[Morbidity of leukemia in the Cracow Region in the years 1951-1960 in the light of the Poisson distribution].
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Humans↗
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Simulation of the primate motor cortex and free arm movements in three-dimensional space: a robot arm system controlled by an artificial neural network.
It has been recently discovered that neuronal activity in the primate motor cortex varies in an orderly fashion with the direction of movement of behaving monkeys in three-dimensional (3-D) space. Furthermore, cell activity is highest in a certain direction, the cell's preferred direction, and decreases progressively in other directions. For a particular movement direction, each cell makes a contribution in the direction of its preferred direction to yield a neuronal population vector that points in the direction of movement well before the movement begins. Simulation of motor cortical activity is useful with a randomly selected Poisson distribution. Poisson spike trains are used as input to an artificial neural network (ANN) that produces motor actions in the form of a Cartesian coordinate to a PUMA robotic arm system. The ANN consists of a three-layered feed-forward system that uses a specific cosine algorithm as synaptic weights between the interconnected units described in the angle between the preferred direction vector of the neuron and the movement vector. The robot responds to commands, generating actual trajectories in close agreement with desired trajectories. It is shown that the time-varying motor output is controlled by the impulse activity with a good estimate of the direction of movement with 100-150 cells.
Animals↗
Lorenz curves and their use in describing the distribution of 'the total burden' of dental caries in a population.
PURPOSE: 1) to describe the distribution of the total burden of dental caries in Danish adolescents over a 15-year period using Lorenz curves and, 2) to compare the observed distributions with Poisson distributions. METHOD: caries data for 15-year-old adolescents reported to the database for the national reporting system for the Danish Municipal Dental Service for Children and Adolescents in 1980 (n = 61,621) and 1995 (n = 50,359). RESULTS: The DMFS cut-off point for a given percentile had decreased from 1980 to 1995 and Lorenz curves showed a pattern of increasing inequality, even when only diseased individuals (i.e. with DMFS > or = 1) were included. The dispersion was larger than could be expected, if caries developed according to a random pattern modelled by e.g. a Poisson distribution. CONCLUSIONS: Lorenz curves may be a useful tool in the analysis of caries data, with special reference to determining the appropriateness of implementing high-risk preventive strategies.
Adolescent↗
A simple method to calculate the confidence interval of a standardized mortality ratio (SMR)
In analyzing standardized mortality ratios (SMRs), it is of interest to calculate a confidence interval for the true SMR. The exact limits of a specific interval can be obtained by means of the Poisson distribution either within an iterative procedure or by one of the tables. The limits can be approximated in using one of various shortcut methods. In this paper, a method is described for calculating the exact limits in a simple and easy way. The method is based on the link between the chi 2 distribution and the Poisson distribution. Only a table of the chi 2 distribution is necessary.
Confidence Intervals↗
Methodological issues in the development of the Canadian Cancer Incidence Atlas.
The Canadian Cancer Incidence Atlas is among recent national atlases using incidence rather than mortality data. Methods used to assess the significance and spatial correlation of the age-standardized rates (ASIRs) for the 290 census divisions are described. The expected number of cases by area was used to determine cancer sites with sufficient cases to be mapped. ASIR significance was assessed using a simulation based on a Poisson distribution. The consistency of the observed case distributions with the Poisson distribution was examined. The bootstrap confidence interval (CI) for the ASIR developed by Swift was used in the atlas. Spatial correlation was assessed with Moran's I/I(max) and the significance determined by a simulation in order to allow for area population variation. Data quality indicators typically used for cancer registries were presented, supplemented by a registry questionnaire.
Atlases as Topic↗
[An analysis of the cellular distribution of chromosome aberrations induced in human lymphocytes after a single irradiation and under conditions of preliminary adaptive exposure].
Irradiation by an adaptive dose 0.05 Gy at the G0 stage decreased the number of chromosome aberrations induced in lymphocytes by a challenge dose 0.5 Gy at the G2 stage. Adaptive response was not observed at the G1 stage, when the cells were exposed to adaptive dose 0.05 Gy and challenge dose 1.0 Gy respectively after 24 h and 29 h incubation with PHA. In lymphocytes exposed to 1.0 Gy at the G1 stage, cellular distribution of chromosomal aberrations followed the Poisson distribution, while in lymphocytes exposed to 0.5 Gy at the G2 stage, the distribution of aberrations differed from the Poisson distribution and was nearer to the degenerated Poisson distribution. The adaptive dose 0.05 Gy did not alter the distribution of chromosome aberrations induced by the challenge dose at the G1 or the G2 stages. The role of independent and whole-cellular repair in the formation of chromosome and chromatid aberration is discussed.
