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PubMed1998

Count-rate statistics of the gamma camera.

The temporal distribution of decay events recorded by a gamma camera in 'list mode' differs from the Poisson distribution because of dead-time effects. We propose a new model for the dead-time behaviour of a gamma camera. The most important feature of our model is that the loss of events occurs in pairs or higher multiples due to the so-called 'pile-up' effect. We analyse the consequences of pile-up for the temporal distribution of events recorded by a gamma camera. The probability distribution for the time intervals between events recorded by the camera is calculated from first principles. We construct estimators for the parameter of the new distribution. We distinguish between the estimation of the total count rate and the estimation of a certain subset of the total count rate. Computer simulation confirms that our estimators are less influenced by dead-time effects than the standard estimator.

Computer Simulation↗

PubMedDate not supplied

[Radiation damages in human lymphocytes studied by micronucleus and chromosomal analysis].

It was shown that the dependence of the micronucleus number and chromosome aberration on irradiation dose is linear quadratic, the values of linear coefficient being different. The distribution of ameliorators and children from the areas with higher irradiation level by micronucleus test conforms to Poisson distribution, while the distribution by chromosomal analysis approaches to binomial distribution.

Adult↗

PubMed1994

Sample size calculations for single group post-marketing cohort studies.

In pharmacoepidemiology, single group cohort is the most frequently proposed design to determine if the incidence rate of an adverse drug reaction among the exposed differs from a reference value. In many situations, the number of events expected in the cohort is too small to conduct sample size calculations based on the normal distribution. This paper proposes, for a single group cohort study, calculations and tables derived from the Poisson distribution. The results are based on a one-sided test with a 0.05 significance level and a power of 0.9 and 0.8. Two parameters have to be specified a priori: the expected incidence of the event under the null hypothesis and the minimum risk ratio to be detected. The required sample size and the critical number of events to reject the null hypothesis are directly derived from the tables. Results show that the normal approximation may lead to an underestimation of the required sample size.

Cohort Studies↗

PubMed2001

Population dynamics: Poisson approximation and its relation to the Langevin process.

We discuss how to simulate a stochastic evolution process in terms of difference equations with Poisson distributions of independent events when the problem is naturally described by discrete variables. For large populations the Poisson approximation becomes a discrete integration of the Langevin approximation [T. G. Kurtz, J. Appl. Prob. 7, 49 (1970); 8, 344 (1971)]. We analyze when the latter gives a reasonable representation of the original evolution for finite size systems. A simple example of an epidemic process is used to organize the discussion and to perform statistical tests that underline the goodness of the proposed method.

Poisson Distribution↗

PubMed1996

The Ames test: the two-fold rule revisited.

Mutagenicity in the Ames assay is evaluated by comparing the number of revertants observed in treated cultures to those in untreated cultures. Often, some form of the '2-fold rule' is employed, whereby a compound is judged mutagenic if a 2-fold or greater increase is seen in a treated culture. In order to understand the underpinnings of this approach, we study some of its statistical properties. We assume that the number of revertants on any plate from a given two-group experiment follows a Poisson distribution and we address the following questions: (1) what is the false-positive error probability of observing at least a doubling of the number of colonies from the control to the treatment group?; (2) if a given mean number of colonies is postulated for a control group, what number of colonies above the observed control mean provides a false-positive rate of 5%? We also present results for question 1 in the case where the number of revertants follows a negative binomial distribution.

False Positive Reactions↗

PubMed1994

A model for the neuronal implementation of selective visual attention based on temporal correlation among neurons.

We propose a model for the neuronal implementation of selective visual attention based on temporal correlation among groups of neurons. Neurons in primary visual cortex respond to visual stimuli with a Poisson distributed spike train with an appropriate, stimulus-dependent mean firing rate. The spike trains of neurons whose receptive fields do not overlap with the "focus of attention" are distributed according to homogeneous (time-independent) Poisson process with no correlation between action potentials of different neurons. In contrast, spike trains of neurons with receptive fields within the focus of attention are distributed according to non-homogeneous (time-dependent) Poisson processes. Since the short-term average spike rates of all neurons with receptive fields in the focus of attention covary, correlations between these spike trains are introduced which are detected by inhibitory interneurons in V4. These cells, modeled as modified integrate-and-fire neurons, function as coincidence detectors and suppress the response of V4 cells associated with non-attended visual stimuli. The model reproduces quantitatively experimental data obtained in cortical area V4 of monkey by Moran and Desimone (1985).

