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PubMed1992

An inferential procedure for the Poisson intervention parameter.

To describe a health chance mechanism whose incidence rate is altered in the middle of a data collection period due to preventive treatments taken by health service agencies, a model called Intervened Poisson Distribution (cf. Shanmugam, 1985, Biometrics 41, 1025-1029) was introduced. In this article, we derive a statistic to test the hypothesis concerning the effectiveness of such preventive treatments, and compare its power with another suggested test (cf. Streit, 1987, Biometrics 43, 999-1000).

Health Services↗

PubMed1992

Repeatability and reproducibility of egg counts of Schistosoma haematobium in urine.

Egg output in urinary schistosomiasis can be influenced by several factors, such as time of collection of urine, day to day variations, seasonal variations and environmental conditions. Additionally there are unavoidable random errors inherent in every test procedure. To assess the precision of Schistosoma haematobium egg counts, carried out after paper filtration, two measures are determined, namely repeatability (r) and reproducibility (R). 10 aliquots of 10 urine samples are examined by 5 microscopists and values for r and R are calculated following the methods of the British Standards Institution (BSI, 1987). Results show unexpectedly high values for the 2 measures in relation to the overall means in all 10 urine samples, and analyses of variance confirm that there are large variations between aliquots of equal volume drawn from the same urine specimen, highly significant in all 10 urine specimens; variations between microscopists are considerably lower and only highly significant in one urine specimen. The Poisson heterogeneity test for all urine samples refutes in 9 out of 10 cases the hypothesis that aliquots of equal volume taken from a well mixed urine sample could reasonably be drawn from a Poisson distribution. It is therefore concluded that egg counts are very valuable for community studies and should always be performed, but results must be interpreted with more caution than before and great care taken in analyzing counts (especially in longitudinal studies), in classifying them and in relating them to morbidity.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed1990

Murphy's law of limiting dilution cloning.

Conventional practice and literature on limiting dilution cloning address the irrelevant problem of selection of a single progenitor from a uniform population, and provide optimistic estimates of monoclonality for interesting cultures and subcultures. Any cell line established via these estimates is suspect and may be polyclonally metastable. Cultures derived by limiting dilution of the progenitors of independently Poisson distributed populations obey a counterintuitive relation with the characteristics of a Murphy's law: the probability that an interesting culture is monotypic or monoclonal is less than that of a random non-sterile culture, decreases for increasingly rare interesting cultures, and is bounded below by the probability of sterility. A priori and empiric a posteriori estimates of the probability that interesting subcultures are monotypic or monoclonal are derived consistent with this principle.

Cells, Cultured↗

PubMed1989

Logistic and Poisson models for infection by multicomponent plant viruses.

A model for the relationship between virus concentration and infectivity of multicomponent plant viruses is based on a combination of logistic and Poisson equations. Two separate equations are derived from the Poisson distribution assuming, (i) that infections occur only when a set of components containing the complete multicomponent genome is established at an infection site, but that any excess of components present does not reduce the probability of infection (no interference postulate); and (ii) that infection can occur only if a set of components containing the full genome reaches an infection site before it can be preempted by an incomplete set (competitive interference postulate). Postulate (i) affects the form of a dilution series without affecting N, the maximum possible number of infections (lesions), and postulate (ii) changes the value of N but not the form of the dilution series. There is a close correlation between the logit slope of a logistic dilution series and the form of the corresponding multiple Poisson dilution series for viruses with 2, 3 or 4 components. Calibrated by Poisson equations, the logit slope may thus suggest whether or not the virus components have invaded independently and infected similar infection sites. The methods of fitting the combined logistic-Poisson model are demonstrated by applying it to data for cowpea chlorotic mottle virus.

Models, Theoretical↗

PubMed1989

Influenza mortality and excess deaths in the elderly, 1967-82.