Adaptation, Physiological↗
[Current aspects on evaluation of assays of factor-VIII activity, factor-VIII associated protein and factor-VIII neutralizing antibody (author's transl)].
In evaluating factor-VIII activity it should be noted that regarding the remaining activity of deficient plasma a linear reference curve is achieved. In the standard population factor-VIII activity and factor-VIII associated protein are distributed approximately lognormally. Due to this distribution certain results have been gained for the optimal choice of localisation and dispersion measures. It is assumed that the proportions of neutralized factor-VIII activity in plasma are distributed according to Poisson. The applicability of the Poisson distribution was also proved for the free factor-VIII activity portion. Due to the Poisson distribution the antibody unit is clearly defined, thus eliminating a further discussion on the establishment of an arbitrary standardized antibody unit.
Antibodies↗
Fitting discrete probability distributions to evolutionary events.
The assumptions underlying the use of the Poisson distribution are essentially that the probability of an event is small but nearly identical for all occurrences and that the occurrence of an event does not alter the probability of recurrence of such events. These assumptions do not seem to be met for evolutionary events since (i) the probability of fixing nucleotide codon substitutions is not equal for all substitutions at a codon, and probably varies for the same substitution in different lineages; (ii) the probability of fixing codon substitutions varies among positions of a cistron; and (iii) the fixation of a nucleotide codon substitution at one position in a cistron modifies, and may even promote, the fixation of a codon substitution elsewhere along the cistron. Natural selection presumably is the causative factor that acts to modify the probability of a nucleotide codon substitution's being fixed in a population. The use of the negative binomial distribution is consistent with the evidence that selective pressure on amino acid or nucleotide codon positions varies both among codon positions of a cistron and at a particular position during evolutionary time. If the number of fixations of nucleotide codon substitutions per position of cistrons encoding cytochromes c are phyletically inferred (phylogeny based on a paleontological record) rather than phenetically inferred (based on paired comparisons of extant species' differences in the absence of a phylogeny) the distribution of these fixation data cannot be described adequately by a single Poisson distribution. The fit of these same data to a negative binomial distribution is very satisfactory. It has been argued that the fit of phenetically inferred fixation data, which do not take account of parallel or reverse fixations, to the Poisson distribution was supportive evidence for the hypothesis that protein evolution results from the fixation of selectively neutral codon substitutions. This argument now appears to be undercut by the evidence that data on nucleotide codon fixation are more probably distributed according to the negative binomial distribution. The fact that fixation data can be described by a particular discrete probability distribution does not of itself provide insight into the mechanisms of the evolutionary process. However, the facts-(i) that the assumptions underlying the use of the negative binomial distribution adequately deal with the varying probability of fixing amino acid or nucleotide codon substitutions at and among the positions of a cistron and (ii) that the negative binomial distribution provides an excellent fit for the phyletically inferred fixation data-suggest that the negative binomial is a very appropriate discrete probability distribution for describing evolutionary events. Amino acids or their nucleotide codon substitutions may be fixed at a position of a cistron as though selectively neutral relative to the codon being replaced, even though the codon position will not be selectively neutral, since many amino acids cannot function there. The negative binomial distribution treats this situation well whereas a single Poisson distribution could only be satisfactory if all codon positions that could vary were selectively neutral.
Amino Acid Sequence↗
A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives.
Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives.
Animals↗
A simple statistical approach that represents the frequency distribution of plasmids in clinical isolates of the enterobacteria.
The frequency distribution of plasmids in a representative collection of Escherichia coli and other enterobacteria was compared with the frequencies predicted by the Poisson distribution. The distribution of E. coli plasmids did not differ significantly (p greater than 0.2) whereas the difference between observed and predicted distributions of plasmids in combined populations of other enterobacteria was significant (p less than 0.001). Previous studies had suggested that plasmid-free strains contributed disproportionately to the overall frequency distribution. Therefore, plasmid-free strains were excluded and the frequency distribution of plasmids in plasmid-containing strains compared with frequencies predicted by a modified Poisson distribution conditional upon n not equal to 0. The results obtained showed that the frequency distribution of plasmids in E. coli and in other enterobacteria did not differ significantly from the predicted distribution (p less than 0.2 and p greater than 0.6 respectively). The frequency distribution of plasmids in previously published studies was compared with predicted frequencies by means of the Poisson distribution and the modified Poisson distribution conditional upon n not equal to 0. The results indicate that the modified Poisson distribution described provides an adequate description of plasmid frequency distributions and represents the observed frequencies better than the distribution predicted directly from the Poisson formula.