Animals↗

PubMed1990

Monitoring tsetse fly populations. II. The effect of climate on trap catches of Glossina pallidipes.

In Part I it was shown that the sampling distribution of trap catches of tsetse flies, Glossina pallidipes Austen, at Nguruman, Kenya, using unbaited biconical traps follows a Poisson distribution. In this paper we examine the effect of humidity and temperature on day-to-day and seasonal variations in the trap catches. It is shown that the seasonal variation is significantly correlated with maximum daily temperature, the catches increasing with temperature when the maximum temperature is below 34 degrees C and decreasing with temperature when it is above 34 degrees C. The correlation between trap catches and relative humidity is not as good as the correlation with the maximum temperature, and the two together do not improve the fit to the trap catches. The day-to-day variation is significantly greater than the intrinsic variation due to the stochastic nature of the sampling process and for some traps it is correlated with temperature and humidity. An autoregressive model gives a half-life for the decay of departures from the mean of about 1 day and it is suggested that this indicates the movement of flies in response to animal movement or to climatic factors other than temperature or humidity. After removing the temperature dependent part of the seasonal variation and the autoregressive component of the data, the male and female catches are still significantly correlated.

Animals↗

PubMed1985

Some goodness-of-fit methods for the Poisson plus added zeros distribution.

Methods for making inferences about the Poisson plus added zeros distribution and the truncated Poisson distribution are presented and illustrated with bacteriological data. Some of the methods are designed for testing the compatibility of the zero frequency with the Poisson distribution, whereas others are given for testing the goodness of fit for the truncated Poisson. In particular, a modified form of the Fisher index of dispersion is presented which is suitable for the truncated case. It is shown that the use of the usual expression of the index of dispersion for testing the adequacy of the truncated Poisson is not correct and leads to accepting inadequate fits more frequently than expected on the basis of test of significance. Furthermore, three test statistics are presented for testing the compatability of the zero frequency with the Poisson distribution. The results of the simulation show that two test statistics, one due to Cochran (W. G. Cochran, Biometrics 10:417-451, 1954) and the other to Rao and Chakravarti (C. R. Rao and I. M. Chakravarti, Biometrics 12:264-282, 1956), are preferable to those from the likelihood ratio test.

Bacteria↗

PubMed1991

Power and detectable risk of seven tests for standardized mortality ratios.

Power and minimum detectable risk are calculated for seven one-sided tests of standardized mortality ratios with Poisson-distributed events. Each test contrasts the number of observed deaths (D) with the number expected (E). Three tests use exact Poisson probabilities: 1) the exact test, which computes a p value as the probability of equaling or exceeding the number of observed events; 2) the optimal randomized exact test which, although not used in practice, serves as a standard for the other statistics; and 3) the exact "mid-p" procedure, which counts only one-half the probability of the observed event. The remaining four tests use normal approximations to the Poisson ("Z statistics"): 4) Z = magnitude of D-E/square root of E; 5) the Z statistic corrected for continuity, Z = (magnitude of D-E)-0.5)/square root of E; 6) a statistic based on a square root transformation, Z = 2(square root of D-square root of E); and 7) a statistic created by Byar, which, when D is greater than E, is Z = square root of 9D[1-1/(9D)-3 square root of D/E]. Power differences among these procedures with one-sided alpha of 0.05, 0.025, and 0.01 are small as long as four or more events are expected. If fewer than four events are expected, the uncorrected Z has unacceptably high type I error. Simple approximations to the power and detectable risk of these tests are evaluated and prove satisfactory. Differences in minimum detectable risk, actual and approximated, are slight for E of 2.0 or more.

Humans↗

PubMedDate not supplied

[Main principles of radiobiology].

