognormal distribution was fitted to the observed frequency distibution patterns throughout three trials, but in the second trial undertaken on September 17, 1976, both the lognormal and negative binomial were found to fit the observed data, probably because of rarity of heavy infection cases and high frequency of noninfected cases.

Journal Article↗

PubMed1981

Steiger on refraction: a reappraisal.

Seventy years ago Steiger, a Swiss ophthalmologist, found the distribution of corneal powers to follow a normal (binomial) curve. He noted a wide range of values among emmetropes, and he also knew that their axial lengths varied significantly. He expected that normal distributions would be found for other components of refraction and also for refraction as a whole, and in seeking a controlling mechanism he recalled the multifactorial pattern of inheritance of such characteristics as stature. The present study employs modern mathematical techniques to test the validity of 2 related hypotheses: that the components of refraction are correlated and that a polygenic mode of inheritance is responsible for determining the refractive power of the eye. In the light of this study and of other modern knowledge about refraction Steiger's work is reassessed. Most of his views are vindicated, although his assumption of a normal distribution for refraction as a whole could not be justified. His contribution to the understanding of refraction establishes him among the great names in ophthalmology.

Adult↗

PubMed1995

Quantal analysis of EPSCs recorded from small numbers of synapses in hippocampal cultures.

1. We have studied the statistical properties of excitatory post-synaptic currents (EPSCs) measured at small numbers of synaptic contacts between pairs of hippocampal neurons maintained in dissociated cell culture. Synaptic transmission at few synapses was enabled by microperfusion of a small region of the postsynaptic cell with Ca-containing solution, while blocking transmission at all other synaptic boutons by bathing them in low-Ca solution. Frequency histograms of the amplitudes of EPSCs recorded in this way showed no clear quantization. Numbers of active synapses, estimated immunohistochemically with the use of light microscopy, ranged from 4 to 14 in different experiments. 2. Miniature EPSCs (mEPSCs), originating in the same small population of synapses as produced the evoked EPSCs, were elicited by microperfusion of bath solution made hypertonic by the addition of sucrose. These "sucrose-evoked" mEPSCs appeared to be identical to "spontaneous" mEPSCs in every respect except control over their frequency and site of origin. Sucrose-evoked mEPSCs originating in few synapses still exhibited a broad amplitude distribution. Thus, if mEPSCs constitute the postsynaptic response to a single quantum of neurotransmitter (the "quantal amplitude"), their broad amplitude distribution would tend to obliterate evidence of quantization in evoked EPSC amplitudes, even if evoked release was, indeed, quantal. 3. This idea, which is a corollary of the Katz model of quantal transmission, was tested quantitatively by assuming 1) neurotransmitter release obeys uniform binomial statistics, and 2) the quantal amplitude has a distribution given by the observed distribution of sucrose-evoked mEPSCs. The expected distribution, calculated on the basis of these two assumptions, was fitted to the observed distribution of evoked EPSC amplitudes by varying two free parameters, the binomial parameters N and p. In five cells out of six that were fully analyzed, the Poisson limit of the binomial model (N large, p small) provided a very good fit to the data. This and other evidence suggests that the release probability at a single presynaptic terminal is low. In two out of the six cells, the binomial model, with N constrained to the histochemically determined bouton count, yielded acceptable fits; for the remaining cells the constrained binomial model could be rejected. 4. It is concluded that the Katz model of quantized release of neurotransmitter gives an adequate description of excitatory synaptic transmission in hippocampal cultures, when one assumes the broad distribution of mEPSC amplitudes reflects the distribution of the postsynaptic effect of a single quantum of transmitter.

Animals↗

PubMed1978

Variability of chimaeras and mosaics.

Aggregation chimaeras and X-inactivation mosaics in mice are alike in general appearance, but chimaeras are very much more variable in the proportions of the cell types (p) seen for example in coat pigmentation. The distribution of p in chimaeras is not binomial, but is uniform, or flat, between the two extremes. The greater variability of chimaeras arises from two sampling events that occur when cellular heterogeneity is already present in chimaeras but before it arises in mosaics. These are the differentiation of the inner cell mass from the trophectoderm and of the primary ectoderm from the primary endoderm. The second of these generates the flat distribution of chimaeras as a consequence of the two cell types being unmixed at that time. The two sampling events generate single-colour individuals in roughly the proportions observed. Consideration of the second sampling event provides evidence that the primordial germ cells must originate in the primary ectoderm and not in the yolk-sac. Estimation of numbers of progenitor cells on the supposition of binomial sampling is not valid unless the clone-size is known or the cells in the sample are not contiguous. Data on coat pigmentation are consistent with the assumptions that X-inactivation is random in about 21 cells, that the sampling of melanoblasts is binomial (because they are not contiguous), and that the melanocytes of the head and body are descended from about 34 progenitor cells.

