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PubMed1994

False-positives in spontaneous reporting: should we worry about them?

Spontaneous reporting remains the most used and, undoubtedly, the most cost-effective approach for the identification of adverse drug reactions (ADRs). Most of the limitations of this method are well recognised but the possibility of receiving false-positive reports of coincidental drug-event associations has received little attention. In this paper we propose a method based on the Poisson distribution for computing the maximum number of reports of an ADR that could be expected to be reported coincidentally. Three parameters are required: (i) the background risk of the event in the reference population, (ii) the total number of patients treated with the drug considered and, (iii) the proportion of cases that have been reported to the pharmacovigilance system. For most empirical situations occurring in the post-marketing surveillance setting, the expected number remains low and only a maximum of one to three cases could be accepted as possibly coincidental. For rare adverse events such as agranulocytosis or toxic epidermal necrolysis, coincidental associations are so unlikely that a number of reports greater than three constitutes a strong warning and requires further investigation. These findings suggest that for rare events, reports of coincidental drug-event associations are too unlikely to be considered as an important limitation of spontaneous reporting.

Drug-Related Side Effects and Adverse Reactions↗

PubMed1995

Trends in colorectal cancer over a half century in Rochester, Minnesota, 1940 to 1989.

Recent reports of increasing incidence, especially in men, led us to update through 1989 an earlier study of colorectal cancer incidence in Rochester that covered the period 1940 through 1979. The combined data reflected cancer trends in the community over half a century. Data resources of the Rochester Epidemiology Project were used to identify new cases of colon and rectal cancer among Rochester residents. Incidence rates were estimated using decennial census data, and 95% confidence intervals were based on the Poisson distribution. The GLIM statistical package was used to evaluate trends over time. Age-adjusted (US white 1970) incidence rates of colorectal cancer for men were 53.7, 61.3, 53.7, 54.2, and 52.5 per 100,000 person-years, respectively, for the decades 1940 to 1949, 1950 to 1959, 1960 to 1969, 1970 to 1979, and 1980 to 1989. Comparable rates for women were 42.7, 49.3, 42.9, 40.7, and 40.9 per 100,000 person-years. No statistically significant changes were seen in the incidence of colon and rectum cancer for men or women. There was no consistent trend in tumor stage at diagnosis and the mean size of the initial lesion did not change with time. The incidence of colorectal cancer has not changed over the past 50 years in this community where case ascertainment has been consistent and complete.

Adult↗

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↗

PubMed1994

Translating stochastic density-dependent individual behavior with sensory constraints to an Eulerian model of animal swarming.

Density-dependent social behaviors such as swarming and schooling determine spatial distribution and patterns of resource use in many species. Lagrangian (individual-based) models have been used to investigate social groups arising from hypothetical algorithms for behavioral interactions, but the Lagrangian approach is limited by computational and analytical constraints to relatively small numbers of individuals and relatively short times. The dynamics of "group properties", such as population density, are often more ecologically useful descriptions of aggregated spatial distributions than individual movements and positions. Eulerian (partial differential equation) models directly predict these group properties; however, such models have been inadequately tied to specific individual behaviors. In this paper, I present an Eulerian model of density-dependent swarming which is derived directly from a Lagrangian model in which individuals with limited sensing distances seek a target density of neighbors. The essential step in the derivation is the interpretation of the density distribution as governing the occurrence of animals as Poisson points; thus the number of individuals observed in any spatial interval is a Poisson-distributed random variable. This interpretation appears to be appropriate whenever a high degree of randomness in individual positions is present. The Eulerian model takes the form of a nonlinear partial integro-differential equation (PIDE); this equation accurately predicts statistically stationary swarm characteristics, such as expected expected density distribution. Stability analysis of the PIDE correctly predicts transients in the stochastic form of the aggregation model. The model is presented in one-dimensional form; however, it illustrates an approach that can be equally well applied in higher dimensions, and for more sophisticated behavioral algorithms.

Algorithms↗

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↗

PubMed1984

Distribution of SCEs in lymphocytes in persons with normal, slightly increased, and heavily increased SCEs.