During all the history of the development of radiation biology a problem of "energy paradox"--low consumption of energy of ionizing and non-ionizing radiation in realization of irradiation effect--has been in the focus. The first principle, which contributed much to quantitative concepts of radiation biology, is a hit principle. The hit principle, as is well known, is based on physical properties of ionizing radiations: their discontinuity, quantization and probabilistic distribution in space. Hits, i.e. acts of energy interaction with substance elements, do not depend on each other and are obeyed to Poisson distribution. The other well-known principle--a target principle--is based on the understanding that a living system has some peculiarities: a structure of elements as well as their functions are heterogeneous, unequal and differ in response to the same hits. Along with a unique DNA macromolecule, a critical target structure, biological membranes (BM) with their barrier-matrix, energy and regulatory functions, which make a basis of living processes, are also can be considered as a sensitive target structure. One more principle--a principle of amplification of primary radiation lesions in critical target structures is based on the radiation post-effect, a well-known phenomenon in radiation biology. The fourth principle is a principle of target damage recovery (regulations of cell homeostasis) that means a system response to irradiation involving mechanisms of protection and reparation of lesions in DNA and BM. The progress in molecular biology and radiation biophysics achieved for the last two decades provided an especially powerful impetus to the development of those principles, which are based on the analysis of the radio-biological effects developing in time. The main principles of radiation biology consider peculiarities of physical and biological action of ionizing radiation.

Animals↗

PubMedDate not supplied

Time-dependent mitotic recombination in Saccharomyces cerevisiae.

The time-dependent appearance of prototrophic recombinants between heterologously located artificial repeats has been studied in Saccharomyces cerevisiae. While initial prototrophic colony numbers from independent cultures were highly variable, additional recombinants were found to arise daily at roughly constant rates irrespective of culture. These late-appearing recombinants could be accounted for neither by detectable growth on the selective media nor by delayed appearance of recombinants present at the time of selective plating. Significantly, at no time did the distributions of recombinants fully match those expected according to the Luria-Delbruck model and, in fact, after the first day, the distributions much more closely approximated a Poisson distribution. Prototrophic recombinants accumulated not only on the relevant selective medium, but also on media unrelated to the acquired prototrophy.

Amino Acids↗

PubMed1985

Improved evaluation of binding of ligands to membranes containing several receptor-subtypes.

In order to evaluate accurately affinity characteristics and relative size of populations of receptor-subtypes in one system we analysed three relevant problems encountered in binding assays. Binding to receptors caused a decrease in the free ligand concentration (i.e. "depletion"). The neglect of depletion may lead to significant distortions of the estimates of affinity and size of receptor-subtype population when the concentrations of both receptor and ligand are of similar magnitude. The distortion is particularly marked when the affinity of a competing ligand is higher than the affinity of the radioligand. We present a formula that describes binding inhibition in a system with receptor-subtypes under conditions of depletion. Binding data usually exhibit heteroscedasticity (i.e. heterogeneous variance), which can not be neglected especially in a system with receptor heterogeneity. Assuming a log normal distribution of experimental errors and a Poisson distribution for errors due to radioactivity counting we derived a function for the transformation of binding data. Transformed data show homoscedasticity, as illustrated with experiments on membranes of guinea-pig lung using ICI 118,551 as inhibitor of 3H-(-)-bupranolol binding to beta 1- and beta 2-adrenoceptors. The hypothesis that affinity characteristics of receptor subtypes are independent of the tissue class can not be tested accurately by the use of standard methods because of interferences of errors between experiments. We propose a method to account for differences between experiments. Assuming invariance of affinity characteristics one is able to perform common fits of data from different tissue classes.(ABSTRACT TRUNCATED AT 250 WORDS)

Adrenergic beta-Antagonists↗

PubMed1997

The basal rate of cell proliferation in normal human parathyroid tissue: implications for the pathogenesis of hyperparathyroidism.

