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PubMed1998

A general theory of the sampling process with applications to the "veil line".

When a community of species is sampled, nonappearing species are not those with abundances that fall shy of some arbitrary mark, the "veil line" proposed by E. F. Preston in 1948 (Ecology 29, 254-283). Instead, they follow a hypergeometric distribution, which has no resemblance to the veil line. There is therefore no justification for the truncation of distributions proposed to describe the abundances of species in natural communities. The mistake of the veil line points to the need for a general theory of sampling. If a community has a distribution g of species abundances and if samples taken of the community tend to follow distribution f, what is the relationship of f to g? The seeds of such a theory are available in the work of E. C. Pielou. Using the Poisson distribution as a close approximation to the hypergeometric, one may immediately write and (in most cases) solve the transformation from g to f. The transformation appears to preserve distribution formulas to within constants and parameters, providing yet another reason to rule out the use of truncation. Well beyond this application, the theory provides a foundation for rethinking the sampling process and its implications for ecology.

Animals↗
PubMed1980

Ranking of glucocorticoid creams and ointments.

20 corticosteroids ointments and 19 corticosteroid creams available on the Swedish market in January 1977 were tested for their blanching effect. Three ointments and three creams showing pronounced blanching were tested only without occlusion. Hydrocortisone preparations were tested only with occlusion. Other preparations were tested with and without occlusion. All ointments and creams were tested at four randomized sites on the flexor aspect of the forearm in each of 11 or 12 subjects. When used occlusion was applied for 6 hours. Repeated readings were made, using scores 0, 1, 2, and 3. The reading at the time when most preparations showed blanching were analysed statistically. The scores for blanching showed a Poisson distribution when the mean score was less than or equal to 1. Classification of preparations according to blanching was facilitated by the fact that statistical methods for Poisson distribution could be used. A ranking of corticosteroids based on vasoconstriction was obtained, and four different groups for ointments and four for creams emerged. The arbitrary nature of any ranking and grouping of steroids is evident from the data presented.

Administration, Topical↗
PubMed1998

The evolutionary history of Drosophila buzzatii. XXXIV. The distribution of the retrotransposon Osvaldo in original and colonizing populations.

The frequency distribution of the retrotransposon Osvaldo in the haploid genome of Drosophila buzzatii has been studied in five natural populations from the Iberian Peninsula and six natural populations from Argentina. In Iberian populations, Osvaldo insertion sites do not follow a Poisson distribution, most probably due to eight euchromatic sites with high occupancy, found in all populations. The estimated alpha and beta parameters, which measure the relative importance of drift and negative selection in shaping frequency distributions, indicate that drift is the main force acting upon the distribution of Osvaldo in natural populations of D. buzzatii in the Iberian Peninsula. On the other hand, Osvaldo distribution in populations from Argentina is similar to the distribution of elements with low copy numbers, such as those described for Drosophila melanogaster and Drosophila simulans: there are no indications for deviation from a Poisson distribution, there is a low occupancy per insertion site, and genetic drift has no apparent effect on the frequency distribution. We propose that the unusual distribution found in the populations from the Iberian Peninsula is a consequence of the colonization process. Iberian Peninsula populations suffered a genomic redistribution of Osvaldo, most probably after a founder effect. Consequently, certain copies that arrived at high frequencies are showing a high occupancies today, and the mean copy number of Osvaldo is higher in Iberian Peninsula populations than in populations from Argentina. All other copies are the result of recent (after colonization) transposition events.

Animals↗
PubMed1986

Sensitivity of neurons in the auditory midbrain of the grassfrog to temporal characteristics of sound. II. Stimulation with amplitude modulated sound.