The distribution of SCEs in lymphocytes was examined for 165 healthy persons (58 non-smokers and 107 smokers with cigarette consumption ranging from 1 to greater than 20 per day), and for 1 patient treated with melphalan, a cytostatic drug. The data from the healthy persons did not follow a Poisson distribution. A mixed Poisson that allowed different lambda values for the 30 cells scored from each person and postulated a gamma distribution for the lambda s within the 30 cells fitted all the data examined including those from the melphalan-treated patient. In the latter case the 7 samples taken at various times after the treatment could all be represented satisfactorily with a common parameter, c, in the gamma distribution for the lambda s, even though the mean SCEs/cell varied from 9.8 to 36.8. Because the c parameter determines the spread of lambda values within the 30 cells, this suggested that the effect of the cytostatic drug was to increase all the lambda s by a constant amount. The sum of the SCEs taken over all 30 cells in a sample is a convenient summary statistic, and the transformation y = square root s + square root s + 1 behaves as a normal variate with a constant variance within a group.

Adolescent↗

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↗

PubMed1984

Dose-effect relationship of chromosome aberrations induced by 23 MeV alpha particles in human lymphocytes.

The dose-effect relationship and intercellular distribution of chromosome aberrations were studied in human peripheral blood lymphocytes irradiated in vitro with 23 MeV alpha particles. The frequency of dicentrics, mu, was best expressed by a linear-quadratic model, mu = 7.55 X 10(-1) D + 2.1 X 10(-2) D2, although the dose-quadratic component was not significantly different from zero giving a fit to a linear model mu = 7.93 X 10(-1) D also (D in Gy). The intercellular distributions of dicentrics were over-dispersed compared with Poisson distribution, and the dispersion index as expressed by the relative variance increased with the increase of mean dicentric yield. Stochastic considerations based on the relative variance indicated the presence of inter-track interaction in the formation of dicentrics by alpha particles. Modification of the dose-response relationship by selective loss of cells with more damage is discussed.

Adult↗

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↗

PubMed1981

Chromosome aberrations induced by protons up to 31 MeV in cultured human cells.

Chromosome aberrations were induced in cultured human cells by proton beams of 31, 12, and 8 MeV. The frequencies of isochromatid breaks and dicentrics have been analysed as a function of proton energy and dose. Both effects are largely dependent on proton energy; isochromatid breaks increased linearly with the dose, whereas dicentrics show a definite parabolic behaviour. The experimental data were fitted to the analytic form Y = KDn and Y = alpha D + beta D2 and the best fitted values of the parameters are reported and discussed. The values of RBE for the isochromatid breaks are in the ratio 1.7:1.3:1 for 8, 12, and 31 MeV respectively. In the case of the dicentrics the RBE values are dose-dependent function of the type CD-n. The three distributions of dicentrics among the cells do not fit a Poisson distribution.

Cell Line↗

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↗

PubMed1981

[Frequency of chromosome aberrations induced in human peripheral lymphocytes by in vitro 60Co gamma quanta at doses of 1 to 5 Gr. in an analysis of the 1st-division cells at different fixation times].

The quantitative analysis of chromosomal aberrations in the first division cells of 50-, 54-, 58-, 52- and 66-hour peripheral blood lymphocytes cultures of healthy donors was performed after irradiation in vitro with 60Co gamma-quantums at doses 1--5 Gy. Cells of the first division were identified by a differential staining of sister chromatid method using 5-bromdeoxyuridine. No significant differences in frequencies of aberrant cells and aberrations of chromosomal type were found between cultures fixed at different times. The distribution of dicentrics in cells did not differ from the Poisson distribution regardless of fixation times and doses. On the basis of these findings it is concluded that chromosomes of human peripheral blood lymphocytes passing the cell cycle at different rates have approximately equal radiosensitivity.

Chromosome Aberrations↗

PubMed1981

[Radiotherapeutically induced chromosome aberrations: studies in "biological dosimetry"].

The yield of chromosome aberrations (dicentric chromosomes, ring chromosomes) induced in lymphocytes of four radiotherapy patients was determined. In each case this yield was drastically increased when compared with the spontaneous incidence, the dicentric frequencies increasing by the following factors: 604, 525, 600, and 725. With the aid of the dicentric yield obtained, the following equivalent whole body doses were estimated ("biological dosimetry"): 309, 286, 308, and 341 rd. Comparing the observed with the theoretical number of cells with 0, 1, 2, 3 ... dicentrics ("distribution analysis"), we found a highly significant departure from the Poisson distribution, as was to be expected after partial body irradiation. The distribution analysis seems principally suited to discriminate between partial and whole body irradiation.

Adult↗

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↗