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PubMed2003

Modeling the dependence between number of trials and success probability in beta-binomial-Poisson mixture distributions.

Beta-binomial models are widely used for overdispersed binomial data, with the binomial success probability modeled as following a beta distribution. The number of binary trials in each binomial is assumed to be nonrandom and unrelated to the success probability. In many behavioral studies, however, binomial observations demonstrate more complex structures. In this article, a general beta-binomial-Poisson mixture model is developed, to allow for a relation between the number of trials and the success probability for overdispersed binomial data. An EM algorithm is implemented to compute both the maximum likelihood estimates of the model parameters and the corresponding standard errors. For illustration, the methodology is applied to study the feeding behavior of green-backed herons in two southeastern Missouri streams.

Algorithms↗
PubMed1994

Evidence that most human Alu sequences were inserted in a process that ceased about 30 million years ago.

The primate Alu interspersed repeats can be subdivided into classes on the basis of shared nucleotides at a set of diagnostic positions. Each of the classes of Alu sequences is apparently the result of past retrotransposition of transcripts of highly conserved class-specific source genes that differed from each other at the diagnostic positions. The nucleotides at the majority of positions are identical among the source genes and therefore were identical among all of the Alu sequences at the time of their insertion. These CONSBI (conserved before insertion) positions are useful because the changes that have occurred after insertion are recognizable and the divergence resulting from nucleotide substitutions, insertions, and deletions is informative. The divergence of Alu sequences at the CONSBI positions is a measure of the time since a class was inserted. The greatest majority of Alu sequences are in one class (identified as class II), and it is particularly suitable for such examination, since nearly full-length sequences are now known for nearly a thousand members of this class. The average divergence of class II members indicates that the class has an average age of about 40 million years. The distribution in divergence of class II accurately fits a sum of two Poisson distributions. The implication is that class II Alu sequences were derived from two massive past events of insertion of many Alu sequences. In this model the younger subset of class II sequences (corresponding to about 300,000 copies in the genome) has an average divergence of 5% at CONSBI positions. The older set of class II sequences (corresponding to about 150,000 genomic copies) has a 9% average divergence. Based on the drift rate of primate DNA sequences, the events of insertion probably occurred 30-50 million years ago. The goodness of the fit to the Poisson distribution indicates that no significant number of members of class II have been inserted since 30 million years ago.

Animals↗
PubMedDate not supplied

A pseudo-Poisson noise model for simulation of positron emission tomographic projection data.

Although radioactive decay obeys Poisson statistics, because of the corrections that are applied to the projection data prior to reconstruction, the noise in positron emission tomography (PET) projections does not follow a Poisson distribution. Use of Poisson noise when simulating PET projections in order to test the performance of reconstruction and processing techniques is therefore not appropriate. The magnitude of PET projection noise was observed to be as much as 10 to 100 times greater than Poisson noise in some instances. A quadratic function was found to fit the relationship between noise power spectral density and total projection count. The coefficients of the quadratic function were determined for projections of different tracer distributions and types. Using these observations, a method of simulating PET projections was developed based on a pseudo-Poisson noise model. Projections simulated according to this method are good approximations to real projection data and take into account the characteristics of individual PET cameras and particular tracer distributions. Such simulated projections have been valuable in predicting the performance of reconstruction algorithms. This approach can also be applied to single photon emission tomography.

Computer Simulation↗
PubMed1991

[Clustering of suicides under age 20--seasonal trends and the influence of newspaper reports].

The existence of temporal clustering of suicides was analyzed by comparing the distribution of weekly numbers of suicides under age 20 in Japan (1982-1987) with a Poisson distribution. The linkage between newspaper reports about teenage suicides and these clusters of suicides was examined in an ecologic study. The following results were obtained: 1) The distribution of weekly numbers of suicides under age 20 was not consistent with a Poisson distribution. The observed numbers for weeks with clustering was higher than the expected numbers. Therefore it is suspected that teenage suicides was not an independent occurrence but clustered in specific weeks with clustering observed in April and between the 15th and 25th weeks in 1986. 2) The age and sex characteristics of those who committed suicide during the observed clusters every April did not differ from that of suicide victims for the rest of the year. The incidence ratio for suicide between 15th and 25th weeks in 1986 compared to the same period for other years was higher in girls than in boys, and higher in younger teenagers than older teenagers. Analysis by prefecture of suicides which occurred between the 15th and 25th weeks in 1986 showed high incidences for Hokkaido, Tohoku, Chugoku, and Shikoku blocks, and low incidences for the Kanto and Kinki blocks. 3) Twenty news articles reporting teenage suicides with headings much larger than four columns appeared in the Asahi Newspaper in 1982-87. Significant linkage between newspaper reports about teenage suicides and trend of weekly numbers of suicides in 1985 and 1986 was not observed. 4) Weekly numbers of suicides significantly increased following newspaper reports on January 23rd 1985 and on April 8th 1986, describing a suicide caused by battering, and a jumping suicide of a young singer who was popular among teenagers, respectively. However no increase in the number of suicides was observed following other newspaper reports.