BACKGROUND: The basal rate of cell proliferation in the human parathyroid gland is generally believed to be low, but has never previously been measured directly, although, as in other tissues, it is relevant to the pathogenesis of neoplasia. METHODS: We retrieved embedded tissue blocks of parathyroids removed at autopsy from 39 patients without hypercalcaemia or abnormal renal function, aged 18 to 76 years (mean 47.6). New sections were cut and examined for expression of Ki-67, a cell-cycle marker, using the MIB-1 antibody with microwave antigen retrieval, and tonsil as positive control. Using an eyepiece graticule with unbiased square-counting frame, positively labelled chief cells were counted in large squares and total chief cells in small squares in fields selected by systematic random sampling from multiple regions. A minimum of 15 x 10(3) chief cells were accumulated in each case. The prevalence of Ki-67 positive cells per 10(4) cells (label index or LI) was converted to cell birth rate assuming that the duration of Ki-67 expression was 24 hours. In ten cases, the entire section was examined; a map of the distribution of the positive cells was reconstructed, and divided into outer and inner regions. RESULTS: The geometric mean value for LI was 1.44/ 10(4), and multiplicative SD 2.54. The corresponding geometric mean cell-birth rate was 5.24%/year and 95% confidence interval 0.81-33.8%/year. We found no significant effect of age, sex, race, or duration of tissue storage. The distribution of cells conformed to a Poisson distribution, and there was no difference between central and peripheral regions. CONCLUSIONS: (1) Our results establish the human parathyroid gland as a conditionally renewing tissue with very low basal cell-birth rate; other reports of much higher LI values are probably due to selective and consequently biased sampling. (2) Since the total number of cell divisions is a major determinant of the total number of mutations, our results place some constraints of possible mechanisms for parathyroid neoplasia.

Adolescent↗

PubMed2000

Statistical analysis of the effect of high dilutions of arsenic in a large dataset from a wheat germination model.

This paper describes the statistical analysis of a series of experiments using a simple biological model (wheat germination in vitro), where a large number of wheat seeds were treated with homeopathic potencies of Arsenic trioxide. Some potencies, such as As2O3 40x, 42x and 45x, have repeatedly shown a significant stimulating effect on germination compared to controls, whereas As2O3 35x has a significant inhibiting effect. In some experiments the seeds were stressed before the experiment with a sublethal dose of the same substance. We performed a statistical analysis, both for stressed and non-stressed seed groups, using Poisson distribution as a suitable model for representing the number of non-germinated seeds in a standard experiment with 33 seeds in the same Petri dish. Finally, we have considered the most repeated potencies (30x and 45x), computing the sample odds ratio (OR) and a 95% confidence interval (CI) for the population OR. Our results show significant reproducible effects of some As2O3 decimal potencies, particularly As2O3 45x. In stressed seeds, even decimal potencies of water seem to give significant results compared to control, whereas high dilutions of As2O3 without potentization never show significant effects.

Arsenic Trioxide↗

PubMed1983

Cyclophosphamide-induced in vivo sister chromatid exchanges (SCE) in Mus musculus. III. Quantitative genetic analysis.

In vivo cyclophosphamide (CP)-induced sister chromatid exchanges (SCEs) were evaluated in females from five genetic strains of mice (C57BL/6J, C3H/S, 129/ReJ, BALB/c and DBA/2) and their F1 hybrids. Baseline (noninduced) SCE values differ significantly among strains, 129/ReJ having the lowest and DBA/2 having the highest mean SCE per cell values. In general, the baseline SCE of a given F1 is within the range of its corresponding parental strains or near the lower parental value. Furthermore, there is a genotype-dependent increase in mean SCEs per cell with CP dose. Strain differences in SCE induction are noted particularly at the two higher CP doses (4.50 and 45.0 mg/kg). In general, F1 hybrids involving a strain with high induced SCEs and a strain with low induced SCEs exhibit mean SCE values that are closer to the value of the lower strain. F1s involving two strains with high SCEs or two strains with low SCEs yield SCEs not different from parental strains. The method of diallel cross analysis showed the order of dominance of these strains in SCE induction to be 129/ReJ BALB/c C3H/S DBA/2 C57BL/6J. These results support the involvement of predominantly nonadditive genetic factors as major gene(s) in SCE induction. In addition, involvement of random and independent events in SCE induction is suggested by the distribution of SCEs which follows a Poisson distribution.