This study assessed the influence of influenza on mortality from heart and lung diseases in people over 70 years of age. The data used were obtained from the Dutch Bureau of Statistics. With a regression model, the observed monthly mortality from heart and lung diseases (influenza not included) in people over 70 years is explained with a yearly variable, a monthly variable and the overall monthly number of influenza mortality cases, assuming that monthly mortality has a Poisson distribution. The monthly excess mortality from heart and lung diseases (influenza not included) due to influenza among elderly people (greater than 70 years) is estimated. This study suggests that 1400 deaths per million per year were due to influenza in people over 70 years of age in the study period of 16 years. It can be concluded that one influenza death in the population over 70 years 'generates' almost two deaths diagnosed as heart and lung diseases in the elderly.

Aged↗

PubMed1992

Relationship between frequency of infectious human immunodeficiency virus type 1-harboring cells and kinetics of viral replication: a simple procedure for quantitation of infectious virus-carrying cells in blood samples.

Statistical analysis of a limiting dilution assay (LDA) showed that the occurrence of infectious human immunodeficiency virus type 1 (HIV-1)-harboring cells in serially diluted samples of peripheral blood mononuclear cells (PBMCs) of HIV-1-seropositive patients fits the model describing a single-hit Poisson distribution. This observation led to the discovery that there is a direct correlation (r = 0.957) between the number of HIV-1-positive cells and the time when viral culture produces 1 ng of the HIV-1 p24 gag protein per ml. Frequency estimates based on this relationship were highly accurate (P less than 0.01) within the first 15 days of viral culture, which consisted of coculture of 10(6) normal PBMCs with the equivalent number of test PBMCs. This approach was less cumbersome than LDA and was sensitive enough to detect a single infectious HIV-1-harboring cell among as many as 320,000 cells. The values obtained for 57 patients agreed well with the data in the literature and showed that the frequencies of infectious cells in PBMCs reflect the advancement in the clinical stage, being 1/38,000, 1/11,000, and 1/7,000 for asymptomatic patients (Centers for Disease Control [CDC] group II/III), patients with AIDS-related complex (CDC group IVa), and patients with AIDS (CDC group IVb/c), respectively. A nearly 10-fold disparity in mean frequencies was observed when these values were correlated with the numbers of CD4-positive cells (1/9,000, 1/1,500, and 1/300, respectively, for asymptomatic patients, patients with AIDS-related complex, and patients with AIDS). The described method provides a simple means of determining infectious HIV-1-positive cells in blood samples.

HIV Infections↗

PubMed1991

Pairwise comparisons of mitochondrial DNA sequences in stable and exponentially growing populations.

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.

Animals↗

PubMed1986

Quantal release of acetylcholine evoked by focal depolarization at the Torpedo nerve-electroplaque junction.

To analyse evoked acetylcholine (ACh) release in the electric organ of Torpedo marmorata, a loose patch-clamp technique was used that allowed with a single extracellular electrode both focal depolarization of nerve endings and recording of the post-synaptic currents produced by the released transmitter. Two different types of post-synaptic response could be evoked by depolarizing pulses of increasing intensity: a graded response appearing with a delay of 0.6 ms (pulses of 0.2 ms duration), and an all-or-none response characterized by a mean delay of 1.4 ms. Both responses had a similar maximal amplitude and a similar rise time of 0.6 ms. The graded response was evoked in all places where spontaneous miniature electroplaque currents (m.e.e.s) could be recorded. It was not modified by 1 microM-tetrodotoxin (TTX), but was Ca2+ dependent and was abolished by Cd2+ (0.2 mM) or Mg2+ (10 mM). The all-or-none response could be evoked in only 30% of places where m.e.c.s. were recorded, it was highly TTX sensitive, Ca2+ dependent, and abolished by Cd2+ (0.2 mM) or Mg2+ (10 mM). K+ channel blocking agents, such as 4-aminopyridine (4-AP) or tetraethylammonium (TEA), which are known to prolong the duration of action potentials, prolonged the delay of the all-or-none response, but not that of the graded response. At low strength stimulation, the graded response was clearly evoked in a quantal way, with the quantum corresponding to the amplitude of spontaneous m.e.c.s. The amplitude distribution of the evoked responses closely followed a Poisson distribution. The maximum synchronous release of transmitter was found to be approximately 1.3 quanta/micron2 of presynaptic membrane and a mean quantal size of about 7000 ACh molecules was estimated from the charge transfer of m.e.c.s. The nerve terminal time constant was calculated from strength-duration curves obtained with depolarizing pulses just able to evoke either the all-or-none response or the first few quanta of the graded response. Respective mean values of 0.22 and 0.40 ms were found. Increasing the duration of the depolarizing pulse had two consequences: it differently affected the delay of the all-or-none response and that of the graded response; it increased the mean quantal content of the graded response. Both effects could not simply be accounted for by the influence of the nerve terminal time constant.(ABSTRACT TRUNCATED AT 400 WORDS)