Adolescent↗
PubMed1990

Variability in expression of common fragile sites: in search of a new criterion.

Fragile sites are nonrandom, heritable sites on chromosomes that can be induced to form gaps, breaks, and rearrangements under specific conditions. There is currently no established criterion to define a common fragile site. We applied seven published criteria to our data from three groups of subjects: (1) three pairs of like-sexed twins, (2) four unaffected von Hippel-Lindau (VHL) family members, and (3) six patients affected with VHL disease. Substantial differences were present in the numbers of sites considered positive by these criteria. While some of this variability can be attributed to technical factors, our data illustrate the problems in comparing results from different studies to assess the significance of fragile sites. A recently published criterion is based upon the Poisson distribution. We found this criterion to be flawed in its presentation, and furthermore, the Poisson distribution did not provide an adequate approximation to our data. We propose here an alternative approach based upon the negative binomial distribution.

Binomial Distribution↗
PubMed1986

On estimating canopy photosynthesis and stomatal conductance in a deciduous forest with clumped foliage.

The foliage in a fully-leafed deciduous forest canopy is clumped. Consequently, theory indicates that the probability of beam penetration will be estimated more accurately with a model based on the negative binomial distribution than with a model based on the Poisson distribution, incorporating an assumption of a spherical leaf inclination angle distribution. Flux densities of photosynthetically active radiation (PAR) were measured in and above a deciduous forest canopy and were computed with the canopy radiative transfer models based on the negative binomial and Poisson distributions. These radiation values were used to compute canopy photosynthesis and stomatal conductance. Canopy photosynthesis and stomatal conductance, based on the negative binomial model, overestimated values computed from measured PAR profiles by 8 and 9%. respectively. The canopy photosynthesis and stomatal conductance values computed with the spherical Poisson model under-estimated measured values by 17 and 10%, respectively. Thus, the negative binomial radiative transfer model improves estimates of canopy photosynthesis and, to a lesser extent, stomatal conductance, inside a deciduous forest.

Journal Article↗
PubMed1992

The origin of His+ revertants of Salmonella typhimurium obtained on selective medium.

The spontaneous reversion to His+ of the Salmonella typhimurium alleles hisD3052 and hisG46 was investigated. In fluctuation tests, the expected "jackpot" distribution of His+ revertants was not observed. The experimental distributions were close to Poisson distribution. The redistribution test showed no significant differences in the His+ colony counts between spread and unspread plates. An attempt at indirect selection of His+ revertants in fluid medium failed. It was also shown that the mean number of His+ reversion events and the mean number of revertants per plate were similar. At the same time, kanamycin-resistant mutants had jackpot distribution. Selection for His+ revertants (histidine starvation) did not increase mutation to Kanr.

Alleles↗
PubMedDate not supplied

[An evaluation of the statistical significance and calculation of the confidence interval for the standardized mortality ratio].

The standardized mortality ratio (SMR) is the ratio of the number of deaths observed (D) to the number expected (E), on the basis of the mortality rates of some reference population. Several procedures have been proposed in order to test its significance and to estimate its confidence intervals. In this study, the SMR of two causes of death in 27 health areas of Castilla-La Mancha have been calculated. The significance has been evaluated by exact Poisson test and by four methods approximating the Poisson distribution by the normal: 1) a Z statistic based on the assumption that a Poisson variate with expectation E has a standard deviation equal to square root of E; 2) the Z statistic with a continuity correction; 3) a Z statistic based on the square root transformation of a Poisson variable and 4) an approximation of the exact test by Byar. Also, the confidence intervals have been estimated by exact method and by three approximate procedures: 1) by Byar; 2) by Z statistic uncorrected and 3) by the square root transformation of the Poisson distribution. With the exact methods and Byar procedure the results were very similar; therefore, using the last to testing significance and estimate the confidence intervals of SMR, is suggested.

Confidence Intervals↗
PubMed1995

Nonrandom arrangement of bovine satellite I DNA within the interphase nucleus of Madin-Darby bovine kidney cells.

The distribution of bovine satellite DNA was examined in Madin-Darby bovine kidney cells for each hour of interphase. Cells were grown on coverslips and probed using biotinylated cloned fragments of bovine satellite I DNA. Hybridization was detected using a streptavidin-alkaline phosphatase conjugate. Cells were projected onto a grid of fixed dimensions and the distribution of hybridization signal was recorded. A chi 2 analysis of fit compared this distribution of signals to a random distribution generated from the poisson distribution. Nuclear localization of bovine satellite I DNA was found to be nonrandom throughout interphase except at the G1/S border and S = 6 h. Moreover, distinct patterns of hybridization were also observed at specific times during interphase.