Enterobacteriaceae↗
Evaluation of the bias in using the time to the first event when the inter-event intervals have a Weibull distribution.
Currently the analysis of clinical trials for treatment of paroxysmal atrial fibrillation (PAF) relies on the assumption that the events are distributed according to a Poisson distribution. We contend that the occurrence of PAF events are clearly not Poisson and tend to occur in clusters. A candidate parametric model of the inter-event interval, the Weibull distribution, is presented. When the events are distributed according to a Poisson distribution, the time to the first event (TFE) has the same distribution as the inter-event intervals (IEI) due to the 'memoryless' property of the Poisson distribution, hence the TFE can be used instead of the IEI. When the events do not form a Poisson distribution, the TFE does not have the same distribution as the IEI. We show that for the Weibull distribution, when the TFE is used to model the IEI, both the mean and the survivor distribution are biased. The bias in the survivor function is a function both of time and the parameters of the distribution. Therefore when two groups have different parameters for their distributions (as in the case of different treatment effects), the discrepancy between the survivor distribution of the IEI and the survivor distribution of the TFE is affected differentially. We demonstrate the low coverage probabilities of the mean and the survivor function which result when the underlying distribution is Weibull with shape parameter kappa < 1.0. It is likely that this problem will arise for other clustered event processes. This suggests that careful empirical investigation of the distribution of IEI for recurrent events is necessary before choosing to analyse the data using the TFE.
Atrial Fibrillation↗
The significance of leukemia and lymphoma cells in cerebrospinal fluid contaminated by blood containing malignant cells: a probabilistic approach based on the Poisson frequency distribution.
The significance of malignant cells in a body fluid is often difficult to determine if that fluid is contaminated by blood containing malignant cells. This problem is most often seen in examination of CSF from patients with lymphoma or leukemia. We suggest a statistical model of this problem in which the numbers of malignant cells in the blood and the fluid specimen are related to the number of red blood cells. Using the Poisson distribution, the probability of finding the observed number of malignant cells in the fluid is calculated and used as the basis for suggesting whether these cells are likely to represent contamination effect or true involvement of the fluid by the malignancy. The limitations and applicability of this process are discussed.
Blood Cells↗
[Mortality rate and its statistical properties].
The rate is an epidemiologic measure which has a widespread use in describing the occurrence of diseases. In this paper, with a didactic approach, the definition of the mortality (morbidity) rate is introduced following two ways of reasoning: firstly, in the context of survival analysis, as an instantaneous conditional probability of failure (either disease or death) (instantaneous risk) and, secondly, as a traditional measure of rapidity of change in time. We then proceed to highlight the differences, in terms of definition, interpretation, and application, between the concepts of rate and risk. As a next step the statistical properties of the rate are explored and it is explained why the variability of the measure is simply associated with the numerator (events) and not with the denominator (person-times) of the rate. In this context the Poisson distribution is commonly considered the probability distribution which better describes the statistical variability of the observed events, and examples of such a distribution are presented. When the number of deaths is sufficiently elevated the Poisson distribution can be adequately approximated by the Gauss distribution, which is simpler and in common use in occupational medicine, and formulas are presented to compute mean and variance of the rate in this situation. When the number of deaths is small a suggestion is made of making a log transformation of the rate (or of the deaths) before using the Gauss distribution: formulas are proposed for this situation, too. As a practical application of the statistical properties presented and as a concluding example, a confidence interval for the rate is computed. Numerical and graphical comparisons of the results deriving from the use of different formulas are described.
Confidence Intervals↗
Estimating the variance of standardized rates of recurrent events, with application to hospitalizations among the elderly in New England.