Acetylcholine↗

PubMed1988

The detection and importance of outliers in the in vivo micronucleus assay.

Micronucleus tests are generally analysed statistically for differences between the means of treated and control groups. 'Outliers' may either be rejected or grouped together with data from less responsive animals. In either case, a valuable indicator of a small, more sensitive (responder) population sub-group may then be missed. To alleviate this problem, we have developed an additional strategy, based on historic data, for the detection of any single animal with a significant increase in micronucleated polychromatic erythrocytes in an otherwise insignificant treatment group. Forty-one sets of negative control data (of five male and five female CD-1 mice each) have been analysed. Within each set there were no significant male to female differences and data were consistent with a Poisson distribution. Pooled data from all 41 sets showed slightly hyper-Poisson variation and were adequately described by the negative binomial distribution. The negative binomial probability generating function was used to show that six or more micronuclei per 1000 polychromatic cells from one treated animal would be significant for our laboratory, methodology and strain of mouse, provided that concurrent negative control data conformed with historic values. Changes in methodology desirable for this type of analysis include increasing the number of mice in each test group and possible compensation by a reduction in the number of test groups.

Animals↗

PubMed1986

Quantitative autoradiographic analysis of estradiol retention by cells in the preoptic area, hypothalamus and amygdala.

These experiments were done to compare quantitatively, on a cell-by-cell basis, estradiol retention by cells in the medial preoptic area, arcuate nucleus, ventrolateral subdivision of the ventromedial nucleus, and the caudal half of the medial nucleus of the amygdala. The steroid autoradiograms were prepared from 2 mu sections of brains from ovariectomized, adrenalectomized adult female rats that had been infused intravenously with [3H] estradiol (E2) in a regimen which kept circulating hormone concentration at or above proestrus levels for 3-4 h. Even in these brain regions, containing the most dense collections of E2-concentrating cells, a maximum of only 27-61% of the cells concentrated E2. Therefore, in these regions only a particular subset of the cells retain hormone; other cells in the region do not retain hormone. Frequency distribution histograms of the number of grains per cell versus the number of cells in each region showed a wide range in the amount of E2 retained per cell, and no modes among E2-retaining cells. The data followed a distribution markedly different from that predicted by a simple Poisson distribution, confirming that E2-retention does not result from a random, passive process such as diffusion. The overall quantitative characteristics of the frequency distribution histograms were similar across the four brain areas. Therefore, we propose that the different E2-sensitive functions of these brain areas must depend on differences in the neural connectivity or differences in hormone regulated peptide content of the areas.

Amygdala↗

PubMed1986

Distribution of 125I-insulin in cardiocytes at steady state binding conditions at 37 degrees C.