Animals↗

PubMed1992

Exact calculation of probabilities of false positives and false negatives for low background counting.

The purpose of this paper is to demonstrate the derivation and use of exact formulas, and their algorithms, for calculating the probabilities alpha of Type I errors, and beta of Type II errors, for low blank total counts (Poisson-distributed). The calculations are carried out to examine the alpha and beta probabilities at low blank levels of the decision level (DL) and minimum detectable amount (MDA) formulations as adopted in the Health Physics Society Standard, "Performance Criteria for Radiobioassay." These formulations are consistent with those published by L.A. Currie, which have received wide acceptance in defining lower limits of detection (LLD). Although Currie's formulation was derived assuming a normal distribution in net counts, the behavior of the distribution of net counts at low count levels, which is a distribution of the difference between two Poisson variates, is such that the MDA formulation in the standard could be considered acceptable for the purpose of providing one simple formulation of MDA. The derivations in this note can also be useful in other problems involving differences in Poisson variates, such as those in certain population studies.

Background Radiation↗

PubMed2001

Spectral statistics of the two-body random ensemble revisited.

Using longer spectra we reanalyze spectral properties of the two-body random ensemble studied 30 years ago. At the center of the spectra the old results are largely confirmed, and we show that the nonergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow us to test and reach the limits of validity of French's correction for the number variance. At the edge of the spectra we discuss the problems of unfolding in more detail. With a Gaussian unfolding of each spectrum the nearest-neighbor spacing distribution between ground state and first exited state is shown to be stable. Using such an unfolding the distribution tends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining similar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance with the procedure used for the data.

Journal Article↗

PubMed1978

Quantal analysis of transmitter release at an inhibitory synapse in the central nervous system of the leech.

The quantal nature of transmitter release has been analysed at central inhibitory synapses in the leech nervous system between an interneurone (HN) and a motoneurone (HE) that regulate the heartbeat. 1. Ganglia were bathed in leech Ringer fluid containing 20 mM-Mg and 1.8 mM-Ca and the membrane of the presynaptic HN interneurone was hyperpolarized by current injection. Under these conditions successive inhibitory potentials in the HE motoneurone, evoked by impulses in the HN interneurone, showed striking fluctuations in amplitude. 2. Assuming a Poisson distribution of the i.p.s.p.s and estimating the number of failures from the amplitude histograms of the observed responses, the mean size of the quantal unit was estimated as 0.25 +/- 0.015 mV (S.E. of mean, n = 26). When m, the mean number of quanta released per trial, was varied by changing the membrane potential of the presynaptic HN cell (Nicholls & Wallace, 1978), the experimentally observed amplitude distributions could be predicted by the Poisson theory. 3. An independent estimate of the unit size was obtained by noise analysis. A long subthreshold depolarizing pulse applied to the presynaptic HN interneurone evoked a sustained hyperpolarization of the HE motoneurone, apparently caused by an increase in the rate of on-going release of quanta by the HN cell terminals. From the mean change in membrane potential and the increase in variance, the size of the unit was calculated as 0.21 +/- 0.039 mV (S.E. of mean, n = 11). For ten pairs of cells an estimate of unit amplitude was made both from the Poisson analysis and the analysis of variance, again with good agreement. For these cells the estimated unit sizes were 0.24 +/- 0.023 mV (S.E. of mean, n = 10) from the failures and 0.21 +/- 0.043 m V (S.E. of mean, n = 10) from the noise. 4. A similar analysis was made of the inhibitory synaptic potentials evoked in one HN interneurone by stimulation of its contralateral homologue. Transmission again appeared to be qualtal; the mean unit amplitude from Poisson analysis was 0.31 +/- 0.022 mV (S.E. of mean, n = 19) and from the noise 0.29 +/- 0.027 mV (S.E. of mean, n = 3). 5. We conclude that transmitter is released from the terminals of the HN interneurone in quantal units that evoke miniature i.p.s.p.s of about 0.25 mV in the post-synaptic cells. Furthermore, modulation of transmission proudced by variation in the presynaptic resting potential and during presynaptic inhibition results from changes in the mean number of quanta released by each impulse.

Animals↗