The coding of fine-temporal structure of sound, especially of frequency of amplitude modulation, was investigated on the single-unit level in the auditory midbrain of the grassfrog. As stimuli sinusoidally amplitude modulated sound bursts and continuous sound with low-pass Gaussian noise amplitude modulation have been used. Both tonal and wideband noise carriers have been applied. The response to sinusoidally amplitude modulated sound bursts was studied in two aspects focussing on two types of possible codes: a rate code and a synchrony code. From the iso-intensity rate histogram five basic average response characteristics as function of modulation frequency have been observed: low-pass, band-pass, high-pass, bimodal and non-selective types. The synchronization capability, expressed in a synchronization index, was non-significant for 38% of the units and a low-pass function of modulation frequency for most of the other units. The stimulus-response relation to noise amplitude modulated sound was investigated by a non-linear system theoretical approach. On the basis of first- and second-order Wiener-Volterra kernels possible neural mechanisms accounting for temporal selectivity were obtained. About one quarter of the units had response characteristics that were invariant to changes in sound pressure level and spectral content of the carrier. These units may function as feature detectors of fine-temporal structure of sound. The spectro-temporal sensitivity range of the auditory midbrain of the grassfrog appeared not to be restricted to and showed no preference for the spectro-temporal characteristics of the ensemble of conspecific calls. Comparison of response characteristics to periodic click trains as studied in the companion paper (Epping and Eggermont, 1986) and sinusoidally amplitude modulated sound bursts revealed that the observed temporal sensitivity is due to a combination of sensitivities to sound periodicity and pulse duration. It was found that for most units the first-order kernels for Gaussian amplitude modulated stimuli and Poisson distributed click stimuli were alike. In contrast second-order kernels for the Gaussian amplitude modulated stimuli often represented only static non-linearities, while second-order kernels for Poisson distributed clicks (Epping and Eggermont, 1986) mostly revealed dynamic non-linearities.

Acoustic Stimulation↗
PubMed1988

Induced and natural break sites in the chromosomes of Hawaiian Drosophila.

gamma-Irradiation of a laboratory strain of the Hawaiian species Drosophila heteroneura yielded 310 breaks in the five major acrocentric polytene chromosomes. Their map positions conform to the Poisson distribution, unlike most of the 436 natural breaks mapped in 105 closely related species endemic to Hawaii. Genome element E is longer and has more induced breaks than the others. Both in Hawaiian and related species groups, this element shows increased polymorphism and fixation of naturally occurring inversions. The X chromosome (element A) also accumulates many natural breaks; the majority of the resulting aberrations become fixed rather than remain as polymorphisms. Although size may play a small role in initial break distribution, the major effects relative to the establishment of a rearrangement in natural populations are ascribed to the interaction of selection and drift. Nonconformance of the natural breaks to the Poisson distribution appears to be due to the tendency for breaks to accumulate both in the proximal euchromatic portion of each arm and in heterochromatic regions that are not replicated in the polytene chromosomes.

Animals↗
PubMed1977

Estimates of quantal-release and binomial statistical-release parameters at rat neuromuscular junction.

Quantal-release and binomial statistical-release parameters were examined in the isolated rat diaphragm phrenic nerve preparation. The muscle resting potentials were reduced by cutting the muscle fibers to prevent muscle action potentials and contractions. The cutting technique was modified to allow persistent observation of miniature end-plate potentials (MEPPs) and end-plate potentials (EPPs) with intracellular recording techniques. Direct estimates of quantal release were examined and compared with predicted binomial and Poisson distributions. The results indicate that release is binomial when the nerve is stimulated with low- or high-frequency stimuli. The indirect method of estimating quantal release (variance method), which assumes release is described by a Poisson distribution, seriously overestimates quantal release. The binomial analysis indicates that the statistical store is small (less than 90 quanta) and that most of these quanta are released with each nerve impulse.

Animals↗
PubMed2005

Brownian dynamics of mixed surfactant micelles.

We investigate micelle formation in a system containing two or more different amphiphiles with different geometries using a stochastic molecular-dynamics (MD) simulation method. For a binary system containing two amphiphiles, we calculate the critical micelle concentration (CMC) and cluster distribution for the mixture at several mole fractions and compare the simulation results with those predicted by analytic theories in the dilute limit and with experiments. We find that the CMC obtained from molecular mean-field theory agrees well with our simulation results. Motivated by the industrial use of mixed surfactant systems, we then extend our studies to a system containing six different chain lengths drawn from a Poisson distribution. We find that unlike a binary mixture of amphiphiles, the different species cancel the effects of each other so that the cluster distribution for the mixture has a shape of a system consisted entirely of amphiphiles of length equal to the mean chain length of the Poisson distribution.

Journal Article↗
PubMed1986

The question of the total gene number in Drosophila melanogaster.