The distribution of 125I-insulin in cardiocytes was analyzed by light microscope autoradiography. Semithin sections were used to distinguish between surface-bound and internalized tracer. At 37 degrees C, when steady state binding conditions were reached, 40 to 60% of the cell-bound tracer was located in the plasma membrane region and the remainder was in the cell interior. Autoradiograms of whole cells were used to study the distribution of tracer molecules on the cell surface. Because Poisson distributions of silver grains were observed on 90% of the cells, it was concluded that the distribution of the insulin-receptor complexes was close to random. In contrast to the findings of Schlessinger et al., no aggregation of insulin-receptor complexes into patches was observed.

Animals↗

PubMed1989

Graphical and statistical approaches to data analysis for in situ hybridization.

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed1985

The anion selectivity of GABA-mediated post-synaptic potentials in mouse hippocampal cells.

Intracellular recordings were made from CA1 and dentate cells of the mouse hippocampal slice. When potassium acetate was used to fill the electrodes, spontaneous synaptic activity was rarely seen in CA1 or dentate cells. In contrast, when electrodes filled with potassium chloride were used, spontaneous depolarizing post-synaptic potentials (p.s.p.s) were prominent. That these p.s.p.s were mediated by gamma-aminobutyric acid (GABA) was supported by the following: they were blocked by electrophoretic application of bicuculline methiodide; their appearance was associated with the reversal of the evoked GABA-mediated recurrent inhibitory post-synaptic potential (i.p.s.p.) and their appearance was associated with the positive displacement of the reversal potential for the response to GABA applied by electrophoresis close to the cell soma. The interval distribution for the p.s.p.s could not be fitted by a Poisson distribution. The anionic selectivity of the conductance evoked by GABA was investigated by using the potassium salts of a range of anions to fill the electrodes. Depolarizing spontaneous p.s.p.s were seen in all cells impaled with electrodes containing potassium chloride, iodide, bromide, nitrate, or chlorate. In these cells, the reversal potential for the response to electrophoretically applied GABA was displaced in the depolarizing direction and the evoked recurrent i.p.s.p. was reversed. When anions with hydrated shells larger than chlorate (bicarbonate, sulphate, chromate, acetate or citrate) were used, spontaneous depolarizing p.s.p.s were not seen, and the reversal potential for the response to somatic GABA application and for the evoked recurrent i.p.s.p. lay between -70 and -75 mV.

Action Potentials↗

PubMed1978

The distribution of bumps in the tail of the locust photoreceptor afterpotential.

An extended tail or prolonged depolarizing afterpotential (PDA) follows the receptor potential of a locust retinula cell when the stimulating light is in the intensity range that saturates the receptor potential. The amplitude and duration of this afterpotential depend on the intensity and duration of the stimulus. As the afterpotential decays, apparently exponentially, it becomes resolved into bumps, which we call light-induced dark bumps (LID bumps). The intervals between light-induced dark bumps are distributed in a way that is indistinguishable from a random (Poisson) distribution. As previously demonstrated, LID bumps are indistinguishable from bumps directly induced by low intensity light in light-adapted cells, which in turn grade into the slightly larger bumps produced, each by a single photon, in dark-adapted cells. The light-induced dark bumps continue for up to an hour in darkness, slowly becoming like dark-adapted bumps in amplitude and shape. To account for the random occurrence and discrete features of bumps after so long a latency, we propose that intense light generates a significant amount of an intermediate molecule or packet which decays slowly to start the same process that normally generates bumps with a short delay.

Animals↗

PubMed1988

Comparison of frequency distributions in flow cytometry.

A number of methods have previously been considered for the statistical comparison of flow cytometric frequency distributions. For two distributions, the foremost of these is the Kolmogorov-Smirnov (K-S) test, which has been criticized as "too sensitive." We discuss some alternative methods based on the Poisson distribution. The assumption of Poisson variation within channels allows the use of channel-by-channel confidence intervals and chi-square tests. These are simple and more appropriate for discrete data than the K-S test. Graphical displays of these and other techniques are presented. We also attempt to set the problem in an appropriate context. We argue that any statistical procedure must rest on a reasonable understanding of the nature of the variability in the system. This understanding takes the form of an appropriate probability model, which may be approximate but must provide a reasonably accurate description of the data. Incomplete understanding of the data can lead to inappropriate analysis. We discuss the assumptions that underlie our techniques and consider extensions to more complex situations.