Animals↗
PubMed1994

Characteristics of somatotopic organization and spontaneous neuronal activity in the region of the thalamic principal sensory nucleus in patients with spinal cord transection.

1. We explored the region of the principal sensory nucleus of thalamus (Vc) during stereotactic surgical procedures for treatment of patients with pain after spinal cord transection (n = 23). Receptive fields (RFs) of thalamic single neurons and locations of sensations evoked by stimulation (projected field, PF) were determined by standard methods. The cellular thalamic region where sensations were evoked at < 25 microA was termed the "region of Vc." The region of Vc in spinal patients was subdivided into different areas according to RF and PF locations. Areas that were distant from the representation of the anesthetic part of the body were termed "spinal control" areas, whereas those that were adjacent to or included in the representation of the area of absolute sensory loss were termed "border zone/anesthetic" areas. The region of Vc in movement disorder patients were termed the "control" area. 2. Border zone/anesthetic areas of thalamus often exhibited increased representations of the border of the anesthetic part of the body in comparison with the representation of the same parts of the body in control and spinal control areas. 3. In control and spinal control areas the locations of RFs and PFs were usually well matched. However, in border zone/anesthetic areas of the thalamus there was frequently a mismatch between the location of RFs and PFs (RF/PF mismatch). In border zone/anesthetic areas, RFs were often located on the border of the anesthetic part of the body whereas PFs were referred to anesthetic parts of the body. 4. Analysis of first- and higher-order properties of spontaneous neuronal activity revealed that spike trains could be classified into two groups with distinct patterns of activity. The R group (n = 49) was characterized by independence of sequential interspike intervals (ISIs), a Poisson distribution of ISIs, initially inhibitory or flat autocovariance function (acvf), and low level of high-frequency bursting. The O group (n = 26) was characterized by correlation of sequential ISIs, large sustained postspike facilitation on the acvf, and high prevalence of high-frequency bursting--all consistent with a bursting pattern of activity. A third group of spike trains (n = 17) had an initially inhibitory or flat acvf and a unimodal, positively shifted, ISI distribution that did not meet criteria for a Poisson distribution. 5. Spike trains in the R group were much more common in control and control spinal areas, whereas those in the O group were more common in border zone/anesthetic areas.(ABSTRACT TRUNCATED AT 400 WORDS)

Brain Mapping↗
PubMed1986

Extracorporeal irradiation of blood: dosimetry corrected for shortened erythrocyte lifespans.

The amount of radiation delivered to erythrocytes during extracorporeal irradiation of blood (ECIB) has been described using Poisson distribution statistics. The Poisson expression for erythrocyte radiation dose distribution was simplified by considering the slight dilution of blood with fluid that is initially in the extracorporeal tubing. An algorithm was devised that allows curtailed lifespans of irradiated erythrocytes to be taken into account in a short computer program of radiation dosimetry for ECIB. Radiation doses to erythrocytes with and without lifespan corrections are compared.

Blood Cells↗
PubMed1992

Theoretical epidemiology on bovine ephemeral fever outbreaks in Tanegashima Island, Kagoshima Prefecture of Japan in 1988.

From the end of September to November 1988, a compact scale of bovine ephemeral fever (BEF) outbreaks occurred suddenly in Tanegashima island of Kagoshima Prefecture, southern part of Kyusyu island of Japan. The BEF outbreak pattern showed epidemical characteristics as follows; (1) outbreak spread from few foci to zone during one month, and (2) the disease might be transmitted in farms with a fixed probability of adequate contact. By using the above aspects, we attempted to analyze the disease theoretically with the application of Poisson distribution and Reed-Frost model. The BEF incidence in farms was in well accord with the Poisson distribution. As the very rare event occurred in unit time or in unit area in this epidemic, the cattle population at risk were equivalently susceptible to BEF virus in this island, due to the influence of no vaccination to BEF control before the first outbreak. Similarly, the epidemic curve of the Reed-Frost model was proved to fit well the incidence observed in a farm, and the probability of adequate contact was induced as p = 0.226. If the cattle population is less than 5 in this farm, the outbreak would not occur in the first instance.

Animals↗
PubMed1999

[Study on family aggregation of cases of advanced schistosomiasis japonica].

AIM: To explore the family aggregation of advanced schistosomiasis japonica. METHODS: Eighty-one cases of advanced schistosomiasis(AS) and 67 cases of non-advanced schistosomiasis with history of infections in Yushan County, Jiangxi Province were chosen as proband groups and control groups respectively, then grades 1 and 2 relatives of them were investigated on AS. Family aggregation of AS was analyzed through comparing the prevalence rate between the close and distant relatives of probands and controls and fitting the observed distribution of AS cases among the population by zero-truncated Poisson distribution and zero-truncated negative binomial distribution. RESULTS: The prevalence rate was higher in the close relatives (Group I relatives) of the probands than in the distant relatives(Group II relatives) of the probands and in the controls' relatives. The observed distribution of AS was beyond the probability of the zero-truncated Poisson distribution, but consistent with the zero-truncated negative binomial distribution. CONCLUSION: Family aggregation of advanced schistosomiasis does exist.