A statistical analysis has been carried out on the distribution and allelism of nearly 500 sex-linked, X-ray-induced, cytologically normal and rearranged lethal mutations in Drosophila melanogaster that were obtained by G. Lefevre. The mutations were induced in four different regions of the X chromosome: (1) 1A1-3E8, (2) 6D1-8A5, (3) 9E1-11A7 and (4) 19A1-20F4, which together comprise more than one-third of the entire chromosome.--The analysis shows that the number of alleles found at different loci does not fit a Poisson distribution, even when the proper procedures are taken to accommodate the truncated nature of the data. However, the allele distribution fits a truncated negative binomial distribution quite well, with cytologically normal mutations fitting better than rearrangement mutations. This indicates that genes are not equimutable, as required for the data to fit a Poisson distribution.--Using the negative binomial parameters to estimate the number of genes that did not produce a detectable lethal mutation in our experiment (n0) gave a larger number than that derived from the use of the Poisson parameter. Unfortunately, we cannot estimate the total numbers of nonvital loci, loci with undetectable phenotypes and loci having extremely low mutabilities. In any event, our estimate of the total vital gene number was far short of the total number of bands in the analyzed regions; yet, in several short intervals, we have found more vital genes than bands; in other intervals, fewer. We conclude that the one-band, one-gene hypothesis, in its literal sense, is not true; furthermore, it is difficult to support, even approximately.--The question of the total gene number in Drosophila will, not doubt, eventually be solved by molecular analyses, not by statistical analysis of mutation data or saturation studies.

Alleles↗
PubMed1984

Temporal characteristics of seizures and epileptiform discharges.

The time relations of epileptic events have been studied in 3 sets of data: (I) counts of individual epileptiform discharges in twelve 48 h EEG recordings, (IIa) seizure calendars of 30 therapy-resistant outpatients participating in a drug trial, (IIb) seizure calendars of 10 mentally subnormal epileptic patients resident in a long-stay unit. The EEG data I were characterized most often by a Poisson distribution of intervals between discharges and the occurrence of marked periodicities, particularly at night. The periods of rhythmic nocturnal events ranged from 13 to 142 min and did not appear to correspond to the REM/non-REM cycle. In the seizure data IIa and b a Poisson distribution of intervals between events was found in half the patients. Periodicities occurred only in group IIa and did not correspond to weekly or monthly cycles. A stochastic process is considered to be the model which best fits these data.

Adolescent↗
PubMed1983

Clustering of rare events.

The clustering of cases of a rare disease is considered. The number of events observed for each unit is assumed to have a Poisson distribution, the mean of which depends upon the population size and the cluster membership of that unit. Here a cluster consists of those units that are homogeneous in their rate of occurrence of the rare events under study. A sample of units is modeled by a mixture of Poisson distributions, one for each cluster, the mixing parameters being the proportions of all units represented by the components of the mixture. Maximum likelihood and Bayes approaches are employed to determine criteria for separating a sample into groups of units with homogeneous rates. A likelihood ratio test for the significance of a two-component mixture is presented as an example. The performance of the criteria is illustrated with data on the spatial occurrence of sudden infant deaths (SIDs) in North Carolina counties over a four-year period. The results suggest that the practice of dividing the counties into high- and low-risk categories on the basis of the ordered rates alone should be questioned. Tests based upon combinatorial methods are also presented to examine the significance of the number of contiguous counties among those with high rates.

Biometry↗
PubMed1986

Sensitivity of neurons in the auditory midbrain of the grassfrog to temporal characteristics of sound. I. Stimulation with acoustic clicks.

The coding of fine-temporal structure of sound, especially pulse repetition rate, was investigated on the single-unit level in the auditory midbrain of the grassfrog. As stimuli periodic click trains and Poisson distributed click ensembles have been used. The response to periodic click trains was studied in two aspects, focussing on two types of possible codes: a rate code and a synchrony code. From the iso-intensity rate histogram five basic average response rate characteristics as function of pulse repetition rate have been established: low-pass, band-pass, high-pass, bimodal and non-selective unit types. The synchronization capability, expressed in a synchronization index, was for a small majority of units non-significant and a low-pass function of pulse repetition rate for most of the other units. The rate code showed the largest diversity of response types and an enhanced selectivity to pulse repetition rate. The stimulus-response relation to Poisson distributed click ensembles was investigated by a non-linear system theoretical approach. On the basis of first- and second-order Poisson kernels possible neural mechanisms accounting for temporal selectivity were determined. A considerable fraction of units exhibited response characteristics that were invariant to changes in sound pressure level and average click rate. These units may function as feature detectors of fine-temporal structure of sound. The spectro-temporal sensitivity range of the auditory midbrain of the grassfrog appeared to be broad and not particularly tuned to the ensemble of conspecific cells.