Flow Cytometry↗

PubMed1988

Mitosis counting in seminoma: an exercise of questionable significance.

Two pathologists reviewed and classified 45 cases of testicular seminoma, evaluating each case for multiple histologic variables, including mitotic rate. In addition to recording the mitotic count for each of thirty 0.1963-mm2 high-power fields, the investigators recorded the distribution of mitotic counts in many non-spermatocytic seminomas. Statistically significant differences for mitotic rate in the nonspermatocytic tumors were noted between the observers; one observer found a mean mitotic rate of 1.815/high-power field for 43 such tumors, whereas the other noted a mean mitotic rate of 1.388/high-power field (p = 0.001). These differences led to disagreement on the classification of 3 tumors. Of the 4 cases considered to be high-mitotic-rate seminomas by one or both observers, all patients had presented with stage I disease. Three of the patients were followed up for 23, 55, and 56 months, and all were free of disease; the fourth was lost to follow-up. The patient with the highest mitotic rate was free of disease at 55 months of follow-up. On the basis of our findings we question the value of the designation high-mitotic-rate seminoma. Analysis of the distribution of mitotic counts within the tumors revealed them to be Poisson distributed. With these data and other empirically derived data, it was possible to estimate the probability of misclassification of seminoma based on mitotic rate, the diagnostic mitotic rate threshold, and the number of fields counted for mitoses. Similar analysis might be valuable for other tumors, particularly those of smooth muscle origin, in which mitotic rate is of diagnostic or prognostic value.

Adult↗

PubMed1989

Two kinds of "recombination nodules" in Neurospora crassa.

Two morphological types of recombination nodules, termed early and late, are recognized in Neurospora crassa. Eighty nuclei at different substages were used to determine numbers of nodules per nucleus, distribution of nodules along the nucleolus-organizing chromosome, and distribution of nodules among the two largest chromosomes. Early nodules appear at the synaptonemal complex at early zygotene and increase in number during zygotene until a dramatic reduction occurs at zygotene-pachytene transition. Thereafter early nodules are steadily eliminated until they disappear by diplotene. Late nodules are also present during zygotene. Their number doubles at the zygotene-pachytene transition and stays at this level until diplotene. The total number of nodules is rather constant through zygotene and pachytene. Distribution of bivalents with 0, 1, 2, etc. nodules follows a Poisson distribution at zygotene, but not at pachytene, where variance is less than the mean, indicating positive interference. Nodules are distributed nonrandomly along the nucleolus-organizer bivalent. The pattern differs slightly in nuclei of different origin. Nuclei with unusual synaptonemal complexes sustain normal levels of recombination by having the same amount of nodules as normal nuclei. In abnormal nuclei nodules are preferentially associated with normal segments. It is proposed that early nodules do not participate in any form of recombination but have a role in finding an appropriate site for a crossing-over event. Morphological change to the late type indicates that the site has been reached and the exchange event can be mediated by the late nodule.

Chromosomes↗

PubMed1987

Sampling and distribution of Anopheles quadrimaculatus immatures in rice fields.

Dipper samples of Anopheles quadrimaculatus immatures from stocked enclosures in Arkansas rice fields were used to develop regression equations relating dipper sample counts to absolute density. Confidence limits were developed for mean number of immatures collected at each density and stadia, including combined stadia. These data can be used to estimate absolute density from mean dipper count. Distribution of rice field immatures approximated but did not fit the Poisson distribution. Sample size was calculated for 10, 25 and 50% of the true mean, at various levels of Type I and II error. A sample size of N = 6,424 was necessary to detect differences within 10% of the true mean, with 5 and 10% probability of Type I and II error, respectively.

Agriculture↗