Usual approaches for estimating the variance of a standardized rate may not be applicable to rates of recurrent events. Where individuals are prone to repeated health events, Greenwood and Yule (J R Stat Soc [A], 1920;83:255-79) advocated use of the negative binomial distribution to account for departures from the assumption of randomness of recurrent events required by the Poisson distribution. In this paper, the authors implemented the negative binomial distribution in the computation of annual hospitalization rates within certain hospital market areas. Data used were from 1,549,915 New England residents aged 65 years or more who were enrolled in Medicare between October 1, 1988, and September 30, 1989, and who had 458,593 hospital admissions during that year. New England was partitioned into 170 hospital market areas ranging in population size from 162 to 70,821 elderly Medicare enrollees. The negative binomial distribution demonstrated substantially better fits than the Poisson distribution to the numbers of hospitalizations within hospital market areas. Estimated standard errors for indirectly standardized rates based on the negative binomial distribution were 25-51 percent higher than estimated standard errors that assumed an underlying Poisson distribution. Using regression analysis to smooth overdispersion parameters across hospital market areas produced similar results. The approach described in this paper may be useful in estimation of confidence intervals for standardized rates of recurrent events when these events do not recur randomly.
Age Factors↗
Frequency of elevated urinary beta 2-microglobulin levels in relatives of patients with asymptomatic low-molecular-weight proteinuria.
We studied urinary beta 2-microglobulin levels in a total of 29 apparently healthy relatives (aged 0.8-70 years) of 8 male patients with asymptomatic low-molecular-weight proteinuria in six families. The frequency of levels above the age- and sex-associated 95% confidence limit was 7 of 29 (24%), 4 of 12 (33%) in first-degree relatives, 2 of 6 (33%) fathers, and 2 of 6 (33%) mothers. These frequencies were significantly above those in the general population (P less than 0.01, by a normal distribution test, a binomial distribution, and Poisson distribution test for the sample proportion). The increased frequency in fathers argues against an X-linked pattern of inheritance for this entity, suggesting that there is heterogeneity in the inheritance.
Adolescent↗
[Optimum number of mixed peripheral blood samples by membrane filtration technique for mass blood survey of filariasis].
The membrane filtration technique has been used widely in the evaluation of effect of control and survey of filariasis. The present study was made to explore an optimum number of mixed peripheral blood samples and a mathematical model of work load for this method in surveying filariasis. By analysing the correlation between the microfilaremia rate and the optimum number of mixed peripheral blood samples and applying the theory of Binomial Distribution or Poisson Distribution, the authors reckoned a table for estimating the number of filariasis cases in villages with different microfilarial rates and different population as well as the optimum number of mixed peripheral blood samples.
Animals↗
[Dynamics of the distribution of variables in morphology].
This paper discusses examples of exponentially distributed, Poisson-distributed, and binomially distributed random variables from morphology and describes secular and historical processes as well as phenomena of aging as factors of the dynamics of such distributions, the major focus being on tests of morphometric variables for the existence of normal distributions. In those cases where hypotheses of the existence of particular distributions of random morphometric variables are established it is necessary that consideration be given to metrological and stereological factors pertaining to the process of measuring and the geometry of the structures being measured, respectively. Karyometric results are used to demonstrate the splitting of a single statistical population into several populations as a result of the process of aging of the human organism.
Aged↗
Distribution of the number of clonogens surviving fractionated radiotherapy: a long-standing problem revisited.
PURPOSE: A long-standing problem is addressed: what form of the probability distribution for the number of clonogenic tumor cells remaining after fractionated radiotherapy should be used in the analysis aimed at evaluating the efficacy of cancer treatment? Over a period of years, a lack of theoretical results leading to a closed-form analytic expression for this distribution, even under very simplistic models of cell kinetics in the course of fractionated radiotherapy, was the most critical deterrent to the development of relevant methods of data analysis. MATERIALS AND METHODS: Rigorous mathematical results associated with a model of fractionated irradiation of tumors based on the iterated birth and death stochastic process are discussed. RESULTS: A formula is presented for the exact distribution of the number of clonogenic tumor cells at the end of treatment. It is shown that, under certain conditions, this distribution can be approximated by a Poisson distribution. An explicit formula for the parameter of the limiting Poisson distribution is given and sample computations aimed at evaluation of the convergence rate are reported. Another useful limit that retains a dose-response relationship in the distribution of the number of clonogens has been found. Practical implications of the key theoretical findings are discussed in the context of survival data analysis. CONCLUSIONS: This study answers some challenging theoretical questions that have been under discussion over a number of years. The results presented in this work provide mechanistic motivation for parametric regression models designed to analyze data on the efficacy of radiation therapy.
Humans↗