Acoustic Stimulation↗
PubMed2001

The use of mixture models for identifying high risks in disease mapping.

Conventional approaches for estimating risks in disease mapping or mortality studies are based on Poisson inference. Frequently, overdispersion is present and this extra variability is modelled by introducing random effects. In this paper we compare two computationally simple approaches for incorporating random effects: one based on a non-parametric mixture model assuming that the population arises from a discrete mixture of Poisson distributions, and the second using a Poisson-normal mixture model which allows for spatial autocorrelation. The comparison is focused on how well each of these methods identify the regions which have high risks. Such identification is important because policy makers may wish to target regions associated with such extreme risks for financial assistance while epidemiologists may wish to target such regions for further study. The Poisson-normal mixture model is presented from both a frequentist, or empirical Bayes, and a fully Bayesian point of view. We compare results obtained with the parametric and non-parametric models specifically in terms of detecting extreme mortality risks, using infant mortality data of British Columbia, Canada, for the period 1981-1985, breast cancer data from Sardinia, for the period 1983-1987, and Scottish lip cancer data for 1975-1980. However, we also investigate the performance of these models in a simulation study. The key finding is that discrete mixture models seem to be able to locate regions which experience high risks; normal mixture models also work well in this regard, and perform substantially better when spatial autocorrelation is present.

Adult↗
PubMed2006

Impact of changing the statistical methodology on hospital and surgeon ranking: the case of the New York State cardiac surgery report card.

BACKGROUND: Risk adjustment is central to the generation of health outcome report cards. It is unclear, however, whether risk adjustment should be based on standard logistic regression, fixed-effects or random-effects modeling. OBJECTIVE: The objective of this study was to determine how robust the New York State (NYS) Coronary Artery Bypass Graft (CABG) Surgery Report Card is to changes in the underlying statistical methodology. METHODS: Retrospective cohort study based on data from the NYS Cardiac Surgery Reporting System on all patient undergoing isolated CABG surgery in NYS and who were discharged between 1997 and 1999 (51,750 patients). Using the same risk factors as in the NYS models, fixed-effects and random-effects models were fitted to the NYS data. Quality outliers were identified using 1) the ratio of observed-to-expected mortality rates (O/E ratio) and confidence intervals (CIs) calculated using both parametric (Poisson distribution) and nonparametric (bootstrapping) techniques; and 2) shrinkage estimators. RESULTS: At the surgeon level, the standard logistic regression model, the fixed-effects model, and the fixed-effects component of the random-effects model demonstrated near-perfect agreement on the identity of quality outliers using a quality indicator based on the O/E ratio and the Poisson distribution. Shrinkage estimators identified the fewest outliers, whereas the O/E ratios with bootstrap CI identified the greatest number of outliers. The results were similar for hospitals, except that the fixed-effects model identified more outliers than either the NYS model or the fixed-effects component of the random-effects model. CONCLUSION: Shrinkage estimators based on random-effects models are slightly more conservative in identifying quality outliers compared with the traditional approach based on fixed-effects modeling and standard regression. Explicitly modeling surgeon provider effect (fixed-effects and random-effects models) did not significantly alter the distribution of quality outliers when compared with standard logistic regression (which does not model provider effect). Compared with the standard parametric approach, the use of a bootstrap approach to construct 95% confidence interval around the O/E ratio resulted in more providers being identified as quality outliers.

Benchmarking↗
PubMedDate not supplied

A proposal for statistical evaluation of the detection of gunshot residues on a suspect.