Adult↗
PubMed1999

Monitoring epidemiologic surveillance data using hidden Markov models.

The analysis of routinely collected surveillance data is an important challenge in public health practice. We present a method based on a hidden Markov model for monitoring such time series. The model characterizes the sequence of measurements by assuming that its probability density function depends on the state of an underlying Markov chain. The parameter vector includes distribution parameters and transition probabilities between the states. Maximum likelihood estimates are obtained with a modified EM algorithm. Extensions are provided to take into account trend and seasonality in the data. The method is demonstrated on two examples: the first seeks to characterize influenza-like illness incidence rates with a mixture of Gaussian distributions, and the other, poliomyelitis counts with mixture of Poisson distributions. The results justify a wider use of this method for analysing surveillance data.

Disease Outbreaks↗
PubMed2005

The probability distribution of attendance to hospital emergency units for school students in Alexandria.

The present work is a retrospective study designed to examine the assumption that emergency arrivals at the Sporting Students' Hospital in Alexandria follow a Poisson distribution. Data about all arrivals at the emergency room (ER) for the year, 2000 (43076 arrivals) was extracted from the records of the emergency department and classified by age, sex, school, reason for visit, date and time of visit. Data analysis revealed that 12.9% of the total arrivals indicated hospital admission either to the inpatient units (12.5%) or the ICU (0.4%). Goodness of fit test showed that admissions to the ICU fit the Poisson distribution but those admitted to the inpatient units did not follow the assumed distribution. However the latter group did not fit exactly the normal distribution which indicated that deviance from the Poisson is due to the large mean non-elective admissions (14.74% per day). Hence the Poisson assumption is not excluded as the inpatient emergency admissions are still randomly distributed and independent. Univariate and multivariate Poisson regression of the daily emergency admissions gave another clue to the goodness of fit of emergency admissions to the Poisson process. Regression analysis showed significantly higher loge number of emergency admissions among the age group 12 or more, male students, medical conditions in contrast to injuries, governmental schools, and at 04:00-11:59 pm in contrast to midnight to 07:59 am. Results of the present study indicated the random nature of demand for emergency admission which affects use of bed stock. A prospective study of these admissions on daily basis is needed.

Adolescent↗
PubMedDate not supplied

[Negative binomial distribution versus Poisson in the analysis of recurrent phenomena].

OBJECTIVE: The aim is to unfold the difficulties likely to arise in risk calculations through aggregated database when the studied phenomenon is recurrent and to display the negative binomial distribution as a valid and simple alternative to analyse this kind of phenomenon. METHODS: When the studied phenomenon is recurrent, the analysis by means of the Poisson regression can provoke overdispersion or extra-poisson variance, what leads to underestimating the standard errors in coefficients and may divert into the statistical significance of factors which as a matter of fact are not associated with the phenomenon beforehand. The negative binomial can grasp part of the variance which the Poisson is unable to identify. In order to check this out, the fit of both distributions were compared, based on the number of hospitalizations of individuals aged between 65 and 69, during 1996. This comparison was carried out by means of two different aggregated databases: by individuals and by variables. RESULTS: There were differences in the fitted models by means of both distributions in both databases. By the analysis of the residuals, when using the base by individuals, the negative binomial fits correctly 67.9% of the observations badly fitted by the Poisson. Using the aggregated variables database, the percentage is 50%. In both cases, Poisson estimates four out of the six studied variables as significant. As to the negative binomial, there are two significant based on individuals and one in the variable database. CONCLUSION: The existence of overdispersion is frequent in recurrent-type phenomena. When this occurs, the negative binomial distribution is more appropiate than the Poisson.

Aged↗
PubMed1995

Infectivity of algal viruses studied by chlorophyll fluorescence.

Algal virus infection proceeds via the specific recognition of the host cell wall, penetration of the cell wall and transfer of genetic material into the cytoplasm of the host cell. This process is similar to that which occurs when bacteriophage infect bacteria so that techniques and concepts developed to study bacteriophage are applicable to algal virus studies. By measuring virus-induced changes in chlorophyll fluorescence we have redefined classical studies on the distribution of infectivity. We show that infectivity does not follow a Poisson distribution with a fixed mean, n. By analysing the infectivity of algal viruses over a broad range of virus:cell ratios we have obtained a corrected Poisson distribution that reflects the probability of multiple virus particles attached per cell and is equally applicable to algal viruses and bacteriophage.

Chlorella↗