Animals↗

PubMedDate not supplied

[Distribution and mechanism of the regulation of the pleurocercoid population count of Triaenophorus nodulosus (Cestoda, Triaenophoridae)].

The character of the distribution of pleurocercoids of Triaenophorus nodulosus depending on the host age is shown. Their distribution in perch at the age of 0+-4+ is over dispersed in its character and is described by negative binomial. At the age of 5+ to 8+ the distribution of parasites is of regular character that is apparently due to changes in the mechanism of regulation of the parasites number. The regulation mechanism of the number of pleurocercoids of T. nodulosus is discussed.

Aging↗

PubMed1995

Additivity test for composition of binomial effects in chromosome aberrations after radiation injury.

Additivity of clastogenic effects of two doses of radiation to human peripheral blood lymphocytes is considered. We compare the effects of combined tritium and gamma irradiation with the sum of the effects of either irradiation administered separately. Our solution is based on combination of de Moivre and Cramèr-Slucky theorems. The results for 14 subjects where the deletion types of chromosome aberrations were counted indicate a Normal distribution of the sample additivity index, oscillating non-significantly around zero, with one outlier towards adaptivity and another towards synergism of the effect of the two doses absorbed by the cells.

Adult↗

PubMed2026

Stretched penile length in boys with hypospadias: Population-based analysis using validated nomogram.

BACKGROUND: Hypospadias affects 1 in 200-300 male births. Parents are often concerned about penile adequacy beyond the urethral defect itself, yet few studies have systematically compared stretched penile length (SPL) in hypospadias against population-based reference standards. OBJECTIVE: To evaluate SPL distribution patterns in boys with Types I and II hypospadias and compare them with established normative data. METHODS: The authors studied 876 consecutive boys aged 1-14 years with unoperated Types I (distal) and II (mid-shaft) hypospadias. Two observers independently measured SPL using the validated SPLINT technique. The SPL measurements were compared against age-matched normative data from 1276 Indian children. Exact binomial probability tests were used for percentile distributions, chi-square tests for subtype comparisons and t-tests for mean deviations. RESULTS: The cohort included 479 Type I and 397 Type II cases. SPL distribution showed a marked leftward shift: 71% fell below the 50th percentile (expected 50%, p < 0.001) and 41.5% below the 25th percentile. Lower percentiles were overrepresented, 20.7% were below the 10th percentile and 20.8% in the 10th-25th range. Upper percentiles were depleted: only 7.4% in the 75th-90th range and 1.7% above the 90th percentile (all p < 0.001). Mean SPL was reduced by 6.8% (95% CI: -8.18 to -5.42%) in Type I and 7.5% (95% CI: -9.05 to -5.92%) in Type II. The two subtypes showed no significant distributional difference (χ2 = 6.22, p = 0.18), suggesting that meatal position does not predict SPL reduction. CONCLUSIONS: Boys with distal and mid-shaft hypospadias show clinically meaningful SPL reduction that follows a continuous distribution rather than an all-or-none pattern. SPL reduction appears independent of meatal position. These findings support routine SPL assessment using population-specific references and can guide preoperative counselling.

Humans↗

PubMed1995

A bivariate limiting distribution of tumor latency time.

The model of radiation carcinogenesis, proposed earlier by Klebanov, Rachev, and Yakovlev [8] substantiates the employment of limiting forms of the latent time distribution at high dose values. Such distributions arise within the random minima framework, the two-parameter Weibull distribution being a special case. This model, in its present form, does not allow for carcinogenesis at multiple sites. As shown in the present paper, a natural two-dimensional generalization of the model appears in the form of a Weibull-Marshall-Olkin distribution. Similarly, the study of a randomized version of the model based on the negative binomial minima scheme results in a bivariate Pareto-Marshall-Olkin distribution. In the latter case, an estimate for the rate of convergence to the limiting distribution is given.

Animals↗