The possibility of accidental contamination of a suspect by gunshot residues (GSRs) is considered. If two hypotheses are taken into account ("the suspect has shot a firearm" and "the suspect has not shot a firearm"), the likelihood ratio of the conditional probabilities of finding a number n of GSRs is defined. Choosing two Poisson distributions, the parameter lambda of the first one coincides with the mean number of GSRs that can be found on a firearm shooter, while the parameter mu of the second one is the mean number of GSRs that can be found on a nonshooter. In this scenario, the likelihood ratio of the conditional probabilities of finding a number n of GSRs in the two hypotheses can be easily calculated. The evaluation of the two parameters lambda and mu and of the goodness of the two probability distributions is performed by using different sets of data: "exclusive" lead-antimony-barium GSRs have been detected in two populations of 31 and 28 police officers at diverse fixed times since firearm practice, and in a population of 81 police officers who stated that they had not handled firearms for almost 1 month. The results show that the Poisson distributions well fit the data for both shooters and nonshooters, and that the probability of detection of two or more GSRs is normally greater if the suspect has shot firearms.

Journal Article↗
PubMed1986

Cell survival and radiation induced chromosome aberrations. I. Derivation of formulae for the determination of transmission and survival parameters of aberrations.

Existing mathematical formulations to predict the frequency of radiation induced chromosome aberrations in 2nd post-irradiation division are based on the Poisson distribution [3, 4]. Meanwhile several studies have shown that intercellular distributions exist, deviating from Poisson. In the present study a modified model was developed which permits the application of empirical distributions. Transmission and survival parameters of aberrations can be iteratively computed. A general formula was derived for the calculation of cell survival from 1st to 2nd division.

Cell Survival↗
PubMed1995

Quantifying intracellular radioresponse diversity in irradiated sandwich cultures via micronucleus expression.

Determining the degree of diversity in therapeutic sensitivity exhibited by a tumour population is of considerable clinical importance. In addition to being a contributor to radiation resistance, diversity is the basis for variation in sensitivity over the course of treatment. To study intrapopulation diversity in radiosensitivity following gamma-irradiation (2 Gy), distributions of the number of micronuclei/binucleate cell were obtained for human cervix carcinoma sandwich populations. Cell-to-cell diversity in radioresponse (micronucleus expression) was quantified using the overdispersion index ((variance/mean)--1). As measured by this index, the radioresponse diversity of sandwich cultures sharply increased after introduction of oxygen/nutrients to the cultures, mimicking tumour reperfusion. In addition, a strong correlation was found between this measure of diversity and the extent to which the fraction of cells without micronuclei exceeds that expected from a Poisson distribution. This correlation indicates that for a diverse population there can be a significant departure of the aggregate population sensitivity (determined, for instance, by log-survival in a clonogenic assay) from that inferable from simply averaging per-cell sensitivities (reflected, e.g. by mean number of chromosome aberrations/cell). Our experimental results suggest a model attributing diversity in a population to its being a mixture of distinct subpopulations, each biologically homogeneous with respect to micronucleus expression, and each contributing an individual Poisson-distributed micronucleus response. We demonstrate how such radiodiversity may be quantified and show that reoxygenation of a microenvironmentally heterogeneous population leads to an increase in its radiobiological diversity.

Cell Cycle↗
PubMed1993

[Occurrence of tics, enuresis and hyperkinetic behavior in children with speech disorders].

UNLABELLED: The aim of the study was to assess the share of positive correlation between speech disorders and tics, urination disorders and hyperkinetic behavior. The subjects were: E--experimental group with 700 children (459 boys and 241 girls) 6-14 years old, with speech pathology, C--a group of 510 (271 boys and 239 girls) healthy children from kindergartens and schools, aged 6-10. The transversal method along with clinical and statistical methods were used. RESULTS: correlation between speech discorders and ticks--this phenomenon was regarded as an infrequent event and checked by the Poisson Distribution A and B and the Chi-square test. The obtained results: X2 = 26. 83 P--0 showing that the difference is significant and that tics are more often found in the E than in the C group. Correlation between speech disorders and enuresis--it is necessary to determine features of the incidence of the phenomenon which also rarely occurs. These data were also checked by the Poisson distribution A and B, and Chi-square test. The obtained results: X2 = 59.91 P --> O indicating that in the E group the occurrence of enuresis was significantly higher than in the K group. The correlation between the speech function and hyperkinesis was checked by Chi-square test. Since X2 = 2.31 the difference was not statistically significant.

Adolescent↗